Daily Papers

This paper studies the topic modeling problem of tagged documents and images. Higher-order relations among tagged documents and images are major and ubiquitous characteristics, and play positive roles in extracting reliable and interpretable topics. In this paper, we propose the tag-topic models (TTM) to depict such higher-order topic structural dependencies within the Markov random field (MRF) framework. First, we use the novel factor graph representation of latent Dirichlet allocation (LDA)-based topic models from the MRF perspective, and present an efficient loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Second, we propose the factor hypergraph representation of TTM, and focus on both pairwise and higher-order relation modeling among tagged documents and images. Efficient loopy BP algorithm is developed to learn TTM, which encourages the topic labeling smoothness among tagged documents and images. Extensive experimental results confirm the incorporation of higher-order relations to be effective in enhancing the overall topic modeling performance, when compared with current state-of-the-art topic models, in many text and image mining tasks of broad interests such as word and link prediction, document classification, and tag recommendation.

Modern text-to-image generation models produce high-quality images that are both photorealistic and faithful to the text prompts. However, this quality comes at significant computational cost: nearly all of these models are iterative and require running inference multiple times with large models. This iterative process is needed to ensure that different regions of the image are not only aligned with the text prompt, but also compatible with each other. In this work, we propose a light-weight approach to achieving this compatibility between different regions of an image, using a Markov Random Field (MRF) model. This method is shown to work in conjunction with the recently proposed Muse model. The MRF encodes the compatibility among image tokens at different spatial locations and enables us to significantly reduce the required number of Muse prediction steps. Inference with the MRF is significantly cheaper, and its parameters can be quickly learned through back-propagation by modeling MRF inference as a differentiable neural-network layer. Our full model, SPEGTI, uses this proposed MRF model to speed up Muse by 1.5X with no loss in output image quality.

This paper proposes a vision-based fire and smoke segmentation system which use spatial, temporal and motion information to extract the desired regions from the video frames. The fusion of information is done using multiple features such as optical flow, divergence and intensity values. These features extracted from the images are used to segment the pixels into different classes in an unsupervised way. A comparative analysis is done by using multiple clustering algorithms for segmentation. Here the Markov Random Field performs more accurately than other segmentation algorithms since it characterizes the spatial interactions of pixels using a finite number of parameters. It builds a probabilistic image model that selects the most likely labeling using the maximum a posteriori (MAP) estimation. This unsupervised approach is tested on various images and achieves a frame-wise fire detection rate of 95.39%. Hence this method can be used for early detection of fire in real-time and it can be incorporated into an indoor or outdoor surveillance system.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

In this paper we tackle the problem of generating conformers of a molecule in 3D space given its molecular graph. We parameterize these conformers as continuous functions that map elements from the molecular graph to points in 3D space. We then formulate the problem of learning to generate conformers as learning a distribution over these functions using a diffusion generative model, called Molecular Conformer Fields (MCF). Our approach is simple and scalable, and achieves state-of-the-art performance on challenging molecular conformer generation benchmarks while making no assumptions about the explicit structure of molecules (e.g. modeling torsional angles). MCF represents an advance in extending diffusion models to handle complex scientific problems in a conceptually simple, scalable and effective manner.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

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.

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. This tutorial describes conditional random fields, a popular probabilistic method for structured prediction. CRFs have seen wide application in natural language processing, computer vision, and bioinformatics. We describe methods for inference and parameter estimation for CRFs, including practical issues for implementing large scale CRFs. We do not assume previous knowledge of graphical modeling, so this tutorial is intended to be useful to practitioners in a wide variety of fields.

Analog magnetic tapes have been the main video data storage device for several decades. Videos stored on analog videotapes exhibit unique degradation patterns caused by tape aging and reader device malfunctioning that are different from those observed in film and digital video restoration tasks. In this work, we present a reference-based approach for the resToration of digitized Analog videotaPEs (TAPE). We leverage CLIP for zero-shot artifact detection to identify the cleanest frames of each video through textual prompts describing different artifacts. Then, we select the clean frames most similar to the input ones and employ them as references. We design a transformer-based Swin-UNet network that exploits both neighboring and reference frames via our Multi-Reference Spatial Feature Fusion (MRSFF) blocks. MRSFF blocks rely on cross-attention and attention pooling to take advantage of the most useful parts of each reference frame. To address the absence of ground truth in real-world videos, we create a synthetic dataset of videos exhibiting artifacts that closely resemble those commonly found in analog videotapes. Both quantitative and qualitative experiments show the effectiveness of our approach compared to other state-of-the-art methods. The code, the model, and the synthetic dataset are publicly available at https://github.com/miccunifi/TAPE.

Statistics of grain sizes and orientations in metals correlate to the material's mechanical properties. Reproducing representative volume elements for further analysis of deformation and failure in metals, like 316L stainless steel, is particularly important due to their wide use in manufacturing goods today. Two approaches, initially created for video games, were considered for the procedural generation of representative grain microstructures. The first is the Wave Function Collapse (WFC) algorithm, and the second is constraint propagation and probabilistic inference through Markov Junior, a free and open-source software. This study aimed to investigate these two algorithms' effectiveness in using reference electron backscatter diffraction (EBSD) maps and recreating a statistically similar one that could be used in further research. It utilized two stainless steel EBSD maps as references to test both algorithms. First, the WFC algorithm was too constricting and, thus, incapable of producing images that resembled EBSDs. The second, MarkovJunior, was much more effective in creating a Voronoi tessellation that could be used to create an EBSD map in Python. When comparing the results between the reference and the generated EBSD, we discovered that the orientation and volume fractions were extremely similar. With the study, it was concluded that MarkovJunior is an effective machine learning tool that can reproduce representative grain microstructures.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

Energy-Based Models (EBMs) have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into state-of-the-art training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growing interest in using normalizing flows in order to learn the transformation of a simple prior distribution to the given target distribution. Here we propose a generalized and combined approach to sample target densities: Stochastic Normalizing Flows (SNF) -- an arbitrary sequence of deterministic invertible functions and stochastic sampling blocks. We show that stochasticity overcomes expressivity limitations of normalizing flows resulting from the invertibility constraint, whereas trainable transformations between sampling steps improve efficiency of pure MCMC/LD along the flow. By invoking ideas from non-equilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end, and by which we can compute exact importance weights without having to marginalize out the randomness of the stochastic blocks. We illustrate the representational power, sampling efficiency and asymptotic correctness of SNFs on several benchmarks including applications to sampling molecular systems in equilibrium.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

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.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Recent advancements in multi-modal large language models have propelled the development of joint probabilistic models capable of both image understanding and generation. However, we have identified that recent methods inevitably suffer from loss of image information during understanding task, due to either image discretization or diffusion denoising steps. To address this issue, we propose a novel Multi-Modal Auto-Regressive (MMAR) probabilistic modeling framework. Unlike discretization line of method, MMAR takes in continuous-valued image tokens to avoid information loss. Differing from diffusion-based approaches, we disentangle the diffusion process from auto-regressive backbone model by employing a light-weight diffusion head on top each auto-regressed image patch embedding. In this way, when the model transits from image generation to understanding through text generation, the backbone model's hidden representation of the image is not limited to the last denoising step. To successfully train our method, we also propose a theoretically proven technique that addresses the numerical stability issue and a training strategy that balances the generation and understanding task goals. Through extensive evaluations on 18 image understanding benchmarks, MMAR demonstrates much more superior performance than other joint multi-modal models, matching the method that employs pretrained CLIP vision encoder, meanwhile being able to generate high quality images at the same time. We also showed that our method is scalable with larger data and model size.

