Daily Papers

Evaluating natural language generation (NLG) systems is challenging due to the diversity of valid outputs. While human evaluation is the gold standard, it suffers from inconsistencies, lack of standardisation, and demographic biases, limiting reproducibility. LLM-based evaluation offers a scalable alternative but is highly sensitive to prompt design, where small variations can lead to significant discrepancies. In this work, we propose an inversion learning method that learns effective reverse mappings from model outputs back to their input instructions, enabling the automatic generation of highly effective, model-specific evaluation prompts. Our method requires only a single evaluation sample and eliminates the need for time-consuming manual prompt engineering, thereby improving both efficiency and robustness. Our work contributes toward a new direction for more robust and efficient LLM-based evaluation.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

Unsupervised depth completion and estimation methods are trained by minimizing reconstruction error. Block artifacts from resampling, intensity saturation, and occlusions are amongst the many undesirable by-products of common data augmentation schemes that affect image reconstruction quality, and thus the training signal. Hence, typical augmentations on images viewed as essential to training pipelines in other vision tasks have seen limited use beyond small image intensity changes and flipping. The sparse depth modality in depth completion have seen even less use as intensity transformations alter the scale of the 3D scene, and geometric transformations may decimate the sparse points during resampling. We propose a method that unlocks a wide range of previously-infeasible geometric augmentations for unsupervised depth completion and estimation. This is achieved by reversing, or ``undo''-ing, geometric transformations to the coordinates of the output depth, warping the depth map back to the original reference frame. This enables computing the reconstruction losses using the original images and sparse depth maps, eliminating the pitfalls of naive loss computation on the augmented inputs and allowing us to scale up augmentations to boost performance. We demonstrate our method on indoor (VOID) and outdoor (KITTI) datasets, where we consistently improve upon recent methods across both datasets as well as generalization to four other datasets. Code available at: https://github.com/alexklwong/augundo.

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.

Image-to-image translation is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image using a training set of aligned image pairs. However, for many tasks, paired training data will not be available. We present an approach for learning to translate an image from a source domain X to a target domain Y in the absence of paired examples. Our goal is to learn a mapping G: X rightarrow Y such that the distribution of images from G(X) is indistinguishable from the distribution Y using an adversarial loss. Because this mapping is highly under-constrained, we couple it with an inverse mapping F: Y rightarrow X and introduce a cycle consistency loss to push F(G(X)) approx X (and vice versa). Qualitative results are presented on several tasks where paired training data does not exist, including collection style transfer, object transfiguration, season transfer, photo enhancement, etc. Quantitative comparisons against several prior methods demonstrate the superiority of our approach.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

Inverse graphics -- the task of inverting an image into physical variables that, when rendered, enable reproduction of the observed scene -- is a fundamental challenge in computer vision and graphics. Disentangling an image into its constituent elements, such as the shape, color, and material properties of the objects of the 3D scene that produced it, requires a comprehensive understanding of the environment. This requirement limits the ability of existing carefully engineered approaches to generalize across domains. Inspired by the zero-shot ability of large language models (LLMs) to generalize to novel contexts, we investigate the possibility of leveraging the broad world knowledge encoded in such models in solving inverse-graphics problems. To this end, we propose the Inverse-Graphics Large Language Model (IG-LLM), an inverse-graphics framework centered around an LLM, that autoregressively decodes a visual embedding into a structured, compositional 3D-scene representation. We incorporate a frozen pre-trained visual encoder and a continuous numeric head to enable end-to-end training. Through our investigation, we demonstrate the potential of LLMs to facilitate inverse graphics through next-token prediction, without the use of image-space supervision. Our analysis opens up new possibilities for precise spatial reasoning about images that exploit the visual knowledge of LLMs. We will release our code and data to ensure the reproducibility of our investigation and to facilitate future research at https://ig-llm.is.tue.mpg.de/

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. Motivated by the underlying mathematical structure, NIO is based on a suitable composition of DeepONets and FNOs to approximate mappings from operators to functions. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.

We introduce RE-Adapt, an approach to fine-tuning large language models on new domains without degrading any pre-existing instruction-tuning. We reverse engineer an adapter which isolates what an instruction-tuned model has learned beyond its corresponding pretrained base model. Importantly, this requires no additional data or training. We can then fine-tune the base model on a new domain and readapt it to instruction following with the reverse engineered adapter. RE-Adapt and our low-rank variant LoRE-Adapt both outperform other methods of fine-tuning, across multiple popular LLMs and datasets, even when the models are used in conjunction with retrieval-augmented generation.

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While machine learning (ML) has produced accurate and efficient CG simulations of proteins, fast and reliable backmapping remains a challenge. Rule-based methods produce poor all-atom geometries, needing computationally costly refinement through additional simulations. Recently proposed ML approaches outperform traditional baselines but are not transferable between proteins and sometimes generate unphysical atom placements with steric clashes and implausible torsion angles. This work addresses both issues to build a fast, transferable, and reliable generative backmapping tool for CG protein representations. We achieve generalization and reliability through a combined set of innovations: representation based on internal coordinates; an equivariant encoder/prior; a custom loss function that helps ensure local structure, global structure, and physical constraints; and expert curation of high-quality out-of-equilibrium protein data for training. Our results pave the way for out-of-the-box backmapping of coarse-grained simulations for arbitrary proteins.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar\'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar\'e 2D convolutions up to Poincar\'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr\'echet mean calculations in hyperbolic space. We introduce Poincar\'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar\'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

Digital cameras transform sensor RAW readings into RGB images by means of their Image Signal Processor (ISP). Computational photography tasks such as image denoising and colour constancy are commonly performed in the RAW domain, in part due to the inherent hardware design, but also due to the appealing simplicity of noise statistics that result from the direct sensor readings. Despite this, the availability of RAW images is limited in comparison with the abundance and diversity of available RGB data. Recent approaches have attempted to bridge this gap by estimating the RGB to RAW mapping: handcrafted model-based methods that are interpretable and controllable usually require manual parameter fine-tuning, while end-to-end learnable neural networks require large amounts of training data, at times with complex training procedures, and generally lack interpretability and parametric control. Towards addressing these existing limitations, we present a novel hybrid model-based and data-driven ISP that builds on canonical ISP operations and is both learnable and interpretable. Our proposed invertible model, capable of bidirectional mapping between RAW and RGB domains, employs end-to-end learning of rich parameter representations, i.e. dictionaries, that are free from direct parametric supervision and additionally enable simple and plausible data augmentation. We evidence the value of our data generation process by extensive experiments under both RAW image reconstruction and RAW image denoising tasks, obtaining state-of-the-art performance in both. Additionally, we show that our ISP can learn meaningful mappings from few data samples, and that denoising models trained with our dictionary-based data augmentation are competitive despite having only few or zero ground-truth labels.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

Image relighting is the task of showing what a scene from a source image would look like if illuminated differently. Inverse graphics schemes recover an explicit representation of geometry and a set of chosen intrinsics, then relight with some form of renderer. However error control for inverse graphics is difficult, and inverse graphics methods can represent only the effects of the chosen intrinsics. This paper describes a relighting method that is entirely data-driven, where intrinsics and lighting are each represented as latent variables. Our approach produces SOTA relightings of real scenes, as measured by standard metrics. We show that albedo can be recovered from our latent intrinsics without using any example albedos, and that the albedos recovered are competitive with SOTA methods.

Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep understanding, improvement, and parallel execution. This paper develops a simple, generalized AD algorithm calculated from a simple, natural specification. The general algorithm is then specialized by varying the representation of derivatives. In particular, applying well-known constructions to a naive representation yields two RAD algorithms that are far simpler than previously known. In contrast to commonly used RAD implementations, the algorithms defined here involve no graphs, tapes, variables, partial derivatives, or mutation. They are inherently parallel-friendly, correct by construction, and usable directly from an existing programming language with no need for new data types or programming style, thanks to use of an AD-agnostic compiler plugin.

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

Deep neural networks (DNNs) are vulnerable to backdoor attacks. The backdoor adversaries intend to maliciously control the predictions of attacked DNNs by injecting hidden backdoors that can be activated by adversary-specified trigger patterns during the training process. One recent research revealed that most of the existing attacks failed in the real physical world since the trigger contained in the digitized test samples may be different from that of the one used for training. Accordingly, users can adopt spatial transformations as the image pre-processing to deactivate hidden backdoors. In this paper, we explore the previous findings from another side. We exploit classical spatial transformations (i.e. rotation and translation) with the specific parameter as trigger patterns to design a simple yet effective poisoning-based backdoor attack. For example, only images rotated to a particular angle can activate the embedded backdoor of attacked DNNs. Extensive experiments are conducted, verifying the effectiveness of our attack under both digital and physical settings and its resistance to existing backdoor defenses.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets (KITTI, NCLT, and Nebula) demonstrate the effectiveness of our method.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

We propose iterative inversion -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a distribution shift between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks. Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

The ability of the Generative Adversarial Networks (GANs) framework to learn generative models mapping from simple latent distributions to arbitrarily complex data distributions has been demonstrated empirically, with compelling results showing that the latent space of such generators captures semantic variation in the data distribution. Intuitively, models trained to predict these semantic latent representations given data may serve as useful feature representations for auxiliary problems where semantics are relevant. However, in their existing form, GANs have no means of learning the inverse mapping -- projecting data back into the latent space. We propose Bidirectional Generative Adversarial Networks (BiGANs) as a means of learning this inverse mapping, and demonstrate that the resulting learned feature representation is useful for auxiliary supervised discrimination tasks, competitive with contemporary approaches to unsupervised and self-supervised feature learning.

In this paper, we introduce an SE(3) diffusion model-based point cloud registration framework for 6D object pose estimation in real-world scenarios. Our approach formulates the 3D registration task as a denoising diffusion process, which progressively refines the pose of the source point cloud to obtain a precise alignment with the model point cloud. Training our framework involves two operations: An SE(3) diffusion process and an SE(3) reverse process. The SE(3) diffusion process gradually perturbs the optimal rigid transformation of a pair of point clouds by continuously injecting noise (perturbation transformation). By contrast, the SE(3) reverse process focuses on learning a denoising network that refines the noisy transformation step-by-step, bringing it closer to the optimal transformation for accurate pose estimation. Unlike standard diffusion models used in linear Euclidean spaces, our diffusion model operates on the SE(3) manifold. This requires exploiting the linear Lie algebra se(3) associated with SE(3) to constrain the transformation transitions during the diffusion and reverse processes. Additionally, to effectively train our denoising network, we derive a registration-specific variational lower bound as the optimization objective for model learning. Furthermore, we show that our denoising network can be constructed with a surrogate registration model, making our approach applicable to different deep registration networks. Extensive experiments demonstrate that our diffusion registration framework presents outstanding pose estimation performance on the real-world TUD-L, LINEMOD, and Occluded-LINEMOD datasets.

Several studies have compared the in-distribution (ID) and out-of-distribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation and some surprisingly never even observe an inverse correlation indicative of a necessary trade-off. The possibility of inverse patterns is important to determine whether ID performance can serve as a proxy for OOD generalization capabilities. This paper shows with multiple datasets that inverse correlations between ID and OOD performance do happen in real-world data - not only in theoretical worst-case settings. We also explain theoretically how these cases can arise even in a minimal linear setting, and why past studies could miss such cases due to a biased selection of models. Our observations lead to recommendations that contradict those found in much of the current literature. - High OOD performance sometimes requires trading off ID performance. - Focusing on ID performance alone may not lead to optimal OOD performance. It may produce diminishing (eventually negative) returns in OOD performance. - In these cases, studies on OOD generalization that use ID performance for model selection (a common recommended practice) will necessarily miss the best-performing models, making these studies blind to a whole range of phenomena.

Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps in a two-stage autoregressive manner, which may miss essential details and lead to error accumulation. Towards precise map element learning, we propose a simple yet effective architecture named PivotNet, which adopts unified pivot-based map representations and is formulated as a direct set prediction paradigm. Concretely, we first propose a novel point-to-line mask module to encode both the subordinate and geometrical point-line priors in the network. Then, a well-designed pivot dynamic matching module is proposed to model the topology in dynamic point sequences by introducing the concept of sequence matching. Furthermore, to supervise the position and topology of the vectorized point predictions, we propose a dynamic vectorized sequence loss. Extensive experiments and ablations show that PivotNet is remarkably superior to other SOTAs by 5.9 mAP at least. The code will be available soon.

Image outpainting is a very intriguing problem as the outside of a given image can be continuously filled by considering as the context of the image. This task has two main challenges. The first is to maintain the spatial consistency in contents of generated regions and the original input. The second is to generate a high-quality large image with a small amount of adjacent information. Conventional image outpainting methods generate inconsistent, blurry, and repeated pixels. To alleviate the difficulty of an outpainting problem, we propose a novel image outpainting method using bidirectional boundary region rearrangement. We rearrange the image to benefit from the image inpainting task by reflecting more directional information. The bidirectional boundary region rearrangement enables the generation of the missing region using bidirectional information similar to that of the image inpainting task, thereby generating the higher quality than the conventional methods using unidirectional information. Moreover, we use the edge map generator that considers images as original input with structural information and hallucinates the edges of unknown regions to generate the image. Our proposed method is compared with other state-of-the-art outpainting and inpainting methods both qualitatively and quantitatively. We further compared and evaluated them using BRISQUE, one of the No-Reference image quality assessment (IQA) metrics, to evaluate the naturalness of the output. The experimental results demonstrate that our method outperforms other methods and generates new images with 360{\deg}panoramic characteristics.

We investigate conditional adversarial networks as a general-purpose solution to image-to-image translation problems. These networks not only learn the mapping from input image to output image, but also learn a loss function to train this mapping. This makes it possible to apply the same generic approach to problems that traditionally would require very different loss formulations. We demonstrate that this approach is effective at synthesizing photos from label maps, reconstructing objects from edge maps, and colorizing images, among other tasks. Indeed, since the release of the pix2pix software associated with this paper, a large number of internet users (many of them artists) have posted their own experiments with our system, further demonstrating its wide applicability and ease of adoption without the need for parameter tweaking. As a community, we no longer hand-engineer our mapping functions, and this work suggests we can achieve reasonable results without hand-engineering our loss functions either.

Finite symmetric groups S_n are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over S_n poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over S_n by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at https://github.com/DSL-Lab/SymmetricDiffusers.

Diffusion models have quickly become the state-of-the-art for generation tasks across many different data modalities. An important ability of diffusion models is the ability to encode samples from the data distribution back into the sampling prior distribution. This is useful for performing alterations to real data samples along with guided generation via the continuous adjoint equations. We propose an algebraically reversible solver for diffusion SDEs that can exactly invert real data samples into the prior distribution.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

Modern consumer cameras usually employ the rolling shutter (RS) mechanism, where images are captured by scanning scenes row-by-row, yielding RS distortions for dynamic scenes. To correct RS distortions, existing methods adopt a fully supervised learning manner, where high framerate global shutter (GS) images should be collected as ground-truth supervision. In this paper, we propose a Self-supervised learning framework for Dual reversed RS distortions Correction (SelfDRSC), where a DRSC network can be learned to generate a high framerate GS video only based on dual RS images with reversed distortions. In particular, a bidirectional distortion warping module is proposed for reconstructing dual reversed RS images, and then a self-supervised loss can be deployed to train DRSC network by enhancing the cycle consistency between input and reconstructed dual reversed RS images. Besides start and end RS scanning time, GS images at arbitrary intermediate scanning time can also be supervised in SelfDRSC, thus enabling the learned DRSC network to generate a high framerate GS video. Moreover, a simple yet effective self-distillation strategy is introduced in self-supervised loss for mitigating boundary artifacts in generated GS images. On synthetic dataset, SelfDRSC achieves better or comparable quantitative metrics in comparison to state-of-the-art methods trained in the full supervision manner. On real-world RS cases, our SelfDRSC can produce high framerate GS videos with finer correction textures and better temporary consistency. The source code and trained models are made publicly available at https://github.com/shangwei5/SelfDRSC.

Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we conduct a direct analysis of the visual information contained in representations by asking the following question: given an encoding of an image, to which extent is it possible to reconstruct the image itself? To answer this question we contribute a general framework to invert representations. We show that this method can invert representations such as HOG and SIFT more accurately than recent alternatives while being applicable to CNNs too. We then use this technique to study the inverse of recent state-of-the-art CNN image representations for the first time. Among our findings, we show that several layers in CNNs retain photographically accurate information about the image, with different degrees of geometric and photometric invariance.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG). We relax this non-trivial constrained optimization problem to a tractable form with finite-dimensional parameterization and empirical approximation. Then a theoretical analysis of the extent to which the above transformations deviates from the original problem is provided. Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization. In contrast to traditional approaches based on domain adversarial training and domain labels, DDG jointly learns semantic and variation encoders for disentanglement, enabling flexible manipulation and augmentation on training data. DDG aims to learn intrinsic representations of semantic concepts that are invariant to nuisance factors and generalizable across domains. Comprehensive experiments on popular benchmarks show that DDG can achieve competitive OOD performance and uncover interpretable salient structures within data.

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

Autonomous vehicles rely on HD maps for their operation, but offline HD maps eventually become outdated. For this reason, online HD map construction methods use live sensor data to infer map information instead. Research on real map changes shows that oftentimes entire parts of an HD map remain unchanged and can be used as a prior. We therefore introduce M3TR (Multi-Masking Map Transformer), a generalist approach for HD map completion both with and without offline HD map priors. As a necessary foundation, we address shortcomings in ground truth labels for Argoverse 2 and nuScenes and propose the first comprehensive benchmark for HD map completion. Unlike existing models that specialize in a single kind of map change, which is unrealistic for deployment, our Generalist model handles all kinds of changes, matching the effectiveness of Expert models. With our map masking as augmentation regime, we can even achieve a +1.4 mAP improvement without a prior. Finally, by fully utilizing prior HD map elements and optimizing query designs, M3TR outperforms existing methods by +4.3 mAP while being the first real-world deployable model for offline HD map priors. Code is available at https://github.com/immel-f/m3tr

Cross-View Geo-Localisation is still a challenging task where additional modules, specific pre-processing or zooming strategies are necessary to determine accurate positions of images. Since different views have different geometries, pre-processing like polar transformation helps to merge them. However, this results in distorted images which then have to be rectified. Adding hard negatives to the training batch could improve the overall performance but with the default loss functions in geo-localisation it is difficult to include them. In this article, we present a simplified but effective architecture based on contrastive learning with symmetric InfoNCE loss that outperforms current state-of-the-art results. Our framework consists of a narrow training pipeline that eliminates the need of using aggregation modules, avoids further pre-processing steps and even increases the generalisation capability of the model to unknown regions. We introduce two types of sampling strategies for hard negatives. The first explicitly exploits geographically neighboring locations to provide a good starting point. The second leverages the visual similarity between the image embeddings in order to mine hard negative samples. Our work shows excellent performance on common cross-view datasets like CVUSA, CVACT, University-1652 and VIGOR. A comparison between cross-area and same-area settings demonstrate the good generalisation capability of our model.

Autonomous driving systems require High-Definition (HD) semantic maps to navigate around urban roads. Existing solutions approach the semantic mapping problem by offline manual annotation, which suffers from serious scalability issues. Recent learning-based methods produce dense rasterized segmentation predictions to construct maps. However, these predictions do not include instance information of individual map elements and require heuristic post-processing to obtain vectorized maps. To tackle these challenges, we introduce an end-to-end vectorized HD map learning pipeline, termed VectorMapNet. VectorMapNet takes onboard sensor observations and predicts a sparse set of polylines in the bird's-eye view. This pipeline can explicitly model the spatial relation between map elements and generate vectorized maps that are friendly to downstream autonomous driving tasks. Extensive experiments show that VectorMapNet achieve strong map learning performance on both nuScenes and Argoverse2 dataset, surpassing previous state-of-the-art methods by 14.2 mAP and 14.6mAP. Qualitatively, VectorMapNet is capable of generating comprehensive maps and capturing fine-grained details of road geometry. To the best of our knowledge, VectorMapNet is the first work designed towards end-to-end vectorized map learning from onboard observations. Our project website is available at https://tsinghua-mars-lab.github.io/vectormapnet/.

As there are now millions of publicly available neural networks, searching and analyzing large model repositories becomes increasingly important. Navigating so many models requires an atlas, but as most models are poorly documented charting such an atlas is challenging. To explore the hidden potential of model repositories, we chart a preliminary atlas representing the documented fraction of Hugging Face. It provides stunning visualizations of the model landscape and evolution. We demonstrate several applications of this atlas including predicting model attributes (e.g., accuracy), and analyzing trends in computer vision models. However, as the current atlas remains incomplete, we propose a method for charting undocumented regions. Specifically, we identify high-confidence structural priors based on dominant real-world model training practices. Leveraging these priors, our approach enables accurate mapping of previously undocumented areas of the atlas. We publicly release our datasets, code, and interactive atlas.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

We propose GS-IR, a novel inverse rendering approach based on 3D Gaussian Splatting (GS) that leverages forward mapping volume rendering to achieve photorealistic novel view synthesis and relighting results. Unlike previous works that use implicit neural representations and volume rendering (e.g. NeRF), which suffer from low expressive power and high computational complexity, we extend GS, a top-performance representation for novel view synthesis, to estimate scene geometry, surface material, and environment illumination from multi-view images captured under unknown lighting conditions. There are two main problems when introducing GS to inverse rendering: 1) GS does not support producing plausible normal natively; 2) forward mapping (e.g. rasterization and splatting) cannot trace the occlusion like backward mapping (e.g. ray tracing). To address these challenges, our GS-IR proposes an efficient optimization scheme that incorporates a depth-derivation-based regularization for normal estimation and a baking-based occlusion to model indirect lighting. The flexible and expressive GS representation allows us to achieve fast and compact geometry reconstruction, photorealistic novel view synthesis, and effective physically-based rendering. We demonstrate the superiority of our method over baseline methods through qualitative and quantitative evaluations on various challenging scenes.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nystr\"{o}m method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

In this paper, we introduce Geometry-Inverse-Meet-Pixel-Insert, short for GEO, an exceptionally versatile image editing technique designed to cater to customized user requirements at both local and global scales. Our approach seamlessly integrates text prompts and image prompts to yield diverse and precise editing outcomes. Notably, our method operates without the need for training and is driven by two key contributions: (i) a novel geometric accumulation loss that enhances DDIM inversion to faithfully preserve pixel space geometry and layout, and (ii) an innovative boosted image prompt technique that combines pixel-level editing for text-only inversion with latent space geometry guidance for standard classifier-free reversion. Leveraging the publicly available Stable Diffusion model, our approach undergoes extensive evaluation across various image types and challenging prompt editing scenarios, consistently delivering high-fidelity editing results for real images.

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.