This paper presents an innovative approach to enhancing few-shot learning by integrating data augmentation with model fine-tuning in a framework designed to tackle the challenges posed by small-sample data. Recognizing the critical limitations of traditional machine learning models that require large datasets-especially in fields such as drug discovery, target recognition, and malicious traffic detection-this study proposes a novel strategy that leverages Generative Adversarial Networks (GANs) and advanced optimization techniques to improve model performance with limited data. Specifically, the paper addresses the noise and bias issues introduced by data augmentation methods, contrasting them with model-based approaches, such as fine-tuning and metric learning, which rely heavily on related datasets. By combining Markov Chain Monte Carlo (MCMC) sampling and discriminative model ensemble strategies within a GAN framework, the proposed model adjusts generative and discriminative distributions to simulate a broader range of relevant data. Furthermore, it employs MHLoss and a reparameterized GAN ensemble to enhance stability and accelerate convergence, ultimately leading to improved classification performance on small-sample images and structured datasets. Results confirm that the MhERGAN algorithm developed in this research is highly effective for few-shot learning, offering a practical solution that bridges data scarcity with high-performing model adaptability and generalization.

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is particularly effective in handling high-dimensional inner products and matrix multiplication, in applications of image analysis and large-scale supervised learning.

Most Neural Radiance Fields (NeRFs) exhibit limited generalization capabilities, which restrict their applicability in representing multiple scenes using a single model. To address this problem, existing generalizable NeRF methods simply condition the model on image features. These methods still struggle to learn precise global representations over diverse scenes since they lack an effective mechanism for interacting among different points and views. In this work, we unveil that 3D implicit representation learning can be significantly improved by mask-based modeling. Specifically, we propose masked ray and view modeling for generalizable NeRF (MRVM-NeRF), which is a self-supervised pretraining target to predict complete scene representations from partially masked features along each ray. With this pretraining target, MRVM-NeRF enables better use of correlations across different points and views as the geometry priors, which thereby strengthens the capability of capturing intricate details within the scenes and boosts the generalization capability across different scenes. Extensive experiments demonstrate the effectiveness of our proposed MRVM-NeRF on both synthetic and real-world datasets, qualitatively and quantitatively. Besides, we also conduct experiments to show the compatibility of our proposed method with various backbones and its superiority under few-shot cases.

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which can lead to poor-quality renderings, and reliance on a good initialization. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene-in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) updates by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the 'cloning' of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce a regularizer that promotes the removal of unused Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

Robust Markov Decision Processes (MDPs) and risk-sensitive MDPs are both powerful tools for making decisions in the presence of uncertainties. Previous efforts have aimed to establish their connections, revealing equivalences in specific formulations. This paper introduces a new formulation for risk-sensitive MDPs, which assesses risk in a slightly different manner compared to the classical Markov risk measure (Ruszczy\'nski 2010), and establishes its equivalence with a class of regularized robust MDP (RMDP) problems, including the standard RMDP as a special case. Leveraging this equivalence, we further derive the policy gradient theorem for both problems, proving gradient domination and global convergence of the exact policy gradient method under the tabular setting with direct parameterization. This forms a sharp contrast to the Markov risk measure, known to be potentially non-gradient-dominant (Huang et al. 2021). We also propose a sample-based offline learning algorithm, namely the robust fitted-Z iteration (RFZI), for a specific regularized RMDP problem with a KL-divergence regularization term (or equivalently the risk-sensitive MDP with an entropy risk measure). We showcase its streamlined design and less stringent assumptions due to the equivalence and analyze its sample complexity.

It is widely agreed that reference-based super-resolution (RefSR) achieves superior results by referring to similar high quality images, compared to single image super-resolution (SISR). Intuitively, the more references, the better performance. However, previous RefSR methods have all focused on single-reference image training, while multiple reference images are often available in testing or practical applications. The root cause of such training-testing mismatch is the absence of publicly available multi-reference SR training datasets, which greatly hinders research efforts on multi-reference super-resolution. To this end, we construct a large-scale, multi-reference super-resolution dataset, named LMR. It contains 112,142 groups of 300x300 training images, which is 10x of the existing largest RefSR dataset. The image size is also much larger. More importantly, each group is equipped with 5 reference images with different similarity levels. Furthermore, we propose a new baseline method for multi-reference super-resolution: MRefSR, including a Multi-Reference Attention Module (MAM) for feature fusion of an arbitrary number of reference images, and a Spatial Aware Filtering Module (SAFM) for the fused feature selection. The proposed MRefSR achieves significant improvements over state-of-the-art approaches on both quantitative and qualitative evaluations. Our code and data would be made available soon.

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods typically attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

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.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The proposed RAR is simple: during a standard autoregressive training process with a next-token prediction objective, the input sequence-typically ordered in raster form-is randomly permuted into different factorization orders with a probability r, where r starts at 1 and linearly decays to 0 over the course of training. This annealing training strategy enables the model to learn to maximize the expected likelihood over all factorization orders and thus effectively improve the model's capability of modeling bidirectional contexts. Importantly, RAR preserves the integrity of the autoregressive modeling framework, ensuring full compatibility with language modeling while significantly improving performance in image generation. On the ImageNet-256 benchmark, RAR achieves an FID score of 1.48, not only surpassing prior state-of-the-art autoregressive image generators but also outperforming leading diffusion-based and masked transformer-based methods. Code and models will be made available at https://github.com/bytedance/1d-tokenizer

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte Carlo (MCMC) methods derived from discretizations of the overdamped Langevin diffusions, which are commonly known as Langevin Monte Carlo algorithms. Furthermore, we are also interested in two nonsmooth cases for which a large class of proximal MCMC methods have been developed: (i) a nonsmooth prior is considered with a Gaussian mixture likelihood; (ii) a Laplacian mixture distribution. Such nonsmooth and non-log-concave sampling tasks arise from a wide range of applications to Bayesian inference and imaging inverse problems such as image deconvolution. We perform numerical simulations to compare the performance of most commonly used Langevin Monte Carlo algorithms.

What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstruction error as an energy function. Unlike previous results, the theorems provided here are completely generic and do not depend on the parametrization of the auto-encoder: they show what the auto-encoder would tend to if given enough capacity and examples. These results are for a contractive training criterion we show to be similar to the denoising auto-encoder training criterion with small corruption noise, but with contraction applied on the whole reconstruction function rather than just encoder. Similarly to score matching, one can consider the proposed training criterion as a convenient alternative to maximum likelihood because it does not involve a partition function. Finally, we show how an approximate Metropolis-Hastings MCMC can be setup to recover samples from the estimated distribution, and this is confirmed in sampling experiments.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Modern neural recording techniques allow neuroscientists to obtain spiking activity of multiple neurons from different brain regions over long time periods, which requires new statistical methods to be developed for understanding structure of the large-scale data. In this paper, we develop a bi-clustering method to cluster the neural spiking activity spatially and temporally, according to their low-dimensional latent structures. The spatial (neuron) clusters are defined by the latent trajectories within each neural population, while the temporal (state) clusters are defined by (populationally) synchronous local linear dynamics shared with different periods. To flexibly extract the bi-clustering structure, we build the model non-parametrically, and develop an efficient Markov chain Monte Carlo (MCMC) algorithm to sample the posterior distributions of model parameters. Validating our proposed MCMC algorithm through simulations, we find the method can recover unknown parameters and true bi-clustering structures successfully. We then apply the proposed bi-clustering method to multi-regional neural recordings under different experiment settings, where we find that simultaneously considering latent trajectories and spatial-temporal clustering structures can provide us with a more accurate and interpretable result. Overall, the proposed method provides scientific insights for large-scale (counting) time series with elongated recording periods, and it can potentially have application beyond neuroscience.