Model Inversion (MI) attacks aim to reconstruct privacy-sensitive training data from released models by utilizing output information, raising extensive concerns about the security of Deep Neural Networks (DNNs). Recent advances in generative adversarial networks (GANs) have contributed significantly to the improved performance of MI attacks due to their powerful ability to generate realistic images with high fidelity and appropriate semantics. However, previous MI attacks have solely disclosed private information in the latent space of GAN priors, limiting their semantic extraction and transferability across multiple target models and datasets. To address this challenge, we propose a novel method, Intermediate Features enhanced Generative Model Inversion (IF-GMI), which disassembles the GAN structure and exploits features between intermediate blocks. This allows us to extend the optimization space from latent code to intermediate features with enhanced expressive capabilities. To prevent GAN priors from generating unrealistic images, we apply a L1 ball constraint to the optimization process. Experiments on multiple benchmarks demonstrate that our method significantly outperforms previous approaches and achieves state-of-the-art results under various settings, especially in the out-of-distribution (OOD) scenario. Our code is available at: https://github.com/final-solution/IF-GMI

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Sampling from diffusion models involves a slow iterative process that hinders their practical deployment, especially for interactive applications. To accelerate generation speed, recent approaches distill a multi-step diffusion model into a single-step student generator via variational score distillation, which matches the distribution of samples generated by the student to the teacher's distribution. However, these approaches use the reverse Kullback-Leibler (KL) divergence for distribution matching which is known to be mode seeking. In this paper, we generalize the distribution matching approach using a novel f-divergence minimization framework, termed f-distill, that covers different divergences with different trade-offs in terms of mode coverage and training variance. We derive the gradient of the f-divergence between the teacher and student distributions and show that it is expressed as the product of their score differences and a weighting function determined by their density ratio. This weighting function naturally emphasizes samples with higher density in the teacher distribution, when using a less mode-seeking divergence. We observe that the popular variational score distillation approach using the reverse-KL divergence is a special case within our framework. Empirically, we demonstrate that alternative f-divergences, such as forward-KL and Jensen-Shannon divergences, outperform the current best variational score distillation methods across image generation tasks. In particular, when using Jensen-Shannon divergence, f-distill achieves current state-of-the-art one-step generation performance on ImageNet64 and zero-shot text-to-image generation on MS-COCO. Project page: https://research.nvidia.com/labs/genair/f-distill

The Travelling Salesman Problem (TSP) remains a fundamental challenge in combinatorial optimization, inspiring diverse algorithmic strategies. This paper revisits the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm that has recently gained traction for learning-based TSP solutions. Within this framework, heatmaps encode the likelihood of edges forming part of the optimal tour, and MCTS refines this probabilistic guidance to discover optimal solutions. Contemporary approaches have predominantly emphasized the refinement of heatmap generation through sophisticated learning models, inadvertently sidelining the critical role of MCTS. Our extensive empirical analysis reveals two pivotal insights: 1) The configuration of MCTS strategies profoundly influences the solution quality, demanding meticulous tuning to leverage their full potential; 2) Our findings demonstrate that a rudimentary and parameter-free heatmap, derived from the intrinsic k-nearest nature of TSP, can rival or even surpass the performance of complicated heatmaps, with strong generalizability across various scales. Empirical evaluations across various TSP scales underscore the efficacy of our approach, achieving competitive results. These observations challenge the prevailing focus on heatmap sophistication, advocating a reevaluation of the paradigm to harness both components synergistically. Our code is available at: https://github.com/LOGO-CUHKSZ/rethink_mcts_tsp.

Given a database of bit strings A_1,ldots,A_min {0,1}^n, a fundamental data structure task is to estimate the distances between a given query Bin {0,1}^n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is epsilon-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, - For Hamming distance, our data structure answers any query in widetilde O(mk+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/log k}); - For edit distance, our data structure answers any query in widetilde O(mk^2+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/(log k log n)}). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

We present SHINOBI, an end-to-end framework for the reconstruction of shape, material, and illumination from object images captured with varying lighting, pose, and background. Inverse rendering of an object based on unconstrained image collections is a long-standing challenge in computer vision and graphics and requires a joint optimization over shape, radiance, and pose. We show that an implicit shape representation based on a multi-resolution hash encoding enables faster and robust shape reconstruction with joint camera alignment optimization that outperforms prior work. Further, to enable the editing of illumination and object reflectance (i.e. material) we jointly optimize BRDF and illumination together with the object's shape. Our method is class-agnostic and works on in-the-wild image collections of objects to produce relightable 3D assets for several use cases such as AR/VR, movies, games, etc. Project page: https://shinobi.aengelhardt.com Video: https://www.youtube.com/watch?v=iFENQ6AcYd8&feature=youtu.be

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

In image editing employing diffusion models, it is crucial to preserve the reconstruction quality of the original image while changing its style. Although existing methods ensure reconstruction quality through optimization, a drawback of these is the significant amount of time required for optimization. In this paper, we propose negative-prompt inversion, a method capable of achieving equivalent reconstruction solely through forward propagation without optimization, thereby enabling much faster editing processes. We experimentally demonstrate that the reconstruction quality of our method is comparable to that of existing methods, allowing for inversion at a resolution of 512 pixels and with 50 sampling steps within approximately 5 seconds, which is more than 30 times faster than null-text inversion. Reduction of the computation time by the proposed method further allows us to use a larger number of sampling steps in diffusion models to improve the reconstruction quality with a moderate increase in computation time.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

Autonomous driving for urban and highway driving applications often requires High Definition (HD) maps to generate a navigation plan. Nevertheless, various challenges arise when generating and maintaining HD maps at scale. While recent online mapping methods have started to emerge, their performance especially for longer ranges is limited by heavy occlusion in dynamic environments. With these considerations in mind, our work focuses on leveraging lightweight and scalable priors-Standard Definition (SD) maps-in the development of online vectorized HD map representations. We first examine the integration of prototypical rasterized SD map representations into various online mapping architectures. Furthermore, to identify lightweight strategies, we extend the OpenLane-V2 dataset with OpenStreetMaps and evaluate the benefits of graphical SD map representations. A key finding from designing SD map integration components is that SD map encoders are model agnostic and can be quickly adapted to new architectures that utilize bird's eye view (BEV) encoders. Our results show that making use of SD maps as priors for the online mapping task can significantly speed up convergence and boost the performance of the online centerline perception task by 30% (mAP). Furthermore, we show that the introduction of the SD maps leads to a reduction of the number of parameters in the perception and reasoning task by leveraging SD map graphs while improving the overall performance. Project Page: https://henryzhangzhy.github.io/sdhdmap/.

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Existing methods for relightable view synthesis -- using a set of images of an object under unknown lighting to recover a 3D representation that can be rendered from novel viewpoints under a target illumination -- are based on inverse rendering, and attempt to disentangle the object geometry, materials, and lighting that explain the input images. Furthermore, this typically involves optimization through differentiable Monte Carlo rendering, which is brittle and computationally-expensive. In this work, we propose a simpler approach: we first relight each input image using an image diffusion model conditioned on lighting and then reconstruct a Neural Radiance Field (NeRF) with these relit images, from which we render novel views under the target lighting. We demonstrate that this strategy is surprisingly competitive and achieves state-of-the-art results on multiple relighting benchmarks. Please see our project page at https://illuminerf.github.io/.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Despite increasing progress in development of methods for generating visual counterfactual explanations, especially with the recent rise of Denoising Diffusion Probabilistic Models, previous works consider them as an entirely local technique. In this work, we take the first step at globalizing them. Specifically, we discover that the latent space of Diffusion Autoencoders encodes the inference process of a given classifier in the form of global directions. We propose a novel proxy-based approach that discovers two types of these directions with the use of only single image in an entirely black-box manner. Precisely, g-directions allow for flipping the decision of a given classifier on an entire dataset of images, while h-directions further increase the diversity of explanations. We refer to them in general as Global Counterfactual Directions (GCDs). Moreover, we show that GCDs can be naturally combined with Latent Integrated Gradients resulting in a new black-box attribution method, while simultaneously enhancing the understanding of counterfactual explanations. We validate our approach on existing benchmarks and show that it generalizes to real-world use-cases.

Can we relocalize in a scene represented by a single reference image? Standard visual relocalization requires hundreds of images and scale calibration to build a scene-specific 3D map. In contrast, we propose Map-free Relocalization, i.e., using only one photo of a scene to enable instant, metric scaled relocalization. Existing datasets are not suitable to benchmark map-free relocalization, due to their focus on large scenes or their limited variability. Thus, we have constructed a new dataset of 655 small places of interest, such as sculptures, murals and fountains, collected worldwide. Each place comes with a reference image to serve as a relocalization anchor, and dozens of query images with known, metric camera poses. The dataset features changing conditions, stark viewpoint changes, high variability across places, and queries with low to no visual overlap with the reference image. We identify two viable families of existing methods to provide baseline results: relative pose regression, and feature matching combined with single-image depth prediction. While these methods show reasonable performance on some favorable scenes in our dataset, map-free relocalization proves to be a challenge that requires new, innovative solutions.

In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and inverse problems are computationally prohibitive, there is a growing interest in leveraging recent advances in deep learning to learn the mapping between velocity maps and seismic waveform images directly from data. Despite the variety of architectures explored in previous works, several open questions still remain unanswered such as the effect of latent space sizes, the importance of manifold learning, the complexity of translation models, and the value of jointly solving forward and inverse problems. We propose a unified framework to systematically characterize prior research in this area termed the Generalized Forward-Inverse (GFI) framework, building on the assumption of manifolds and latent space translations. We show that GFI encompasses previous works in deep learning for subsurface imaging, which can be viewed as specific instantiations of GFI. We also propose two new model architectures within the framework of GFI: Latent U-Net and Invertible X-Net, leveraging the power of U-Nets for domain translation and the ability of IU-Nets to simultaneously learn forward and inverse translations, respectively. We show that our proposed models achieve state-of-the-art (SOTA) performance for forward and inverse problems on a wide range of synthetic datasets, and also investigate their zero-shot effectiveness on two real-world-like datasets. Our code is available at https://github.com/KGML-lab/Generalized-Forward-Inverse-Framework-for-DL4SI

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an up-convolutional neural network. We apply the method to shallow representations (HOG, SIFT, LBP), as well as to deep networks. For shallow representations our approach provides significantly better reconstructions than existing methods, revealing that there is surprisingly rich information contained in these features. Inverting a deep network trained on ImageNet provides several insights into the properties of the feature representation learned by the network. Most strikingly, the colors and the rough contours of an image can be reconstructed from activations in higher network layers and even from the predicted class probabilities.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Omnidirectional images (ODIs) have become increasingly popular, as their large field-of-view (FoV) can offer viewers the chance to freely choose the view directions in immersive environments such as virtual reality. The M\"obius transformation is typically employed to further provide the opportunity for movement and zoom on ODIs, but applying it to the image level often results in blurry effect and aliasing problem. In this paper, we propose a novel deep learning-based approach, called OmniZoomer, to incorporate the M\"obius transformation into the network for movement and zoom on ODIs. By learning various transformed feature maps under different conditions, the network is enhanced to handle the increasing edge curvatures, which alleviates the blurry effect. Moreover, to address the aliasing problem, we propose two key components. Firstly, to compensate for the lack of pixels for describing curves, we enhance the feature maps in the high-resolution (HR) space and calculate the transformed index map with a spatial index generation module. Secondly, considering that ODIs are inherently represented in the spherical space, we propose a spherical resampling module that combines the index map and HR feature maps to transform the feature maps for better spherical correlation. The transformed feature maps are decoded to output a zoomed ODI. Experiments show that our method can produce HR and high-quality ODIs with the flexibility to move and zoom in to the object of interest. Project page is available at http://vlislab22.github.io/OmniZoomer/.

Intelligent robots need to interact with diverse objects across various environments. The appearance and state of objects frequently undergo complex transformations depending on the object properties, e.g., phase transitions. However, in the vision community, segmenting dynamic objects with phase transitions is overlooked. In light of this, we introduce the concept of phase in segmentation, which categorizes real-world objects based on their visual characteristics and potential morphological and appearance changes. Then, we present a new benchmark, Multi-Phase, Multi-Transition, and Multi-Scenery Video Object Segmentation (M^3-VOS), to verify the ability of models to understand object phases, which consists of 479 high-resolution videos spanning over 10 distinct everyday scenarios. It provides dense instance mask annotations that capture both object phases and their transitions. We evaluate state-of-the-art methods on M^3-VOS, yielding several key insights. Notably, current appearance-based approaches show significant room for improvement when handling objects with phase transitions. The inherent changes in disorder suggest that the predictive performance of the forward entropy-increasing process can be improved through a reverse entropy-reducing process. These findings lead us to propose ReVOS, a new plug-andplay model that improves its performance by reversal refinement. Our data and code will be publicly available at https://zixuan-chen.github.io/M-cube-VOS.github.io/.

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods.

Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, \ie, conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demonstrated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

We present GI-GS, a novel inverse rendering framework that leverages 3D Gaussian Splatting (3DGS) and deferred shading to achieve photo-realistic novel view synthesis and relighting. In inverse rendering, accurately modeling the shading processes of objects is essential for achieving high-fidelity results. Therefore, it is critical to incorporate global illumination to account for indirect lighting that reaches an object after multiple bounces across the scene. Previous 3DGS-based methods have attempted to model indirect lighting by characterizing indirect illumination as learnable lighting volumes or additional attributes of each Gaussian, while using baked occlusion to represent shadow effects. These methods, however, fail to accurately model the complex physical interactions between light and objects, making it impossible to construct realistic indirect illumination during relighting. To address this limitation, we propose to calculate indirect lighting using efficient path tracing with deferred shading. In our framework, we first render a G-buffer to capture the detailed geometry and material properties of the scene. Then, we perform physically-based rendering (PBR) only for direct lighting. With the G-buffer and previous rendering results, the indirect lighting can be calculated through a lightweight path tracing. Our method effectively models indirect lighting under any given lighting conditions, thereby achieving better novel view synthesis and relighting. Quantitative and qualitative results show that our GI-GS outperforms existing baselines in both rendering quality and efficiency.

Modern retrieval system often requires recomputing the representation of every piece of data in the gallery when updating to a better representation model. This process is known as backfilling and can be especially costly in the real world where the gallery often contains billions of samples. Recently, researchers have proposed the idea of Backward Compatible Training (BCT) where the new representation model can be trained with an auxiliary loss to make it backward compatible with the old representation. In this way, the new representation can be directly compared with the old representation, in principle avoiding the need for any backfilling. However, followup work shows that there is an inherent tradeoff where a backward compatible representation model cannot simultaneously maintain the performance of the new model itself. This paper reports our ``not-so-surprising'' finding that adding extra dimensions to the representation can help here. However, we also found that naively increasing the dimension of the representation did not work. To deal with this, we propose Backward-compatible Training with a novel Basis Transformation (BT^2). A basis transformation (BT) is basically a learnable set of parameters that applies an orthonormal transformation. Such a transformation possesses an important property whereby the original information contained in its input is retained in its output. We show in this paper how a BT can be utilized to add only the necessary amount of additional dimensions. We empirically verify the advantage of BT^2 over other state-of-the-art methods in a wide range of settings. We then further extend BT^2 to other challenging yet more practical settings, including significant change in model architecture (CNN to Transformers), modality change, and even a series of updates in the model architecture mimicking the evolution of deep learning models.

Reverse sampling and score-distillation have emerged as main workhorses in recent years for image manipulation using latent diffusion models (LDMs). While reverse diffusion sampling often requires adjustments of LDM architecture or feature engineering, score distillation offers a simple yet powerful model-agnostic approach, but it is often prone to mode-collapsing. To address these limitations and leverage the strengths of both approaches, here we introduce a novel framework called {\em DreamSampler}, which seamlessly integrates these two distinct approaches through the lens of regularized latent optimization. Similar to score-distillation, DreamSampler is a model-agnostic approach applicable to any LDM architecture, but it allows both distillation and reverse sampling with additional guidance for image editing and reconstruction. Through experiments involving image editing, SVG reconstruction and etc, we demonstrate the competitive performance of DreamSampler compared to existing approaches, while providing new applications.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

This work introduces RevSilo, the first reversible bidirectional multi-scale feature fusion module. Like other reversible methods, RevSilo eliminates the need to store hidden activations by recomputing them. However, existing reversible methods do not apply to multi-scale feature fusion and are, therefore, not applicable to a large class of networks. Bidirectional multi-scale feature fusion promotes local and global coherence and has become a de facto design principle for networks targeting spatially sensitive tasks, e.g., HRNet (Sun et al., 2019a) and EfficientDet (Tan et al., 2020). These networks achieve state-of-the-art results across various computer vision tasks when paired with high-resolution inputs. However, training them requires substantial accelerator memory for saving large, multi-resolution activations. These memory requirements inherently cap the size of neural networks, limiting improvements that come from scale. Operating across resolution scales, RevSilo alleviates these issues. Stacking RevSilos, we create RevBiFPN, a fully reversible bidirectional feature pyramid network. RevBiFPN is competitive with networks such as EfficientNet while using up to 19.8x lesser training memory for image classification. When fine-tuned on MS COCO, RevBiFPN provides up to a 2.5% boost in AP over HRNet using fewer MACs and a 2.4x reduction in training-time memory.

Reliable high-definition (HD) map construction is crucial for the driving safety of autonomous vehicles. Although recent studies demonstrate improved performance, their generalization capability across unfamiliar driving scenes remains unexplored. To tackle this issue, we propose UIGenMap, an uncertainty-instructed structure injection approach for generalizable HD map vectorization, which concerns the uncertainty resampling in statistical distribution and employs explicit instance features to reduce excessive reliance on training data. Specifically, we introduce the perspective-view (PV) detection branch to obtain explicit structural features, in which the uncertainty-aware decoder is designed to dynamically sample probability distributions considering the difference in scenes. With probabilistic embedding and selection, UI2DPrompt is proposed to construct PV-learnable prompts. These PV prompts are integrated into the map decoder by designed hybrid injection to compensate for neglected instance structures. To ensure real-time inference, a lightweight Mimic Query Distillation is designed to learn from PV prompts, which can serve as an efficient alternative to the flow of PV branches. Extensive experiments on challenging geographically disjoint (geo-based) data splits demonstrate that our UIGenMap achieves superior performance, with +5.7 mAP improvement on the nuScenes dataset. Source code will be available at https://github.com/xiaolul2/UIGenMap.

We present VGGT-SLAM, a dense RGB SLAM system constructed by incrementally and globally aligning submaps created from the feed-forward scene reconstruction approach VGGT using only uncalibrated monocular cameras. While related works align submaps using similarity transforms (i.e., translation, rotation, and scale), we show that such approaches are inadequate in the case of uncalibrated cameras. In particular, we revisit the idea of reconstruction ambiguity, where given a set of uncalibrated cameras with no assumption on the camera motion or scene structure, the scene can only be reconstructed up to a 15-degrees-of-freedom projective transformation of the true geometry. This inspires us to recover a consistent scene reconstruction across submaps by optimizing over the SL(4) manifold, thus estimating 15-degrees-of-freedom homography transforms between sequential submaps while accounting for potential loop closure constraints. As verified by extensive experiments, we demonstrate that VGGT-SLAM achieves improved map quality using long video sequences that are infeasible for VGGT due to its high GPU requirements.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

In this paper, we introduce Mask2Map, a novel end-to-end online HD map construction method designed for autonomous driving applications. Our approach focuses on predicting the class and ordered point set of map instances within a scene, represented in the bird's eye view (BEV). Mask2Map consists of two primary components: the Instance-Level Mask Prediction Network (IMPNet) and the Mask-Driven Map Prediction Network (MMPNet). IMPNet generates Mask-Aware Queries and BEV Segmentation Masks to capture comprehensive semantic information globally. Subsequently, MMPNet enhances these query features using local contextual information through two submodules: the Positional Query Generator (PQG) and the Geometric Feature Extractor (GFE). PQG extracts instance-level positional queries by embedding BEV positional information into Mask-Aware Queries, while GFE utilizes BEV Segmentation Masks to generate point-level geometric features. However, we observed limited performance in Mask2Map due to inter-network inconsistency stemming from different predictions to Ground Truth (GT) matching between IMPNet and MMPNet. To tackle this challenge, we propose the Inter-network Denoising Training method, which guides the model to denoise the output affected by both noisy GT queries and perturbed GT Segmentation Masks. Our evaluation conducted on nuScenes and Argoverse2 benchmarks demonstrates that Mask2Map achieves remarkable performance improvements over previous state-of-the-art methods, with gains of 10.1% mAP and 4.1 mAP, respectively. Our code can be found at https://github.com/SehwanChoi0307/Mask2Map.

Inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time O(n^3) where n is the number of pixels in the image. We give a fast parallel backpropagation algorithm with running time O(n) for a square image and provide a GPU implementation of the same. Inverse Convolutions are usually used in Normalizing Flows in the sampling pass, making them slow. We propose to use Inverse Convolutions in the forward (image to latent vector) pass of the Normalizing flow. Since the sampling pass is the inverse of the forward pass, it will use convolutions only, resulting in efficient sampling times. We use our parallel backpropagation algorithm for optimizing the inverse convolution layer resulting in fast training times also. We implement this approach in various Normalizing Flow backbones, resulting in our Inverse-Flow models. We benchmark Inverse-Flow on standard datasets and show significantly improved sampling times with similar bits per dimension compared to previous models.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Maps are fundamental medium to visualize and represent the real word in a simple and 16 philosophical way. The emergence of the 3rd wave information has made a proportion of maps are available to be generated ubiquitously, which would significantly enrich the dimensions and perspectives to understand the characteristics of the real world. However, a majority of map dataset have never been discovered, acquired and effectively used, and the map data used in many applications might not be completely fitted for the authentic demands of these applications. This challenge is emerged due to the lack of numerous well-labelled benchmark datasets for implementing the deep learning approaches into identifying complicated map content. Thus, we develop a large-scale benchmark dataset that includes well-labelled dataset for map text annotation recognition, map scene classification, map super-resolution reconstruction, and map style transferring. Furthermore, these well-labelled datasets would facilitate the state-of-the-art machine intelligence technologies to conduct map feature detection, map pattern recognition and map content retrieval. We hope our efforts would be useful for AI-enhanced cartographical applications.

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by "exploding inverse" in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding inverse and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance via projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical of these two techniques relative to the continuous ideal gradients. Motivated by this analysis we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients. We then validate this work on several inverse image problems and property-guided molecular generation.

We report the effects of replacing the scaled dot-product (within softmax) attention with the negative-log of Euclidean distance. This form of attention simplifies to inverse distance weighting interpolation. Used in simple one hidden layer networks and trained with vanilla cross-entropy loss on classification problems, it tends to produce a key matrix containing prototypes and a value matrix with corresponding logits. We also show that the resulting interpretable networks can be augmented with manually-constructed prototypes to perform low-impact handling of special cases.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Reverse engineering binaries is required to understand and analyse programs for which the source code is unavailable. Decompilers can transform the largely unreadable binaries into a more readable source code-like representation. However, reverse engineering is time-consuming, much of which is taken up by labelling the functions with semantic information. While the automated summarisation of decompiled code can help Reverse Engineers understand and analyse binaries, current work mainly focuses on summarising source code, and no suitable dataset exists for this task. In this work, we extend large pre-trained language models of source code to summarise decompiled binary functions. Furthermore, we investigate the impact of input and data properties on the performance of such models. Our approach consists of two main components; the data and the model. We first build CAPYBARA, a dataset of 214K decompiled function-documentation pairs across various compiler optimisations. We extend CAPYBARA further by generating synthetic datasets and deduplicating the data. Next, we fine-tune the CodeT5 base model with CAPYBARA to create BinT5. BinT5 achieves the state-of-the-art BLEU-4 score of 60.83, 58.82, and 44.21 for summarising source, decompiled, and synthetically stripped decompiled code, respectively. This indicates that these models can be extended to decompiled binaries successfully. Finally, we found that the performance of BinT5 is not heavily dependent on the dataset size and compiler optimisation level. We recommend future research to further investigate transferring knowledge when working with less expressive input formats such as stripped binaries.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Deep neural networks have achieved remarkable progress in enhancing low-light images by improving their brightness and eliminating noise. However, most existing methods construct end-to-end mapping networks heuristically, neglecting the intrinsic prior of image enhancement task and lacking transparency and interpretability. Although some unfolding solutions have been proposed to relieve these issues, they rely on proximal operator networks that deliver ambiguous and implicit priors. In this work, we propose a paradigm for low-light image enhancement that explores the potential of customized learnable priors to improve the transparency of the deep unfolding paradigm. Motivated by the powerful feature representation capability of Masked Autoencoder (MAE), we customize MAE-based illumination and noise priors and redevelop them from two perspectives: 1) structure flow: we train the MAE from a normal-light image to its illumination properties and then embed it into the proximal operator design of the unfolding architecture; and m2) optimization flow: we train MAE from a normal-light image to its gradient representation and then employ it as a regularization term to constrain noise in the model output. These designs improve the interpretability and representation capability of the model.Extensive experiments on multiple low-light image enhancement datasets demonstrate the superiority of our proposed paradigm over state-of-the-art methods. Code is available at https://github.com/zheng980629/CUE.