In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose mean-field Langevin averaged gradient (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose mean-field Langevin anchored best response (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

In this paper, we explore the application of mean field theory, a technique from statistical physics, to deep metric learning and address the high training complexity commonly associated with conventional metric learning loss functions. By adapting mean field theory for deep metric learning, we develop an approach to design classification-based loss functions from pair-based ones, which can be considered complementary to the proxy-based approach. Applying the mean field theory to two pair-based loss functions, we derive two new loss functions, MeanFieldContrastive and MeanFieldClassWiseMultiSimilarity losses, with reduced training complexity. We extensively evaluate these derived loss functions on three image-retrieval datasets and demonstrate that our loss functions outperform baseline methods in two out of the three datasets.

In multi-agent reinforcement learning, the behaviors that agents learn in a single Markov Game (MG) are typically confined to the given agent number. Every single MG induced by varying the population may possess distinct optimal joint strategies and game-specific knowledge, which are modeled independently in modern multi-agent reinforcement learning algorithms. In this work, our focus is on creating agents that can generalize across population-varying MGs. Instead of learning a unimodal policy, each agent learns a policy set comprising effective strategies across a variety of games. To achieve this, we propose Meta Representations for Agents (MRA) that explicitly models the game-common and game-specific strategic knowledge. By representing the policy sets with multi-modal latent policies, the game-common strategic knowledge and diverse strategic modes are discovered through an iterative optimization procedure. We prove that by approximately maximizing the resulting constrained mutual information objective, the policies can reach Nash Equilibrium in every evaluation MG when the latent space is sufficiently large. When deploying MRA in practical settings with limited latent space sizes, fast adaptation can be achieved by leveraging the first-order gradient information. Extensive experiments demonstrate the effectiveness of MRA in improving training performance and generalization ability in challenging evaluation games.

Vision Transformer (ViT) models have recently emerged as powerful and versatile models for various visual tasks. Recently, a work called PMF has achieved promising results in few-shot image classification by utilizing pre-trained vision transformer models. However, PMF employs full fine-tuning for learning the downstream tasks, leading to significant overfitting and storage issues, especially in the remote sensing domain. In order to tackle these issues, we turn to the recently proposed parameter-efficient tuning methods, such as VPT, which updates only the newly added prompt parameters while keeping the pre-trained backbone frozen. Inspired by VPT, we propose the Meta Visual Prompt Tuning (MVP) method. Specifically, we integrate the VPT method into the meta-learning framework and tailor it to the remote sensing domain, resulting in an efficient framework for Few-Shot Remote Sensing Scene Classification (FS-RSSC). Furthermore, we introduce a novel data augmentation strategy based on patch embedding recombination to enhance the representation and diversity of scenes for classification purposes. Experiment results on the FS-RSSC benchmark demonstrate the superior performance of the proposed MVP over existing methods in various settings, such as various-way-various-shot, various-way-one-shot, and cross-domain adaptation.

Medical image arbitrary-scale super-resolution (MIASSR) has recently gained widespread attention, aiming to super sample medical volumes at arbitrary scales via a single model. However, existing MIASSR methods face two major limitations: (i) reliance on high-resolution (HR) volumes and (ii) limited generalization ability, which restricts their application in various scenarios. To overcome these limitations, we propose Cube-based Neural Radiance Field (CuNeRF), a zero-shot MIASSR framework that can yield medical images at arbitrary scales and viewpoints in a continuous domain. Unlike existing MIASSR methods that fit the mapping between low-resolution (LR) and HR volumes, CuNeRF focuses on building a coordinate-intensity continuous representation from LR volumes without the need for HR references. This is achieved by the proposed differentiable modules: including cube-based sampling, isotropic volume rendering, and cube-based hierarchical rendering. Through extensive experiments on magnetic resource imaging (MRI) and computed tomography (CT) modalities, we demonstrate that CuNeRF outperforms state-of-the-art MIASSR methods. CuNeRF yields better visual verisimilitude and reduces aliasing artifacts at various upsampling factors. Moreover, our CuNeRF does not need any LR-HR training pairs, which is more flexible and easier to be used than others. Our code will be publicly available soon.

Segmenting stroke lesions in Magnetic Resonance Imaging (MRI) is challenging due to diverse clinical imaging domains, with existing models struggling to generalise across different MRI acquisition parameters and sequences. In this work, we propose two novel physics-constrained approaches using synthetic quantitative MRI (qMRI) images to enhance the robustness and generalisability of segmentation models. We trained a qMRI estimation model to predict qMRI maps from MPRAGE images, which were used to simulate diverse MRI sequences for segmentation training. A second approach built upon prior work in synthetic data for stroke lesion segmentation, generating qMRI maps from a dataset of tissue labels. The proposed approaches improved over the baseline nnUNet on a variety of out-of-distribution datasets, with the second approach outperforming the prior synthetic data method.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs.

We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds. We provide the code at https://github.com/Daniil-Selikhanovych/ASBM.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen environments, we propose a meta-learning approach to building effective and generalizable MCMC proposals. We parametrize the proposal as a neural network to provide fast approximations to block Gibbs conditionals. The learned neural proposals generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required. We explore several applications including open-universe Gaussian mixture models, in which our learned proposals outperform a hand-tuned sampler, and a real-world named entity recognition task, in which our sampler yields higher final F1 scores than classical single-site Gibbs sampling.

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 study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that the numerical issue lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Neural Fields have emerged as a transformative approach for 3D scene representation in computer vision and robotics, enabling accurate inference of geometry, 3D semantics, and dynamics from posed 2D data. Leveraging differentiable rendering, Neural Fields encompass both continuous implicit and explicit neural representations enabling high-fidelity 3D reconstruction, integration of multi-modal sensor data, and generation of novel viewpoints. This survey explores their applications in robotics, emphasizing their potential to enhance perception, planning, and control. Their compactness, memory efficiency, and differentiability, along with seamless integration with foundation and generative models, make them ideal for real-time applications, improving robot adaptability and decision-making. This paper provides a thorough review of Neural Fields in robotics, categorizing applications across various domains and evaluating their strengths and limitations, based on over 200 papers. First, we present four key Neural Fields frameworks: Occupancy Networks, Signed Distance Fields, Neural Radiance Fields, and Gaussian Splatting. Second, we detail Neural Fields' applications in five major robotics domains: pose estimation, manipulation, navigation, physics, and autonomous driving, highlighting key works and discussing takeaways and open challenges. Finally, we outline the current limitations of Neural Fields in robotics and propose promising directions for future research. Project page: https://robonerf.github.io

Score-based Generative Models (SGMs) have achieved state-of-the-art synthesis results on diverse tasks. However, the current design space of the forward diffusion process is largely unexplored and often relies on physical intuition or simplifying assumptions. Leveraging results from the design of scalable Bayesian posterior samplers, we present a complete recipe for constructing forward processes in SGMs, all of which are guaranteed to converge to the target distribution of interest. We show that several existing SGMs can be cast as specific instantiations of this parameterization. Furthermore, building on this recipe, we construct a novel SGM: Phase Space Langevin Diffusion (PSLD), which performs score-based modeling in a space augmented with auxiliary variables akin to a physical phase space. We show that PSLD outperforms competing baselines in terms of sample quality and the speed-vs-quality tradeoff across different samplers on various standard image synthesis benchmarks. Moreover, we show that PSLD achieves sample quality comparable to state-of-the-art SGMs (FID: 2.10 on unconditional CIFAR-10 generation), providing an attractive alternative as an SGM backbone for further development. We will publish our code and model checkpoints for reproducibility at https://github.com/mandt-lab/PSLD.

Our understanding of the temporal dynamics of the Earth's surface has been advanced by deep vision models, which often require lots of labeled multi-temporal images for training. However, collecting, preprocessing, and annotating multi-temporal remote sensing images at scale is non-trivial since it is expensive and knowledge-intensive. In this paper, we present change data generators based on generative models, which are cheap and automatic, alleviating these data problems. Our main idea is to simulate a stochastic change process over time. We describe the stochastic change process as a probabilistic graphical model (GPCM), which factorizes the complex simulation problem into two more tractable sub-problems, i.e., change event simulation and semantic change synthesis. To solve these two problems, we present Changen2, a GPCM with a resolution-scalable diffusion transformer which can generate time series of images and their semantic and change labels from labeled or unlabeled single-temporal images. Changen2 is a generative change foundation model that can be trained at scale via self-supervision, and can produce change supervisory signals from unlabeled single-temporal images. Unlike existing foundation models, Changen2 synthesizes change data to train task-specific foundation models for change detection. The resulting model possesses inherent zero-shot change detection capabilities and excellent transferability. Experiments suggest Changen2 has superior spatiotemporal scalability, e.g., Changen2 model trained on 256^2 pixel single-temporal images can yield time series of any length and resolutions of 1,024^2 pixels. Changen2 pre-trained models exhibit superior zero-shot performance (narrowing the performance gap to 3% on LEVIR-CD and approximately 10% on both S2Looking and SECOND, compared to fully supervised counterparts) and transferability across multiple types of change tasks.

Multi-modality image fusion aims to combine different modalities to produce fused images that retain the complementary features of each modality, such as functional highlights and texture details. To leverage strong generative priors and address challenges such as unstable training and lack of interpretability for GAN-based generative methods, we propose a novel fusion algorithm based on the denoising diffusion probabilistic model (DDPM). The fusion task is formulated as a conditional generation problem under the DDPM sampling framework, which is further divided into an unconditional generation subproblem and a maximum likelihood subproblem. The latter is modeled in a hierarchical Bayesian manner with latent variables and inferred by the expectation-maximization (EM) algorithm. By integrating the inference solution into the diffusion sampling iteration, our method can generate high-quality fused images with natural image generative priors and cross-modality information from source images. Note that all we required is an unconditional pre-trained generative model, and no fine-tuning is needed. Our extensive experiments indicate that our approach yields promising fusion results in infrared-visible image fusion and medical image fusion. The code is available at https://github.com/Zhaozixiang1228/MMIF-DDFM.

The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the underlying phases of complex systems such as spin-glasses. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. We introduce a single replica method of spin-glass phase detection using the field's variation experienced by each spin in a system configuration. This method focuses on a single replica with quenched random couplings. Each spin inevitably observes a different field from the others. Our results show that the mean and variance of fields named "Spontaneous Configurational Field" experienced by spins are suitable indicators to explore different ferromagnetic, paramagnetic, and mixed phases. To classify different phases of the system with defined indicators we have developed an algorithm based on machine learning to analyze the desired samples.

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is significantly influenced by the choice of the proposal. Recently Hamiltonian Monte Carlo (HMC) sampling has shown success in many practical problems. In this paper, we propose an SMC augmented by HMC (HSMC) for inference and model learning of nonlinear SSM, which can exempt us from learning proposals and reduce the model complexity significantly. Based on the measure preserving property of HMC, the particles directly generated by transition function can approximate the posterior of latent states arbitrarily well. In order to better adapt to the local geometry of latent space, the HMC is conducted on Riemannian manifold defined by a positive definite metric. In addition, we show that the proposed HSMC method can improve SSMs realized by both Gaussian Processes (GP) and Neural Network (NN).

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all aspects of probability theory in which infinitely many random variables appear at a time. These infinite tensor products bigotimes_{i in J} X_i come in two versions: a weaker but more general one for families of objects (X_i)_{i in J} in semicartesian symmetric monoidal categories, and a stronger but more specific one for families of objects in Markov categories. As a first application, we state and prove versions of the zero-one laws of Kolmogorov and Hewitt-Savage for Markov categories. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts.

We resolve difficulties in training and sampling from a discrete generative model by learning a smoothed energy function, sampling from the smoothed data manifold with Langevin Markov chain Monte Carlo (MCMC), and projecting back to the true data manifold with one-step denoising. Our Discrete Walk-Jump Sampling formalism combines the contrastive divergence training of an energy-based model and improved sample quality of a score-based model, while simplifying training and sampling by requiring only a single noise level. We evaluate the robustness of our approach on generative modeling of antibody proteins and introduce the distributional conformity score to benchmark protein generative models. By optimizing and sampling from our models for the proposed distributional conformity score, 97-100% of generated samples are successfully expressed and purified and 70% of functional designs show equal or improved binding affinity compared to known functional antibodies on the first attempt in a single round of laboratory experiments. We also report the first demonstration of long-run fast-mixing MCMC chains where diverse antibody protein classes are visited in a single MCMC chain.

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inference-time compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. We provide the code along with a blog post on the project page: https://remdm.github.io.

Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.

Neural Radiance Fields (NeRFs) have shown promise in applications like view synthesis and depth estimation, but learning from multiview images faces inherent uncertainties. Current methods to quantify them are either heuristic or computationally demanding. We introduce BayesRays, a post-hoc framework to evaluate uncertainty in any pre-trained NeRF without modifying the training process. Our method establishes a volumetric uncertainty field using spatial perturbations and a Bayesian Laplace approximation. We derive our algorithm statistically and show its superior performance in key metrics and applications. Additional results available at: https://bayesrays.github.io.

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of O(d^{3/2}H^{3/2}T), where d is the dimension of the feature mapping, H is the planning horizon, and T is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

Despite recent advancements in language and vision modeling, integrating rich multimodal knowledge into recommender systems continues to pose significant challenges. This is primarily due to the need for efficient recommendation, which requires adaptive and interactive responses. In this study, we focus on sequential recommendation and introduce a lightweight framework called full-scale Matryoshka representation learning for multimodal recommendation (fMRLRec). Our fMRLRec captures item features at different granularities, learning informative representations for efficient recommendation across multiple dimensions. To integrate item features from diverse modalities, fMRLRec employs a simple mapping to project multimodal item features into an aligned feature space. Additionally, we design an efficient linear transformation that embeds smaller features into larger ones, substantially reducing memory requirements for large-scale training on recommendation data. Combined with improved state space modeling techniques, fMRLRec scales to different dimensions and only requires one-time training to produce multiple models tailored to various granularities. We demonstrate the effectiveness and efficiency of fMRLRec on multiple benchmark datasets, which consistently achieves superior performance over state-of-the-art baseline methods. We make our code and data publicly available at https://github.com/yueqirex/fMRLRec.