Modern end-to-end image signal processors (ISPs) can learn complex mappings from RAW/XYZ data to sRGB (or inverse), opening new possibilities in image processing. However, as the diversity of camera models continues to expand, developing and maintaining individual ISPs is not sustainable in the long term, which inherently lacks versatility, hindering the adaptability to multiple camera models. In this paper, we propose a novel pipeline, Uni-ISP, which unifies the learning of ISPs from multiple cameras, offering an accurate and versatile processor to multiple camera models. The core of Uni-ISP is leveraging device-aware embeddings through learning inverse/forward ISPs and its special training scheme. By doing so, Uni-ISP not only improves the performance of inverse/forward ISPs but also unlocks a variety of new applications inaccessible to existing learned ISPs. Moreover, since there is no dataset synchronously captured by multiple cameras for training, we construct a real-world 4K dataset, FiveCam, comprising more than 2,400 pairs of sRGB-RAW images synchronously captured by five smartphones. We conducted extensive experiments demonstrating Uni-ISP's accuracy in inverse/forward ISPs (with improvements of +1.5dB/2.4dB PSNR), its versatility in enabling new applications, and its adaptability to new camera models.

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification tasks. Inspired by previous research in NLP, we demonstrate how the inner representations at any level of the hierarchy can be projected onto the learned class embedding space to uncover how these networks build categorical representations for their predictions. We use our framework to show how image tokens develop class-specific representations that depend on attention mechanisms and contextual information, and give insights on how self-attention and MLP layers differentially contribute to this categorical composition. We additionally demonstrate that this method (1) can be used to determine the parts of an image that would be important for detecting the class of interest, and (2) exhibits significant advantages over traditional linear probing approaches. Taken together, our results position our proposed framework as a powerful tool for mechanistic interpretability and explainability research.

We address the challenges of precise image inversion and disentangled image editing in the context of few-step diffusion models. We introduce an encoder based iterative inversion technique. The inversion network is conditioned on the input image and the reconstructed image from the previous step, allowing for correction of the next reconstruction towards the input image. We demonstrate that disentangled controls can be easily achieved in the few-step diffusion model by conditioning on an (automatically generated) detailed text prompt. To manipulate the inverted image, we freeze the noise maps and modify one attribute in the text prompt (either manually or via instruction based editing driven by an LLM), resulting in the generation of a new image similar to the input image with only one attribute changed. It can further control the editing strength and accept instructive text prompt. Our approach facilitates realistic text-guided image edits in real-time, requiring only 8 number of functional evaluations (NFEs) in inversion (one-time cost) and 4 NFEs per edit. Our method is not only fast, but also significantly outperforms state-of-the-art multi-step diffusion editing techniques.

Many perception systems in mobile computing, autonomous navigation, and AR/VR face strict compute constraints that are particularly challenging for high-resolution input images. Previous works propose nonuniform downsamplers that "learn to zoom" on salient image regions, reducing compute while retaining task-relevant image information. However, for tasks with spatial labels (such as 2D/3D object detection and semantic segmentation), such distortions may harm performance. In this work (LZU), we "learn to zoom" in on the input image, compute spatial features, and then "unzoom" to revert any deformations. To enable efficient and differentiable unzooming, we approximate the zooming warp with a piecewise bilinear mapping that is invertible. LZU can be applied to any task with 2D spatial input and any model with 2D spatial features, and we demonstrate this versatility by evaluating on a variety of tasks and datasets: object detection on Argoverse-HD, semantic segmentation on Cityscapes, and monocular 3D object detection on nuScenes. Interestingly, we observe boosts in performance even when high-resolution sensor data is unavailable, implying that LZU can be used to "learn to upsample" as well.

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To address these limitations, we propose the use of adversarially robust representations as a perceptual primitive for feature inversion. We train an adversarially robust encoder to extract disentangled and perceptually-aligned image representations, making them easily invertible. By training a simple generator with the mirror architecture of the encoder, we achieve superior reconstruction quality and generalization over standard models. Based on this, we propose an adversarially robust autoencoder and demonstrate its improved performance on style transfer, image denoising and anomaly detection tasks. Compared to recent ImageNet feature inversion methods, our model attains improved performance with significantly less complexity.

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting bias. Existing second-order approximations are impractical due to prohibitive computational costs, making standard reverse diffusion processes intractable for posterior sampling. This paper introduces Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler that offers efficiency comparable to first-order Tweedie with a tractable reverse process using second-order approximation. Our theoretical results reveal that the second-order approximation is lower bounded by our surrogate loss that only requires O(1) compute using the trace of the Hessian, and by the lower bound we derive a new drift term to make the reverse process tractable. Our method surpasses SoTA solvers PSLD and P2L, achieving 4X and 8X reduction in neural function evaluations, respectively, while notably enhancing sampling quality on FFHQ, ImageNet, and COCO benchmarks. In addition, we show STSL extends to text-guided image editing and addresses residual distortions present from corrupted images in leading text-guided image editing methods. To our best knowledge, this is the first work to offer an efficient second-order approximation in solving inverse problems using latent diffusion and editing real-world images with corruptions.

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

Following the success of Word2Vec embeddings, graph embeddings (GEs) have gained substantial traction. GEs are commonly generated and evaluated extrinsically on downstream applications, but intrinsic evaluations of the original graph properties in terms of topological structure and semantic information have been lacking. Understanding these will help identify the deficiency of the various families of GE methods when vectorizing graphs in terms of preserving the relevant knowledge or learning incorrect knowledge. To address this, we propose RESTORE, a framework for intrinsic GEs assessment through graph reconstruction. We show that reconstructing the original graph from the underlying GEs yields insights into the relative amount of information preserved in a given vector form. We first introduce the graph reconstruction task. We generate GEs from three GE families based on factorization methods, random walks, and deep learning (with representative algorithms from each family) on the CommonSense Knowledge Graph (CSKG). We analyze their effectiveness in preserving the (a) topological structure of node-level graph reconstruction with an increasing number of hops and (b) semantic information on various word semantic and analogy tests. Our evaluations show deep learning-based GE algorithm (SDNE) is overall better at preserving (a) with a mean average precision (mAP) of 0.54 and 0.35 for 2 and 3-hop reconstruction respectively, while the factorization-based algorithm (HOPE) is better at encapsulating (b) with an average Euclidean distance of 0.14, 0.17, and 0.11 for 1, 2, and 3-hop reconstruction respectively. The modest performance of these GEs leaves room for further research avenues on better graph representation learning.

In image-to-image translation, each patch in the output should reflect the content of the corresponding patch in the input, independent of domain. We propose a straightforward method for doing so -- maximizing mutual information between the two, using a framework based on contrastive learning. The method encourages two elements (corresponding patches) to map to a similar point in a learned feature space, relative to other elements (other patches) in the dataset, referred to as negatives. We explore several critical design choices for making contrastive learning effective in the image synthesis setting. Notably, we use a multilayer, patch-based approach, rather than operate on entire images. Furthermore, we draw negatives from within the input image itself, rather than from the rest of the dataset. We demonstrate that our framework enables one-sided translation in the unpaired image-to-image translation setting, while improving quality and reducing training time. In addition, our method can even be extended to the training setting where each "domain" is only a single image.

Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant research effort to improve image sample quality, there is little work on representation-controlled generation using diffusion models. Specifically, causal modeling and controllable counterfactual generation using DPMs is an underexplored area. In this work, we propose CausalDiffAE, a diffusion-based causal representation learning framework to enable counterfactual generation according to a specified causal model. Our key idea is to use an encoder to extract high-level semantically meaningful causal variables from high-dimensional data and model stochastic variation using reverse diffusion. We propose a causal encoding mechanism that maps high-dimensional data to causally related latent factors and parameterize the causal mechanisms among latent factors using neural networks. To enforce the disentanglement of causal variables, we formulate a variational objective and leverage auxiliary label information in a prior to regularize the latent space. We propose a DDIM-based counterfactual generation procedure subject to do-interventions. Finally, to address the limited label supervision scenario, we also study the application of CausalDiffAE when a part of the training data is unlabeled, which also enables granular control over the strength of interventions in generating counterfactuals during inference. We empirically show that CausalDiffAE learns a disentangled latent space and is capable of generating high-quality counterfactual images.

We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in https://github.com/radarFudan/Curse-of-memory

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

People enjoy food photography because they appreciate food. Behind each meal there is a story described in a complex recipe and, unfortunately, by simply looking at a food image we do not have access to its preparation process. Therefore, in this paper we introduce an inverse cooking system that recreates cooking recipes given food images. Our system predicts ingredients as sets by means of a novel architecture, modeling their dependencies without imposing any order, and then generates cooking instructions by attending to both image and its inferred ingredients simultaneously. We extensively evaluate the whole system on the large-scale Recipe1M dataset and show that (1) we improve performance w.r.t. previous baselines for ingredient prediction; (2) we are able to obtain high quality recipes by leveraging both image and ingredients; (3) our system is able to produce more compelling recipes than retrieval-based approaches according to human judgment. We make code and models publicly available.

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree tree where the weight of each node is the sum of the weights of its children. A treemap for tree is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of tree and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, polygonal partitions, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio O(depth(tree)). However, depth(tree) still depends on the input tree. Hence we introduce a new type of treemaps, namely orthoconvex treemaps, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.

Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which states that when the ground cost is the squared-Euclidean distance, the ``best'' map to morph a continuous measure in P(Rd) into another must be the gradient of a convex function. To exploit that result, [Makkuva+ 2020, Korotin+2020] consider maps T=nabla f_theta, where f_theta is an input convex neural network (ICNN), as defined by Amos+2017, and fit theta with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on theta; the need to approximate the conjugate of f_theta; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier's result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost c and a reference measure rho, we introduce a regularizer, the Monge gap M^c_{rho}(T) of a map T. That gap quantifies how far a map T deviates from the ideal properties we expect from a c-OT map. In practice, we drop all architecture requirements for T and simply minimize a distance (e.g., the Sinkhorn divergence) between Tsharpmu and nu, regularized by M^c_rho(T). We study M^c_{rho}, and show how our simple pipeline outperforms significantly other baselines in practice.

Diffusion models have achieved remarkable success in image generation and editing tasks. Inversion within these models aims to recover the latent noise representation for a real or generated image, enabling reconstruction, editing, and other downstream tasks. However, to date, most inversion approaches suffer from an intrinsic trade-off between reconstruction accuracy and editing flexibility. This limitation arises from the difficulty of maintaining both semantic alignment and structural consistency during the inversion process. In this work, we introduce Dual-Conditional Inversion (DCI), a novel framework that jointly conditions on the source prompt and reference image to guide the inversion process. Specifically, DCI formulates the inversion process as a dual-condition fixed-point optimization problem, minimizing both the latent noise gap and the reconstruction error under the joint guidance. This design anchors the inversion trajectory in both semantic and visual space, leading to more accurate and editable latent representations. Our novel setup brings new understanding to the inversion process. Extensive experiments demonstrate that DCI achieves state-of-the-art performance across multiple editing tasks, significantly improving both reconstruction quality and editing precision. Furthermore, we also demonstrate that our method achieves strong results in reconstruction tasks, implying a degree of robustness and generalizability approaching the ultimate goal of the inversion process.