The Distributionally Robust Markov Decision Process (DRMDP) is a popular framework for addressing dynamics shift in reinforcement learning by learning policies robust to the worst-case transition dynamics within a constrained set. However, solving its dual optimization oracle poses significant challenges, limiting theoretical analysis and computational efficiency. The recently proposed Robust Regularized Markov Decision Process (RRMDP) replaces the uncertainty set constraint with a regularization term on the value function, offering improved scalability and theoretical insights. Yet, existing RRMDP methods rely on unstructured regularization, often leading to overly conservative policies by considering transitions that are unrealistic. To address these issues, we propose a novel framework, the d-rectangular linear robust regularized Markov decision process (d-RRMDP), which introduces a linear latent structure into both transition kernels and regularization. For the offline RL setting, where an agent learns robust policies from a pre-collected dataset in the nominal environment, we develop a family of algorithms, Robust Regularized Pessimistic Value Iteration (R2PVI), employing linear function approximation and f-divergence based regularization terms on transition kernels. We provide instance-dependent upper bounds on the suboptimality gap of R2PVI policies, showing these bounds depend on how well the dataset covers state-action spaces visited by the optimal robust policy under robustly admissible transitions. This term is further shown to be fundamental to d-RRMDPs via information-theoretic lower bounds. Finally, numerical experiments validate that R2PVI learns robust policies and is computationally more efficient than methods for constrained DRMDPs.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as O(n^3) to O(n^7), with n proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting tahe potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

We present Multi-Baseline Radiance Fields (MuRF), a general feed-forward approach to solving sparse view synthesis under multiple different baseline settings (small and large baselines, and different number of input views). To render a target novel view, we discretize the 3D space into planes parallel to the target image plane, and accordingly construct a target view frustum volume. Such a target volume representation is spatially aligned with the target view, which effectively aggregates relevant information from the input views for high-quality rendering. It also facilitates subsequent radiance field regression with a convolutional network thanks to its axis-aligned nature. The 3D context modeled by the convolutional network enables our method to synthesis sharper scene structures than prior works. Our MuRF achieves state-of-the-art performance across multiple different baseline settings and diverse scenarios ranging from simple objects (DTU) to complex indoor and outdoor scenes (RealEstate10K and LLFF). We also show promising zero-shot generalization abilities on the Mip-NeRF 360 dataset, demonstrating the general applicability of MuRF.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Diffusion-based image super-resolution (SR) methods are mainly limited by the low inference speed due to the requirements of hundreds or even thousands of sampling steps. Existing acceleration sampling techniques inevitably sacrifice performance to some extent, leading to over-blurry SR results. To address this issue, we propose a novel and efficient diffusion model for SR that significantly reduces the number of diffusion steps, thereby eliminating the need for post-acceleration during inference and its associated performance deterioration. Our method constructs a Markov chain that transfers between the high-resolution image and the low-resolution image by shifting the residual between them, substantially improving the transition efficiency. Additionally, an elaborate noise schedule is developed to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experiments demonstrate that the proposed method obtains superior or at least comparable performance to current state-of-the-art methods on both synthetic and real-world datasets, even only with 15 sampling steps. Our code and model are available at https://github.com/zsyOAOA/ResShift.

Bayesian neural networks (BNNs) have been an important framework in the study of uncertainty quantification. Deterministic variational inference, one of the inference methods, utilizes moment propagation to compute the predictive distributions and objective functions. Unfortunately, deriving the moments requires computationally expensive Taylor expansion in nonlinear functions, such as a rectified linear unit (ReLU) or a sigmoid function. Therefore, a new nonlinear function that realizes faster moment propagation than conventional functions is required. In this paper, we propose a novel nonlinear function named moment propagating-Gaussian error linear unit (MP-GELU) that enables the fast derivation of first and second moments in BNNs. MP-GELU enables the analytical computation of moments by applying nonlinearity to the input statistics, thereby reducing the computationally expensive calculations required for nonlinear functions. In empirical experiments on regression tasks, we observed that the proposed MP-GELU provides higher prediction accuracy and better quality of uncertainty with faster execution than those of ReLU-based BNNs.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

We introduce a novel state-space architecture for diffusion models, effectively harnessing spatial and frequency information to enhance the inductive bias towards local features in input images for image generation tasks. While state-space networks, including Mamba, a revolutionary advancement in recurrent neural networks, typically scan input sequences from left to right, they face difficulties in designing effective scanning strategies, especially in the processing of image data. Our method demonstrates that integrating wavelet transformation into Mamba enhances the local structure awareness of visual inputs and better captures long-range relations of frequencies by disentangling them into wavelet subbands, representing both low- and high-frequency components. These wavelet-based outputs are then processed and seamlessly fused with the original Mamba outputs through a cross-attention fusion layer, combining both spatial and frequency information to optimize the order awareness of state-space models which is essential for the details and overall quality of image generation. Besides, we introduce a globally-shared transformer to supercharge the performance of Mamba, harnessing its exceptional power to capture global relationships. Through extensive experiments on standard benchmarks, our method demonstrates superior results compared to DiT and DIFFUSSM, achieving faster training convergence and delivering high-quality outputs. The codes and pretrained models are released at https://github.com/VinAIResearch/DiMSUM.git.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Diffusion models achieve superior generation quality but suffer from slow generation speed due to the iterative nature of denoising. In contrast, consistency models, a new generative family, achieve competitive performance with significantly faster sampling. These models are trained either through consistency distillation, which leverages pretrained diffusion models, or consistency training/tuning directly from raw data. In this work, we propose a novel framework for understanding consistency models by modeling the denoising process of the diffusion model as a Markov Decision Process (MDP) and framing consistency model training as the value estimation through Temporal Difference~(TD) Learning. More importantly, this framework allows us to analyze the limitations of current consistency training/tuning strategies. Built upon Easy Consistency Tuning (ECT), we propose Stable Consistency Tuning (SCT), which incorporates variance-reduced learning using the score identity. SCT leads to significant performance improvements on benchmarks such as CIFAR-10 and ImageNet-64. On ImageNet-64, SCT achieves 1-step FID 2.42 and 2-step FID 1.55, a new SoTA for consistency models.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

Neural Radiance Field (NeRF) is a representation for 3D reconstruction from multi-view images. Despite some recent work showing preliminary success in editing a reconstructed NeRF with diffusion prior, they remain struggling to synthesize reasonable geometry in completely uncovered regions. One major reason is the high diversity of synthetic contents from the diffusion model, which hinders the radiance field from converging to a crisp and deterministic geometry. Moreover, applying latent diffusion models on real data often yields a textural shift incoherent to the image condition due to auto-encoding errors. These two problems are further reinforced with the use of pixel-distance losses. To address these issues, we propose tempering the diffusion model's stochasticity with per-scene customization and mitigating the textural shift with masked adversarial training. During the analyses, we also found the commonly used pixel and perceptual losses are harmful in the NeRF inpainting task. Through rigorous experiments, our framework yields state-of-the-art NeRF inpainting results on various real-world scenes. Project page: https://hubert0527.github.io/MALD-NeRF

Prior studies on Remote Sensing Foundation Model (RSFM) reveal immense potential towards a generic model for Earth Observation. Nevertheless, these works primarily focus on a single modality without temporal and geo-context modeling, hampering their capabilities for diverse tasks. In this study, we present SkySense, a generic billion-scale model, pre-trained on a curated multi-modal Remote Sensing Imagery (RSI) dataset with 21.5 million temporal sequences. SkySense incorporates a factorized multi-modal spatiotemporal encoder taking temporal sequences of optical and Synthetic Aperture Radar (SAR) data as input. This encoder is pre-trained by our proposed Multi-Granularity Contrastive Learning to learn representations across different modal and spatial granularities. To further enhance the RSI representations by the geo-context clue, we introduce Geo-Context Prototype Learning to learn region-aware prototypes upon RSI's multi-modal spatiotemporal features. To our best knowledge, SkySense is the largest Multi-Modal RSFM to date, whose modules can be flexibly combined or used individually to accommodate various tasks. It demonstrates remarkable generalization capabilities on a thorough evaluation encompassing 16 datasets over 7 tasks, from single- to multi-modal, static to temporal, and classification to localization. SkySense surpasses 18 recent RSFMs in all test scenarios. Specifically, it outperforms the latest models such as GFM, SatLas and Scale-MAE by a large margin, i.e., 2.76%, 3.67% and 3.61% on average respectively. We will release the pre-trained weights to facilitate future research and Earth Observation applications.