Text-to-image models encounter safety issues, including concerns related to copyright and Not-Safe-For-Work (NSFW) content. Despite several methods have been proposed for erasing inappropriate concepts from diffusion models, they often exhibit incomplete erasure, consume a lot of computing resources, and inadvertently damage generation ability. In this work, we introduce Reliable and Efficient Concept Erasure (RECE), a novel approach that modifies the model in 3 seconds without necessitating additional fine-tuning. Specifically, RECE efficiently leverages a closed-form solution to derive new target embeddings, which are capable of regenerating erased concepts within the unlearned model. To mitigate inappropriate content potentially represented by derived embeddings, RECE further aligns them with harmless concepts in cross-attention layers. The derivation and erasure of new representation embeddings are conducted iteratively to achieve a thorough erasure of inappropriate concepts. Besides, to preserve the model's generation ability, RECE introduces an additional regularization term during the derivation process, resulting in minimizing the impact on unrelated concepts during the erasure process. All the processes above are in closed-form, guaranteeing extremely efficient erasure in only 3 seconds. Benchmarking against previous approaches, our method achieves more efficient and thorough erasure with minor damage to original generation ability and demonstrates enhanced robustness against red-teaming tools. Code is available at https://github.com/CharlesGong12/RECE.

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

The main challenges of 3D pose transfer are: 1) Lack of paired training data with different characters performing the same pose; 2) Disentangling pose and shape information from the target mesh; 3) Difficulty in applying to meshes with different topologies. We thus propose a novel weakly-supervised keypoint-based framework to overcome these difficulties. Specifically, we use a topology-agnostic keypoint detector with inverse kinematics to compute transformations between the source and target meshes. Our method only requires supervision on the keypoints, can be applied to meshes with different topologies and is shape-invariant for the target which allows extraction of pose-only information from the target meshes without transferring shape information. We further design a cycle reconstruction to perform self-supervised pose transfer without the need for ground truth deformed mesh with the same pose and shape as the target and source, respectively. We evaluate our approach on benchmark human and animal datasets, where we achieve superior performance compared to the state-of-the-art unsupervised approaches and even comparable performance with the fully supervised approaches. We test on the more challenging Mixamo dataset to verify our approach's ability in handling meshes with different topologies and complex clothes. Cross-dataset evaluation further shows the strong generalization ability of our approach.

Backpropagation, the cornerstone of deep learning, is limited to computing gradients for continuous variables. This limitation poses challenges for problems involving discrete latent variables. To address this issue, we propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. First, we examine the widely used Straight-Through (ST) heuristic and demonstrate that it works as a first-order approximation of the gradient. Guided by our findings, we propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs. ReinMax does not require Hessian or other second-order derivatives, thus having negligible computation overheads. Extensive experimental results on various tasks demonstrate the superiority of ReinMax over the state of the art. Implementations are released at https://github.com/microsoft/ReinMax.

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

Optimal transport (OT) theory focuses, among all maps T:R^drightarrow R^d that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost c(x, T(x)) between x and its image T(x) be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when c is the ell_2^2 distance, e.g., using entropic maps [Pooladian'22], or neural networks [Makkuva'20, Korotin'20]. We propose a new model for transport maps, built on a family of translation invariant costs c(x, y):=h(x-y), where h:=1{2}|cdot|_2^2+tau and tau is a regularizer. We propose a generalization of the entropic map suitable for h, and highlight a surprising link tying it with the Bregman centroids of the divergence D_h generated by h, and the proximal operator of tau. We show that choosing a sparsity-inducing norm for tau results in maps that apply Occam's razor to transport, in the sense that the displacement vectors Delta(x):= T(x)-x they induce are sparse, with a sparsity pattern that varies depending on x. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data, in the 34000-d space of gene counts for cells, without using dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely-used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Black-Box Knowledge Distillation (B2KD) is a formulated problem for cloud-to-edge model compression with invisible data and models hosted on the server. B2KD faces challenges such as limited Internet exchange and edge-cloud disparity of data distributions. In this paper, we formalize a two-step workflow consisting of deprivatization and distillation, and theoretically provide a new optimization direction from logits to cell boundary different from direct logits alignment. With its guidance, we propose a new method Mapping-Emulation KD (MEKD) that distills a black-box cumbersome model into a lightweight one. Our method does not differentiate between treating soft or hard responses, and consists of: 1) deprivatization: emulating the inverse mapping of the teacher function with a generator, and 2) distillation: aligning low-dimensional logits of the teacher and student models by reducing the distance of high-dimensional image points. For different teacher-student pairs, our method yields inspiring distillation performance on various benchmarks, and outperforms the previous state-of-the-art approaches.

It has been well recognized that neural network based image classifiers are easily fooled by images with tiny perturbations crafted by an adversary. There has been a vast volume of research to generate and defend such adversarial attacks. However, the following problem is left unexplored: How to reverse-engineer adversarial perturbations from an adversarial image? This leads to a new adversarial learning paradigm--Reverse Engineering of Deceptions (RED). If successful, RED allows us to estimate adversarial perturbations and recover the original images. However, carefully crafted, tiny adversarial perturbations are difficult to recover by optimizing a unilateral RED objective. For example, the pure image denoising method may overfit to minimizing the reconstruction error but hardly preserve the classification properties of the true adversarial perturbations. To tackle this challenge, we formalize the RED problem and identify a set of principles crucial to the RED approach design. Particularly, we find that prediction alignment and proper data augmentation (in terms of spatial transformations) are two criteria to achieve a generalizable RED approach. By integrating these RED principles with image denoising, we propose a new Class-Discriminative Denoising based RED framework, termed CDD-RED. Extensive experiments demonstrate the effectiveness of CDD-RED under different evaluation metrics (ranging from the pixel-level, prediction-level to the attribution-level alignment) and a variety of attack generation methods (e.g., FGSM, PGD, CW, AutoAttack, and adaptive attacks).

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Recent text-guided diffusion models provide powerful image generation capabilities. Currently, a massive effort is given to enable the modification of these images using text only as means to offer intuitive and versatile editing. To edit a real image using these state-of-the-art tools, one must first invert the image with a meaningful text prompt into the pretrained model's domain. In this paper, we introduce an accurate inversion technique and thus facilitate an intuitive text-based modification of the image. Our proposed inversion consists of two novel key components: (i) Pivotal inversion for diffusion models. While current methods aim at mapping random noise samples to a single input image, we use a single pivotal noise vector for each timestamp and optimize around it. We demonstrate that a direct inversion is inadequate on its own, but does provide a good anchor for our optimization. (ii) NULL-text optimization, where we only modify the unconditional textual embedding that is used for classifier-free guidance, rather than the input text embedding. This allows for keeping both the model weights and the conditional embedding intact and hence enables applying prompt-based editing while avoiding the cumbersome tuning of the model's weights. Our Null-text inversion, based on the publicly available Stable Diffusion model, is extensively evaluated on a variety of images and prompt editing, showing high-fidelity editing of real images.

We present vMAP, an object-level dense SLAM system using neural field representations. Each object is represented by a small MLP, enabling efficient, watertight object modelling without the need for 3D priors. As an RGB-D camera browses a scene with no prior information, vMAP detects object instances on-the-fly, and dynamically adds them to its map. Specifically, thanks to the power of vectorised training, vMAP can optimise as many as 50 individual objects in a single scene, with an extremely efficient training speed of 5Hz map update. We experimentally demonstrate significantly improved scene-level and object-level reconstruction quality compared to prior neural field SLAM systems. Project page: https://kxhit.github.io/vMAP.

Text-driven diffusion models have significantly advanced the image editing performance by using text prompts as inputs. One crucial step in text-driven image editing is to invert the original image into a latent noise code conditioned on the source prompt. While previous methods have achieved promising results by refactoring the image synthesizing process, the inverted latent noise code is tightly coupled with the source prompt, limiting the image editability by target text prompts. To address this issue, we propose a novel method called Source Prompt Disentangled Inversion (SPDInv), which aims at reducing the impact of source prompt, thereby enhancing the text-driven image editing performance by employing diffusion models. To make the inverted noise code be independent of the given source prompt as much as possible, we indicate that the iterative inversion process should satisfy a fixed-point constraint. Consequently, we transform the inversion problem into a searching problem to find the fixed-point solution, and utilize the pre-trained diffusion models to facilitate the searching process. The experimental results show that our proposed SPDInv method can effectively mitigate the conflicts between the target editing prompt and the source prompt, leading to a significant decrease in editing artifacts. In addition to text-driven image editing, with SPDInv we can easily adapt customized image generation models to localized editing tasks and produce promising performance. The source code are available at https://github.com/leeruibin/SPDInv.

Text-guided diffusion models have become a popular tool in image synthesis, known for producing high-quality and diverse images. However, their application to editing real images often encounters hurdles primarily due to the text condition deteriorating the reconstruction quality and subsequently affecting editing fidelity. Null-text Inversion (NTI) has made strides in this area, but it fails to capture spatial context and requires computationally intensive per-timestep optimization. Addressing these challenges, we present Noise Map Guidance (NMG), an inversion method rich in a spatial context, tailored for real-image editing. Significantly, NMG achieves this without necessitating optimization, yet preserves the editing quality. Our empirical investigations highlight NMG's adaptability across various editing techniques and its robustness to variants of DDIM inversions.

Computer-Aided Design (CAD) models are typically constructed by sequentially drawing parametric sketches and applying CAD operations to obtain a 3D model. The problem of 3D CAD reverse engineering consists of reconstructing the sketch and CAD operation sequences from 3D representations such as point clouds. In this paper, we address this challenge through novel contributions across three levels: CAD sequence representation, network design, and dataset. In particular, we represent CAD sketch-extrude sequences as Python code. The proposed CAD-Recode translates a point cloud into Python code that, when executed, reconstructs the CAD model. Taking advantage of the exposure of pre-trained Large Language Models (LLMs) to Python code, we leverage a relatively small LLM as a decoder for CAD-Recode and combine it with a lightweight point cloud projector. CAD-Recode is trained solely on a proposed synthetic dataset of one million diverse CAD sequences. CAD-Recode significantly outperforms existing methods across three datasets while requiring fewer input points. Notably, it achieves 10 times lower mean Chamfer distance than state-of-the-art methods on DeepCAD and Fusion360 datasets. Furthermore, we show that our CAD Python code output is interpretable by off-the-shelf LLMs, enabling CAD editing and CAD-specific question answering from point clouds.

Offline model-based optimization aims to maximize a black-box objective function with a static dataset of designs and their scores. In this paper, we focus on biological sequence design to maximize some sequence score. A recent approach employs bidirectional learning, combining a forward mapping for exploitation and a backward mapping for constraint, and it relies on the neural tangent kernel (NTK) of an infinitely wide network to build a proxy model. Though effective, the NTK cannot learn features because of its parametrization, and its use prevents the incorporation of powerful pre-trained Language Models (LMs) that can capture the rich biophysical information in millions of biological sequences. We adopt an alternative proxy model, adding a linear head to a pre-trained LM, and propose a linearization scheme. This yields a closed-form loss and also takes into account the biophysical information in the pre-trained LM. In addition, the forward mapping and the backward mapping play different roles and thus deserve different weights during sequence optimization. To achieve this, we train an auxiliary model and leverage its weak supervision signal via a bi-level optimization framework to effectively learn how to balance the two mappings. Further, by extending the framework, we develop the first learning rate adaptation module Adaptive-eta, which is compatible with all gradient-based algorithms for offline model-based optimization. Experimental results on DNA/protein sequence design tasks verify the effectiveness of our algorithm. Our code is available~https://anonymous.4open.science/r/BIB-ICLR2023-Submission/README.md{here.}

We introduce a novel bilateral reference framework (BiRefNet) for high-resolution dichotomous image segmentation (DIS). It comprises two essential components: the localization module (LM) and the reconstruction module (RM) with our proposed bilateral reference (BiRef). The LM aids in object localization using global semantic information. Within the RM, we utilize BiRef for the reconstruction process, where hierarchical patches of images provide the source reference and gradient maps serve as the target reference. These components collaborate to generate the final predicted maps. We also introduce auxiliary gradient supervision to enhance focus on regions with finer details. Furthermore, we outline practical training strategies tailored for DIS to improve map quality and training process. To validate the general applicability of our approach, we conduct extensive experiments on four tasks to evince that BiRefNet exhibits remarkable performance, outperforming task-specific cutting-edge methods across all benchmarks. Our codes are available at https://github.com/ZhengPeng7/BiRefNet.

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods, that leverage pretrained denoisers, and unrolled architectures that are trained end-to-end for specific imaging problems. Iterative methods in the first class are computationally costly and often provide suboptimal reconstruction performance, whereas unrolled architectures are generally specific to a single inverse problem and require expensive training. In this work, we propose a novel non-iterative, lightweight architecture that incorporates knowledge about the forward operator (acquisition physics and noise parameters) without relying on unrolling. Our model is trained to solve a wide range of inverse problems beyond denoising, including deblurring, magnetic resonance imaging, computed tomography, inpainting, and super-resolution. The proposed model can be easily adapted to unseen inverse problems or datasets with a few fine-tuning steps (up to a few images) in a self-supervised way, without ground-truth references. Throughout a series of experiments, we demonstrate state-of-the-art performance from medical imaging to low-photon imaging and microscopy.

Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving, Petrick's method and McBoole's method have been devised to simplify Boolean expressions in order to optimize hardware implementation of digital circuits. However, the algorithmic implementations of these methods are hard-coded and also their computation time is proportional to the number of minterms involved in the expression. In this paper, we propose KarNet, where the ability of Convolutional Neural Networks to model relationships between various cell locations and values by capturing spatial dependencies is exploited to solve Karnaugh maps. In order to do so, a Karnaugh map is represented as an image signal, where each cell is considered as a pixel. Experimental results show that the computation time of KarNet is independent of the number of minterms and is of the order of one-hundredth to one-tenth that of the rule-based methods. KarNet being a learned system is found to achieve nearly a hundred percent accuracy, precision, and recall. We train KarNet to solve four variable Karnaugh maps and also show that a similar method can be applied on Karnaugh maps with more variables. Finally, we show a way to build a fully accurate and computationally fast system using KarNet.

We propose a system for rearranging objects in a scene to achieve a desired object-scene placing relationship, such as a book inserted in an open slot of a bookshelf. The pipeline generalizes to novel geometries, poses, and layouts of both scenes and objects, and is trained from demonstrations to operate directly on 3D point clouds. Our system overcomes challenges associated with the existence of many geometrically-similar rearrangement solutions for a given scene. By leveraging an iterative pose de-noising training procedure, we can fit multi-modal demonstration data and produce multi-modal outputs while remaining precise and accurate. We also show the advantages of conditioning on relevant local geometric features while ignoring irrelevant global structure that harms both generalization and precision. We demonstrate our approach on three distinct rearrangement tasks that require handling multi-modality and generalization over object shape and pose in both simulation and the real world. Project website, code, and videos: https://anthonysimeonov.github.io/rpdiff-multi-modal/

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

Despite the success of Generative Adversarial Networks (GANs) in image synthesis, applying trained GAN models to real image processing remains challenging. Previous methods typically invert a target image back to the latent space either by back-propagation or by learning an additional encoder. However, the reconstructions from both of the methods are far from ideal. In this work, we propose a novel approach, called mGANprior, to incorporate the well-trained GANs as effective prior to a variety of image processing tasks. In particular, we employ multiple latent codes to generate multiple feature maps at some intermediate layer of the generator, then compose them with adaptive channel importance to recover the input image. Such an over-parameterization of the latent space significantly improves the image reconstruction quality, outperforming existing competitors. The resulting high-fidelity image reconstruction enables the trained GAN models as prior to many real-world applications, such as image colorization, super-resolution, image inpainting, and semantic manipulation. We further analyze the properties of the layer-wise representation learned by GAN models and shed light on what knowledge each layer is capable of representing.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

Which functions can be used as activations in deep neural networks? This article explores families of functions based on orthonormal bases, including the Hermite polynomial basis and the Fourier trigonometric basis, as well as a basis resulting from the tropicalization of a polynomial basis. Our study shows that, through simple variance-preserving initialization and without additional clamping mechanisms, these activations can successfully be used to train deep models, such as GPT-2 for next-token prediction on OpenWebText and ConvNeXt for image classification on ImageNet. Our work addresses the issue of exploding and vanishing activations and gradients, particularly prevalent with polynomial activations, and opens the door for improving the efficiency of large-scale learning tasks. Furthermore, our approach provides insight into the structure of neural networks, revealing that networks with polynomial activations can be interpreted as multivariate polynomial mappings. Finally, using Hermite interpolation, we show that our activations can closely approximate classical ones in pre-trained models by matching both the function and its derivative, making them especially useful for fine-tuning tasks. These activations are available in the torchortho library, which can be accessed via: https://github.com/K-H-Ismail/torchortho.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of psi-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10^{-45} to 10^{45}. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer's ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. To the best of our knowledge, there has been no prior work on modeling recursive functions with such a high-variance and factorial growth. Beyond simply computing intersection numbers, we explore the enumerative "world-model" of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the the large-genus asymptotic of psi-class intersection numbers. These findings suggest that the network internalizes the parameters of the asymptotic closed-form and the polynomiality phenomenon of psi-class intersection numbers in a non-linear manner.

We introduce a highly performant 3D object detector for point clouds using the DETR framework. The prior attempts all end up with suboptimal results because they fail to learn accurate inductive biases from the limited scale of training data. In particular, the queries often attend to points that are far away from the target objects, violating the locality principle in object detection. To address the limitation, we introduce a novel 3D Vertex Relative Position Encoding (3DV-RPE) method which computes position encoding for each point based on its relative position to the 3D boxes predicted by the queries in each decoder layer, thus providing clear information to guide the model to focus on points near the objects, in accordance with the principle of locality. In addition, we systematically improve the pipeline from various aspects such as data normalization based on our understanding of the task. We show exceptional results on the challenging ScanNetV2 benchmark, achieving significant improvements over the previous 3DETR in AP_{25}/AP_{50} from 65.0\%/47.0\% to 77.8\%/66.0\%, respectively. In addition, our method sets a new record on ScanNetV2 and SUN RGB-D datasets.Code will be released at http://github.com/yichaoshen-MS/V-DETR.

Recent inversion methods have shown that real images can be inverted into StyleGAN's latent space and numerous edits can be achieved on those images thanks to the semantically rich feature representations of well-trained GAN models. However, extensive research has also shown that image inversion is challenging due to the trade-off between high-fidelity reconstruction and editability. In this paper, we tackle an even more difficult task, inverting erased images into GAN's latent space for realistic inpaintings and editings. Furthermore, by augmenting inverted latent codes with different latent samples, we achieve diverse inpaintings. Specifically, we propose to learn an encoder and mixing network to combine encoded features from erased images with StyleGAN's mapped features from random samples. To encourage the mixing network to utilize both inputs, we train the networks with generated data via a novel set-up. We also utilize higher-rate features to prevent color inconsistencies between the inpainted and unerased parts. We run extensive experiments and compare our method with state-of-the-art inversion and inpainting methods. Qualitative metrics and visual comparisons show significant improvements.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all key problems in the 3D reconstruction of static scenes can be reduced to predicting such point maps. In this paper, we develop an analogous concept for a very different problem: the reconstruction of the 3D shape and pose of deformable objects. To this end, we introduce Dual Point Maps (DualPM), where a pair of point maps is extracted from the same image-one associating pixels to their 3D locations on the object and the other to a canonical version of the object in its rest pose. We also extend point maps to amodal reconstruction to recover the complete shape of the object, even through self-occlusions. We show that 3D reconstruction and 3D pose estimation can be reduced to the prediction of DualPMs. Empirically, we demonstrate that this representation is a suitable target for deep networks to predict. Specifically, we focus on modeling quadrupeds, showing that DualPMs can be trained purely on synthetic 3D data, consisting of one or two models per category, while generalizing effectively to real images. With this approach, we achieve significant improvements over previous methods for the 3D analysis and reconstruction of such objects.

Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work shows that existing machine unlearning techniques do not hold up to thorough evaluation in non-convex settings. In this work, we introduce a new machine unlearning technique that exhibits strong empirical performance even in such challenging settings. Our starting point is the perspective that the goal of unlearning is to produce a model whose outputs are statistically indistinguishable from those of a model re-trained on all but the forget set. This perspective naturally suggests a reduction from the unlearning problem to that of data attribution, where the goal is to predict the effect of changing the training set on a model's outputs. Thus motivated, we propose the following meta-algorithm, which we call Datamodel Matching (DMM): given a trained model, we (a) use data attribution to predict the output of the model if it were re-trained on all but the forget set points; then (b) fine-tune the pre-trained model to match these predicted outputs. In a simple convex setting, we show how this approach provably outperforms a variety of iterative unlearning algorithms. Empirically, we use a combination of existing evaluations and a new metric based on the KL-divergence to show that even in non-convex settings, DMM achieves strong unlearning performance relative to existing algorithms. An added benefit of DMM is that it is a meta-algorithm, in the sense that future advances in data attribution translate directly into better unlearning algorithms, pointing to a clear direction for future progress in unlearning.

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the `conjugate priors' of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions, and (3) a logical description of conjugate priors that highlights the required closure of the priors under updating. The theory is illustrated with several standard examples, also covering multiple updating.

GAN inversion aims to invert a given image back into the latent space of a pretrained GAN model, for the image to be faithfully reconstructed from the inverted code by the generator. As an emerging technique to bridge the real and fake image domains, GAN inversion plays an essential role in enabling the pretrained GAN models such as StyleGAN and BigGAN to be used for real image editing applications. Meanwhile, GAN inversion also provides insights on the interpretation of GAN's latent space and how the realistic images can be generated. In this paper, we provide an overview of GAN inversion with a focus on its recent algorithms and applications. We cover important techniques of GAN inversion and their applications to image restoration and image manipulation. We further elaborate on some trends and challenges for future directions.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

StyleGAN's disentangled style representation enables powerful image editing by manipulating the latent variables, but accurately mapping real-world images to their latent variables (GAN inversion) remains a challenge. Existing GAN inversion methods struggle to maintain editing directions and produce realistic results. To address these limitations, we propose Make It So, a novel GAN inversion method that operates in the Z (noise) space rather than the typical W (latent style) space. Make It So preserves editing capabilities, even for out-of-domain images. This is a crucial property that was overlooked in prior methods. Our quantitative evaluations demonstrate that Make It So outperforms the state-of-the-art method PTI~roich2021pivotal by a factor of five in inversion accuracy and achieves ten times better edit quality for complex indoor scenes.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

Canonical surface mapping generalizes keypoint detection by assigning each pixel of an object to a corresponding point in a 3D template. Popularised by DensePose for the analysis of humans, authors have since attempted to apply the concept to more categories, but with limited success due to the high cost of manual supervision. In this work, we introduce SHIC, a method to learn canonical maps without manual supervision which achieves better results than supervised methods for most categories. Our idea is to leverage foundation computer vision models such as DINO and Stable Diffusion that are open-ended and thus possess excellent priors over natural categories. SHIC reduces the problem of estimating image-to-template correspondences to predicting image-to-image correspondences using features from the foundation models. The reduction works by matching images of the object to non-photorealistic renders of the template, which emulates the process of collecting manual annotations for this task. These correspondences are then used to supervise high-quality canonical maps for any object of interest. We also show that image generators can further improve the realism of the template views, which provide an additional source of supervision for the model.

Sequence modeling approaches have shown promising results in robot imitation learning. Recently, diffusion models have been adopted for behavioral cloning in a sequence modeling fashion, benefiting from their exceptional capabilities in modeling complex data distributions. The standard diffusion-based policy iteratively generates action sequences from random noise conditioned on the input states. Nonetheless, the model for diffusion policy can be further improved in terms of visual representations. In this work, we propose Crossway Diffusion, a simple yet effective method to enhance diffusion-based visuomotor policy learning via a carefully designed state decoder and an auxiliary self-supervised learning (SSL) objective. The state decoder reconstructs raw image pixels and other state information from the intermediate representations of the reverse diffusion process. The whole model is jointly optimized by the SSL objective and the original diffusion loss. Our experiments demonstrate the effectiveness of Crossway Diffusion in various simulated and real-world robot tasks, confirming its consistent advantages over the standard diffusion-based policy and substantial improvements over the baselines.