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

Multitarget Tracking (MTT) is the problem of tracking the states of an unknown number of objects using noisy measurements, with important applications to autonomous driving, surveillance, robotics, and others. In the model-based Bayesian setting, there are conjugate priors that enable us to express the multi-object posterior in closed form, which could theoretically provide Bayes-optimal estimates. However, the posterior involves a super-exponential growth of the number of hypotheses over time, forcing state-of-the-art methods to resort to approximations for remaining tractable, which can impact their performance in complex scenarios. Model-free methods based on deep-learning provide an attractive alternative, as they can, in principle, learn the optimal filter from data, but to the best of our knowledge were never compared to current state-of-the-art Bayesian filters, specially not in contexts where accurate models are available. In this paper, we propose a high-performing deep-learning method for MTT based on the Transformer architecture and compare it to two state-of-the-art Bayesian filters, in a setting where we assume the correct model is provided. Although this gives an edge to the model-based filters, it also allows us to generate unlimited training data. We show that the proposed model outperforms state-of-the-art Bayesian filters in complex scenarios, while matching their performance in simpler cases, which validates the applicability of deep-learning also in the model-based regime. The code for all our implementations is made available at https://github.com/JulianoLagana/MT3 .

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

Retrosynthesis planning is a fundamental challenge in chemistry which aims at designing reaction pathways from commercially available starting materials to a target molecule. Each step in multi-step retrosynthesis planning requires accurate prediction of possible precursor molecules given the target molecule and confidence estimates to guide heuristic search algorithms. We model single-step retrosynthesis planning as a distribution learning problem in a discrete state space. First, we introduce the Markov Bridge Model, a generative framework aimed to approximate the dependency between two intractable discrete distributions accessible via a finite sample of coupled data points. Our framework is based on the concept of a Markov bridge, a Markov process pinned at its endpoints. Unlike diffusion-based methods, our Markov Bridge Model does not need a tractable noise distribution as a sampling proxy and directly operates on the input product molecules as samples from the intractable prior distribution. We then address the retrosynthesis planning problem with our novel framework and introduce RetroBridge, a template-free retrosynthesis modeling approach that achieves state-of-the-art results on standard evaluation benchmarks.

Recent approaches to arbitrary-scale single image super-resolution (ASR) use neural fields to represent continuous signals that can be sampled at arbitrary resolutions. However, point-wise queries of neural fields do not naturally match the point spread function (PSF) of pixels, which may cause aliasing in the super-resolved image. Existing methods attempt to mitigate this by approximating an integral version of the field at each scaling factor, compromising both fidelity and generalization. In this work, we introduce neural heat fields, a novel neural field formulation that inherently models a physically exact PSF. Our formulation enables analytically correct anti-aliasing at any desired output resolution, and -- unlike supersampling -- at no additional cost. Building on this foundation, we propose Thera, an end-to-end ASR method that substantially outperforms existing approaches, while being more parameter-efficient and offering strong theoretical guarantees. The project page is at https://therasr.github.io.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

Purpose: To introduce a deep learning model capable of multi-organ segmentation in MRI scans, offering a solution to the current limitations in MRI analysis due to challenges in resolution, standardized intensity values, and variability in sequences. Materials and Methods: he model was trained on 1,200 manually annotated MRI scans from the UK Biobank, 221 in-house MRI scans and 1228 CT scans, leveraging cross-modality transfer learning from CT segmentation models. A human-in-the-loop annotation workflow was employed to efficiently create high-quality segmentations. The model's performance was evaluated on NAKO and the AMOS22 dataset containing 600 and 60 MRI examinations. Dice Similarity Coefficient (DSC) and Hausdorff Distance (HD) was used to assess segmentation accuracy. The model will be open sourced. Results: The model showcased high accuracy in segmenting well-defined organs, achieving Dice Similarity Coefficient (DSC) scores of 0.97 for the right and left lungs, and 0.95 for the heart. It also demonstrated robustness in organs like the liver (DSC: 0.96) and kidneys (DSC: 0.95 left, 0.95 right), which present more variability. However, segmentation of smaller and complex structures such as the portal and splenic veins (DSC: 0.54) and adrenal glands (DSC: 0.65 left, 0.61 right) revealed the need for further model optimization. Conclusion: The proposed model is a robust, tool for accurate segmentation of 40 anatomical structures in MRI and CT images. By leveraging cross-modality learning and interactive annotation, the model achieves strong performance and generalizability across diverse datasets, making it a valuable resource for researchers and clinicians. It is open source and can be downloaded from https://github.com/hhaentze/MRSegmentator.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditional distributions in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data- and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to 1. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be 1 to have a well-defined ELBO.

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be constructed from given data. In contrast, some studies, including this paper, used the trees to represent stochastic data observation processes behind given data. Moreover, they derived the statistically optimal prediction, which is robust against overfitting, based on the Bayesian decision theory by assuming a prior distribution for the trees. However, these studies still have a problem in computing this Bayes optimal prediction because it involves an infeasible summation for all division patterns of a feature space, which is represented by the trees and some parameters. In particular, an open problem is a summation with respect to combinations of division axes, i.e., the assignment of features to inner nodes of the tree. We solve this by a Markov chain Monte Carlo method, whose step size is adaptively tuned according to a posterior distribution for the trees.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for K classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

Knowing the features of a complex system that are highly relevant to a particular target variable is of fundamental interest in many areas of science. Existing approaches are often limited to linear settings, sometimes lack guarantees, and in most cases, do not scale to the problem at hand, in particular to images. We propose DRCFS, a doubly robust feature selection method for identifying the causal features even in nonlinear and high dimensional settings. We provide theoretical guarantees, illustrate necessary conditions for our assumptions, and perform extensive experiments across a wide range of simulated and semi-synthetic datasets. DRCFS significantly outperforms existing state-of-the-art methods, selecting robust features even in challenging highly non-linear and high-dimensional problems.

Diffusion models have become the dominant approach for visual generation. They are trained by denoising a Markovian process that gradually adds noise to the input. We argue that the Markovian property limits the models ability to fully utilize the generation trajectory, leading to inefficiencies during training and inference. In this paper, we propose DART, a transformer-based model that unifies autoregressive (AR) and diffusion within a non-Markovian framework. DART iteratively denoises image patches spatially and spectrally using an AR model with the same architecture as standard language models. DART does not rely on image quantization, enabling more effective image modeling while maintaining flexibility. Furthermore, DART seamlessly trains with both text and image data in a unified model. Our approach demonstrates competitive performance on class-conditioned and text-to-image generation tasks, offering a scalable, efficient alternative to traditional diffusion models. Through this unified framework, DART sets a new benchmark for scalable, high-quality image synthesis.