We consider a scenario where we have access to the target domain, but cannot afford on-the-fly training data annotation, and instead would like to construct an alternative training set from a large-scale data pool such that a competitive model can be obtained. We propose a search and pruning (SnP) solution to this training data search problem, tailored to object re-identification (re-ID), an application aiming to match the same object captured by different cameras. Specifically, the search stage identifies and merges clusters of source identities which exhibit similar distributions with the target domain. The second stage, subject to a budget, then selects identities and their images from the Stage I output, to control the size of the resulting training set for efficient training. The two steps provide us with training sets 80\% smaller than the source pool while achieving a similar or even higher re-ID accuracy. These training sets are also shown to be superior to a few existing search methods such as random sampling and greedy sampling under the same budget on training data size. If we release the budget, training sets resulting from the first stage alone allow even higher re-ID accuracy. We provide interesting discussions on the specificity of our method to the re-ID problem and particularly its role in bridging the re-ID domain gap. The code is available at https://github.com/yorkeyao/SnP.

We introduce the first metric for evaluating disentanglement at individual hierarchy levels of a structured latent representation. Applied to object-centric generative models, this offers a systematic, unified approach to evaluating (i) object separation between latent slots (ii) disentanglement of object properties inside individual slots (iii) disentanglement of intrinsic and extrinsic object properties. We theoretically show that for structured representations, our framework gives stronger guarantees of selecting a good model than previous disentanglement metrics. Experimentally, we demonstrate that viewing object compositionality as a disentanglement problem addresses several issues with prior visual metrics of object separation. As a core technical component, we present the first representation probing algorithm handling slot permutation invariance.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet expressive inputs, e.g., multi-digit images and image fragments, through a neural sorting network. To learn a mapping from a high-dimensional input to an ordinal variable, the differentiability of sorting networks needs to be guaranteed. In this paper we define a softening error by a differentiable swap function, and develop an error-free swap function that holds a non-decreasing condition and differentiability. Furthermore, a permutation-equivariant Transformer network with multi-head attention is adopted to capture dependency between given inputs and also leverage its model capacity with self-attention. Experiments on diverse sorting benchmarks show that our methods perform better than or comparable to baseline methods.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the mini-batch level but are partially wrong in the comparison with the optimal transportation plan between the original measures. Motivated by the misspecified mappings issue, we propose a novel mini-batch method by using partial optimal transport (POT) between mini-batch empirical measures, which we refer to as mini-batch partial optimal transport (m-POT). Leveraging the insight from the partial transportation, we explain the source of misspecified mappings from the m-OT and motivate why limiting the amount of transported masses among mini-batches via POT can alleviate the incorrect mappings. Finally, we carry out extensive experiments on various applications such as deep domain adaptation, partial domain adaptation, deep generative model, color transfer, and gradient flow to demonstrate the favorable performance of m-POT compared to current mini-batch methods.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

In optimal transport (OT), a Monge map is known as a mapping that transports a source distribution to a target distribution in the most cost-efficient way. Recently, multiple neural estimators for Monge maps have been developed and applied in diverse unpaired domain translation tasks, e.g. in single-cell biology and computer vision. However, the classic OT framework enforces mass conservation, which makes it prone to outliers and limits its applicability in real-world scenarios. The latter can be particularly harmful in OT domain translation tasks, where the relative position of a sample within a distribution is explicitly taken into account. While unbalanced OT tackles this challenge in the discrete setting, its integration into neural Monge map estimators has received limited attention. We propose a theoretically grounded method to incorporate unbalancedness into any Monge map estimator. We improve existing estimators to model cell trajectories over time and to predict cellular responses to perturbations. Moreover, our approach seamlessly integrates with the OT flow matching (OT-FM) framework. While we show that OT-FM performs competitively in image translation, we further improve performance by incorporating unbalancedness (UOT-FM), which better preserves relevant features. We hence establish UOT-FM as a principled method for unpaired image translation.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

We, team AImsterdam, summarize our submission to the fastMRI challenge (Zbontar et al., 2018). Our approach builds on recent advances in invertible learning to infer models as presented in Putzky and Welling (2019). Both, our single-coil and our multi-coil model share the same basic architecture.

We introduce a method to generate 3D scenes that are disentangled into their component objects. This disentanglement is unsupervised, relying only on the knowledge of a large pretrained text-to-image model. Our key insight is that objects can be discovered by finding parts of a 3D scene that, when rearranged spatially, still produce valid configurations of the same scene. Concretely, our method jointly optimizes multiple NeRFs from scratch - each representing its own object - along with a set of layouts that composite these objects into scenes. We then encourage these composited scenes to be in-distribution according to the image generator. We show that despite its simplicity, our approach successfully generates 3D scenes decomposed into individual objects, enabling new capabilities in text-to-3D content creation. For results and an interactive demo, see our project page at https://dave.ml/layoutlearning/

Large language models trained on web-scale corpora can memorize undesirable data containing misinformation, copyrighted material, or private or sensitive information. Recently, several machine unlearning algorithms have been proposed to eliminate the effect of such datapoints from trained models -- that is, to approximate a model that had never been trained on these datapoints in the first place. However, evaluating the effectiveness of unlearning algorithms remains an open challenge. Previous work has relied on heuristics -- such as verifying that the model can no longer reproduce the specific information targeted for removal while maintaining accuracy on unrelated test data. These approaches inadequately capture the complete effect of reversing the influence of datapoints on a trained model. In this work, we propose the RESTOR framework for machine unlearning evaluation, which assesses the ability of unlearning algorithms for targeted data erasure, by evaluating the ability of models to forget the knowledge introduced in these datapoints, while simultaneously recovering the model's knowledge state had it never encountered these datapoints. RESTOR helps uncover several novel insights about popular unlearning algorithms, and the mechanisms through which they operate -- for instance, identifying that some algorithms merely emphasize forgetting but not recovering knowledge, and that localizing unlearning targets can enhance unlearning performance.

Discrete diffusion models have achieved success in tasks like image generation and masked language modeling but face limitations in controlled content editing. We introduce DICE (Discrete Inversion for Controllable Editing), the first approach to enable precise inversion for discrete diffusion models, including multinomial diffusion and masked generative models. By recording noise sequences and masking patterns during the reverse diffusion process, DICE enables accurate reconstruction and flexible editing of discrete data without the need for predefined masks or attention manipulation. We demonstrate the effectiveness of DICE across both image and text domains, evaluating it on models such as VQ-Diffusion, Paella, and RoBERTa. Our results show that DICE preserves high data fidelity while enhancing editing capabilities, offering new opportunities for fine-grained content manipulation in discrete spaces. For project webpage, see https://hexiaoxiao-cs.github.io/DICE/.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/.

Domain shifts such as sensor type changes and geographical situation variations are prevalent in Autonomous Driving (AD), which poses a challenge since AD model relying on the previous domain knowledge can be hardly directly deployed to a new domain without additional costs. In this paper, we provide a new perspective and approach of alleviating the domain shifts, by proposing a Reconstruction-Simulation-Perception (ReSimAD) scheme. Specifically, the implicit reconstruction process is based on the knowledge from the previous old domain, aiming to convert the domain-related knowledge into domain-invariant representations, e.g., 3D scene-level meshes. Besides, the point clouds simulation process of multiple new domains is conditioned on the above reconstructed 3D meshes, where the target-domain-like simulation samples can be obtained, thus reducing the cost of collecting and annotating new-domain data for the subsequent perception process. For experiments, we consider different cross-domain situations such as Waymo-to-KITTI, Waymo-to-nuScenes, Waymo-to-ONCE, etc, to verify the zero-shot target-domain perception using ReSimAD. Results demonstrate that our method is beneficial to boost the domain generalization ability, even promising for 3D pre-training.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

We present a principled approach to uncover the structure of visual data by solving a novel deep learning task coined visual permutation learning. The goal of this task is to find the permutation that recovers the structure of data from shuffled versions of it. In the case of natural images, this task boils down to recovering the original image from patches shuffled by an unknown permutation matrix. Unfortunately, permutation matrices are discrete, thereby posing difficulties for gradient-based methods. To this end, we resort to a continuous approximation of these matrices using doubly-stochastic matrices which we generate from standard CNN predictions using Sinkhorn iterations. Unrolling these iterations in a Sinkhorn network layer, we propose DeepPermNet, an end-to-end CNN model for this task. The utility of DeepPermNet is demonstrated on two challenging computer vision problems, namely, (i) relative attributes learning and (ii) self-supervised representation learning. Our results show state-of-the-art performance on the Public Figures and OSR benchmarks for (i) and on the classification and segmentation tasks on the PASCAL VOC dataset for (ii).

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

Capturing real world lighting is a long standing challenge in imaging and most practical methods acquire High Dynamic Range (HDR) images by either fusing multiple exposures, or boosting the dynamic range of Standard Dynamic Range (SDR) images. Multiple exposure capture is problematic as it requires longer capture times which can often lead to ghosting problems. The main alternative, inverse tone mapping is an ill-defined problem that is especially challenging as single captured exposures usually contain clipped and quantized values, and are therefore missing substantial amounts of content. To alleviate this, we propose a new approach, High Dynamic Range Thermal (HDRT), for HDR acquisition using a separate, commonly available, thermal infrared (IR) sensor. We propose a novel deep neural method (HDRTNet) which combines IR and SDR content to generate HDR images. HDRTNet learns to exploit IR features linked to the RGB image and the IR-specific parameters are subsequently used in a dual branch method that fuses features at shallow layers. This produces an HDR image that is significantly superior to that generated using naive fusion approaches. To validate our method, we have created the first HDR and thermal dataset, and performed extensive experiments comparing HDRTNet with the state-of-the-art. We show substantial quantitative and qualitative quality improvements on both over- and under-exposed images, showing that our approach is robust to capturing in multiple different lighting conditions.

Autonomous driving requires accurate scene understanding, including road geometry, traffic agents, and their semantic relationships. In online HD map generation scenarios, raster-based representations are well-suited to vision models but lack geometric precision, while graph-based representations retain structural detail but become unstable without precise maps. To harness the complementary strengths of both, we propose DiffSemanticFusion -- a fusion framework for multimodal trajectory prediction and planning. Our approach reasons over a semantic raster-fused BEV space, enhanced by a map diffusion module that improves both the stability and expressiveness of online HD map representations. We validate our framework on two downstream tasks: trajectory prediction and planning-oriented end-to-end autonomous driving. Experiments on real-world autonomous driving benchmarks, nuScenes and NAVSIM, demonstrate improved performance over several state-of-the-art methods. For the prediction task on nuScenes, we integrate DiffSemanticFusion with the online HD map informed QCNet, achieving a 5.1\% performance improvement. For end-to-end autonomous driving in NAVSIM, DiffSemanticFusion achieves state-of-the-art results, with a 15\% performance gain in NavHard scenarios. In addition, extensive ablation and sensitivity studies show that our map diffusion module can be seamlessly integrated into other vector-based approaches to enhance performance. All artifacts are available at https://github.com/SunZhigang7/DiffSemanticFusion.

Reverse engineering in the realm of Computer-Aided Design (CAD) has been a longstanding aspiration, though not yet entirely realized. Its primary aim is to uncover the CAD process behind a physical object given its 3D scan. We propose CAD-SIGNet, an end-to-end trainable and auto-regressive architecture to recover the design history of a CAD model represented as a sequence of sketch-and-extrusion from an input point cloud. Our model learns visual-language representations by layer-wise cross-attention between point cloud and CAD language embedding. In particular, a new Sketch instance Guided Attention (SGA) module is proposed in order to reconstruct the fine-grained details of the sketches. Thanks to its auto-regressive nature, CAD-SIGNet not only reconstructs a unique full design history of the corresponding CAD model given an input point cloud but also provides multiple plausible design choices. This allows for an interactive reverse engineering scenario by providing designers with multiple next-step choices along with the design process. Extensive experiments on publicly available CAD datasets showcase the effectiveness of our approach against existing baseline models in two settings, namely, full design history recovery and conditional auto-completion from point clouds.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.