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.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

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.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Modern studies in radiograph representation learning rely on either self-supervision to encode invariant semantics or associated radiology reports to incorporate medical expertise, while the complementarity between them is barely noticed. To explore this, we formulate the self- and report-completion as two complementary objectives and present a unified framework based on masked record modeling (MRM). In practice, MRM reconstructs masked image patches and masked report tokens following a multi-task scheme to learn knowledge-enhanced semantic representations. With MRM pre-training, we obtain pre-trained models that can be well transferred to various radiography tasks. Specifically, we find that MRM offers superior performance in label-efficient fine-tuning. For instance, MRM achieves 88.5% mean AUC on CheXpert using 1% labeled data, outperforming previous R^2L methods with 100% labels. On NIH ChestX-ray, MRM outperforms the best performing counterpart by about 3% under small labeling ratios. Besides, MRM surpasses self- and report-supervised pre-training in identifying the pneumonia type and the pneumothorax area, sometimes by large margins.

Recently, Neural Radiance Field (NeRF) has shown great success in rendering novel-view images of a given scene by learning an implicit representation with only posed RGB images. NeRF and relevant neural field methods (e.g., neural surface representation) typically optimize a point-wise loss and make point-wise predictions, where one data point corresponds to one pixel. Unfortunately, this line of research failed to use the collective supervision of distant pixels, although it is known that pixels in an image or scene can provide rich structural information. To the best of our knowledge, we are the first to design a nonlocal multiplex training paradigm for NeRF and relevant neural field methods via a novel Stochastic Structural SIMilarity (S3IM) loss that processes multiple data points as a whole set instead of process multiple inputs independently. Our extensive experiments demonstrate the unreasonable effectiveness of S3IM in improving NeRF and neural surface representation for nearly free. The improvements of quality metrics can be particularly significant for those relatively difficult tasks: e.g., the test MSE loss unexpectedly drops by more than 90% for TensoRF and DVGO over eight novel view synthesis tasks; a 198% F-score gain and a 64% Chamfer L_{1} distance reduction for NeuS over eight surface reconstruction tasks. Moreover, S3IM is consistently robust even with sparse inputs, corrupted images, and dynamic scenes.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Existing Neural Radiance Fields (NeRF) methods suffer from the existence of reflective objects, often resulting in blurry or distorted rendering. Instead of calculating a single radiance field, we propose a multi-space neural radiance field (MS-NeRF) that represents the scene using a group of feature fields in parallel sub-spaces, which leads to a better understanding of the neural network toward the existence of reflective and refractive objects. Our multi-space scheme works as an enhancement to existing NeRF methods, with only small computational overheads needed for training and inferring the extra-space outputs. We demonstrate the superiority and compatibility of our approach using three representative NeRF-based models, i.e., NeRF, Mip-NeRF, and Mip-NeRF 360. Comparisons are performed on a novelly constructed dataset consisting of 25 synthetic scenes and 7 real captured scenes with complex reflection and refraction, all having 360-degree viewpoints. Extensive experiments show that our approach significantly outperforms the existing single-space NeRF methods for rendering high-quality scenes concerned with complex light paths through mirror-like objects. Our code and dataset will be publicly available at https://zx-yin.github.io/msnerf.

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.

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.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, especially large neural signed distance (SDFs) or radiance fields (NeRFs) via a single multi-layer perceptron (MLP). However, despite the power and simplicity of representing signals with an MLP, these methods still face challenges when modeling large and complex temporal signals due to the limited capacity of MLPs. In this paper, we propose an effective approach to address this limitation by incorporating temporal residual layers into neural fields, dubbed ResFields, a novel class of networks specifically designed to effectively represent complex temporal signals. We conduct a comprehensive analysis of the properties of ResFields and propose a matrix factorization technique to reduce the number of trainable parameters and enhance generalization capabilities. Importantly, our formulation seamlessly integrates with existing techniques and consistently improves results across various challenging tasks: 2D video approximation, dynamic shape modeling via temporal SDFs, and dynamic NeRF reconstruction. Lastly, we demonstrate the practical utility of ResFields by showcasing its effectiveness in capturing dynamic 3D scenes from sparse sensory inputs of a lightweight capture system.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view geospatial imagery or LiDAR point clouds which can be expensive to acquire. Single-view height estimation using neural network based models shows promise however it can struggle with reconstructing high resolution features. The latest advancements in diffusion models for high resolution image synthesis and editing have yet to be utilized for remote sensing imagery, particularly height estimation. Our approach involves training a generative diffusion model to learn the joint distribution of optical and DSM images across both domains as a Markov chain. This is accomplished by minimizing a denoising score matching objective while being conditioned on the source image to generate realistic high resolution 3D surfaces. In this paper we experiment with conditional denoising diffusion probabilistic models (DDPM) for height estimation from a single remotely sensed image and show promising results on the Vaihingen benchmark dataset.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

Text-to-image diffusion models (DMs) develop at an unprecedented pace, supported by thorough theoretical exploration and empirical analysis. Unfortunately, the discrepancy between DMs and autoregressive models (ARMs) complicates the path toward achieving the goal of unified vision and language generation. Recently, the masked generative Transformer (MGT) serves as a promising intermediary between DM and ARM by predicting randomly masked image tokens (i.e., masked image modeling), combining the efficiency of DM with the discrete token nature of ARM. However, we find that the comprehensive analyses regarding the inference for MGT are virtually non-existent, and thus we aim to present positive design choices to fill this gap. We modify and re-design a set of DM-based inference techniques for MGT and further elucidate their performance on MGT. We also discuss the approach to correcting token's distribution to enhance inference. Extensive experiments and empirical analyses lead to concrete and effective design choices, and these design choices can be merged to achieve further performance gains. For instance, in terms of enhanced inference, we achieve winning rates of approximately 70% compared to vanilla sampling on HPS v2 with the recent SOTA MGT Meissonic. Our contributions have the potential to further enhance the capabilities and future development of MGTs.

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

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

Diffusion models have achieved state-of-the-art results on many modalities including images, speech, and video. However, existing models are not tailored to support remote sensing data, which is widely used in important applications including environmental monitoring and crop-yield prediction. Satellite images are significantly different from natural images -- they can be multi-spectral, irregularly sampled across time -- and existing diffusion models trained on images from the Web do not support them. Furthermore, remote sensing data is inherently spatio-temporal, requiring conditional generation tasks not supported by traditional methods based on captions or images. In this paper, we present DiffusionSat, to date the largest generative foundation model trained on a collection of publicly available large, high-resolution remote sensing datasets. As text-based captions are sparsely available for satellite images, we incorporate the associated metadata such as geolocation as conditioning information. Our method produces realistic samples and can be used to solve multiple generative tasks including temporal generation, superresolution given multi-spectral inputs and in-painting. Our method outperforms previous state-of-the-art methods for satellite image generation and is the first large-scale generative foundation model for satellite imagery.

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile, collective behavior requires resolution of the aforementioned challenges, and remains of importance to many state-of-the-art applications such as active matter physics, self-organizing systems, opinion dynamics, and biological or robotic swarms. Here, MARL via mean field control (MFC) offers a potential solution to scalability, but fails to consider decentralized and partially observable systems. In this paper, we enable decentralized behavior of agents under partial information by proposing novel models for decentralized partially observable MFC (Dec-POMFC), a broad class of problems with permutation-invariant agents allowing for reduction to tractable single-agent Markov decision processes (MDP) with single-agent RL solution. We provide rigorous theoretical results, including a dynamic programming principle, together with optimality guarantees for Dec-POMFC solutions applied to finite swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient methods for MARL via centralized training and decentralized execution, together with policy gradient approximation guarantees. In addition, we improve upon state-of-the-art histogram-based MFC by kernel methods, which is of separate interest also for fully observable MFC. We evaluate numerically on representative collective behavior tasks such as adapted Kuramoto and Vicsek swarming models, being on par with state-of-the-art MARL. Overall, our framework takes a step towards RL-based engineering of artificial collective behavior via MFC.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

Large vision-language models are steadily gaining personalization capabilities at the cost of fine-tuning or data augmentation. We present two models for image generation using model-agnostic learning that align semantic priors with generative capabilities. RLDF, or Reinforcement Learning from Diffusion Feedback, is a singular approach for visual imitation through prior-preserving reward function guidance. This employs Q-learning (with standard Q*) for generation and follows a semantic-rewarded trajectory for image search through finite encoding-tailored actions. The second proposed method, noisy diffusion gradient, is optimization driven. At the root of both methods is a special CFG encoding that we propose for continual semantic guidance. Using only a single input image and no text input, RLDF generates high-quality images over varied domains including retail, sports and agriculture showcasing class-consistency and strong visual diversity. Project website is available at https://infernolia.github.io/RLDF.

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li et al. (2019), and this refined framework automates the analysis of a large class of sampling algorithms based on discretizations of contractive SDEs. Using this framework, we establish an O(d/epsilon) mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known O(d/epsilon) result and is optimal (in terms of order) in both dimension d and accuracy tolerance epsilon for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

We develop a portfolio allocation framework that leverages deep learning techniques to address challenges arising from high-dimensional, non-stationary, and low-signal-to-noise market information. Our approach includes a dynamic embedding method that reduces the non-stationary, high-dimensional state space into a lower-dimensional representation. We design a reinforcement learning (RL) framework that integrates generative autoencoders and online meta-learning to dynamically embed market information, enabling the RL agent to focus on the most impactful parts of the state space for portfolio allocation decisions. Empirical analysis based on the top 500 U.S. stocks demonstrates that our framework outperforms common portfolio benchmarks and the predict-then-optimize (PTO) approach using machine learning, particularly during periods of market stress. Traditional factor models do not fully explain this superior performance. The framework's ability to time volatility reduces its market exposure during turbulent times. Ablation studies confirm the robustness of this performance across various reinforcement learning algorithms. Additionally, the embedding and meta-learning techniques effectively manage the complexities of high-dimensional, noisy, and non-stationary financial data, enhancing both portfolio performance and risk management.

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In this work, we demonstrate that NFs are more powerful than previously believed. We present TarFlow: a simple and scalable architecture that enables highly performant NF models. TarFlow can be thought of as a Transformer-based variant of Masked Autoregressive Flows (MAFs): it consists of a stack of autoregressive Transformer blocks on image patches, alternating the autoregression direction between layers. TarFlow is straightforward to train end-to-end, and capable of directly modeling and generating pixels. We also propose three key techniques to improve sample quality: Gaussian noise augmentation during training, a post training denoising procedure, and an effective guidance method for both class-conditional and unconditional settings. Putting these together, TarFlow sets new state-of-the-art results on likelihood estimation for images, beating the previous best methods by a large margin, and generates samples with quality and diversity comparable to diffusion models, for the first time with a stand-alone NF model. We make our code available at https://github.com/apple/ml-tarflow.

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

We introduce AiM, an autoregressive (AR) image generative model based on Mamba architecture. AiM employs Mamba, a novel state-space model characterized by its exceptional performance for long-sequence modeling with linear time complexity, to supplant the commonly utilized Transformers in AR image generation models, aiming to achieve both superior generation quality and enhanced inference speed. Unlike existing methods that adapt Mamba to handle two-dimensional signals via multi-directional scan, AiM directly utilizes the next-token prediction paradigm for autoregressive image generation. This approach circumvents the need for extensive modifications to enable Mamba to learn 2D spatial representations. By implementing straightforward yet strategically targeted modifications for visual generative tasks, we preserve Mamba's core structure, fully exploiting its efficient long-sequence modeling capabilities and scalability. We provide AiM models in various scales, with parameter counts ranging from 148M to 1.3B. On the ImageNet1K 256*256 benchmark, our best AiM model achieves a FID of 2.21, surpassing all existing AR models of comparable parameter counts and demonstrating significant competitiveness against diffusion models, with 2 to 10 times faster inference speed. Code is available at https://github.com/hp-l33/AiM

The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared to long MD simulations. Our open-source implementation is available at https://github.com/lujiarui/Str2Str

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in the domain of image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However, existing methods often struggle with spatial layout consistency when producing high-resolution panoramas, due to the lack of guidance of the global image layout. In this paper, we introduce the Multi-Scale Diffusion (MSD) framework, a plug-and-play module that extends the existing panoramic image generation framework to multiple resolution levels. By utilizing gradient descent techniques, our method effectively incorporates structural information from low-resolution images into high-resolution outputs. A comprehensive evaluation of the proposed method was conducted, comparing it with the prior works in qualitative and quantitative dimensions. The evaluation results demonstrate that our method significantly outperforms others in generating coherent high-resolution panoramas.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of NKD^2 for N data points, K Gaussian components and D dimensions. The resulting algorithm can be applied to high dimensional tasks, and this is confirmed by applying it to the classification datasets MNIST and CIFAR-10. Additionally, in order to show the algorithm's applicability to function approximation and control tasks, it is applied to three reinforcement learning tasks and its data-efficiency is evaluated.

Mamba, a special case of the State Space Model, is gaining popularity as an alternative to template-based deep learning approaches in medical image analysis. While transformers are powerful architectures, they have drawbacks, including quadratic computational complexity and an inability to address long-range dependencies efficiently. This limitation affects the analysis of large and complex datasets in medical imaging, where there are many spatial and temporal relationships. In contrast, Mamba offers benefits that make it well-suited for medical image analysis. It has linear time complexity, which is a significant improvement over transformers. Mamba processes longer sequences without attention mechanisms, enabling faster inference and requiring less memory. Mamba also demonstrates strong performance in merging multimodal data, improving diagnosis accuracy and patient outcomes. The organization of this paper allows readers to appreciate the capabilities of Mamba in medical imaging step by step. We begin by defining core concepts of SSMs and models, including S4, S5, and S6, followed by an exploration of Mamba architectures such as pure Mamba, U-Net variants, and hybrid models with convolutional neural networks, transformers, and Graph Neural Networks. We also cover Mamba optimizations, techniques and adaptations, scanning, datasets, applications, experimental results, and conclude with its challenges and future directions in medical imaging. This review aims to demonstrate the transformative potential of Mamba in overcoming existing barriers within medical imaging while paving the way for innovative advancements in the field. A comprehensive list of Mamba architectures applied in the medical field, reviewed in this work, is available at Github.

The diffusion model has long been plagued by scalability and quadratic complexity issues, especially within transformer-based structures. In this study, we aim to leverage the long sequence modeling capability of a State-Space Model called Mamba to extend its applicability to visual data generation. Firstly, we identify a critical oversight in most current Mamba-based vision methods, namely the lack of consideration for spatial continuity in the scan scheme of Mamba. Secondly, building upon this insight, we introduce a simple, plug-and-play, zero-parameter method named Zigzag Mamba, which outperforms Mamba-based baselines and demonstrates improved speed and memory utilization compared to transformer-based baselines. Lastly, we integrate Zigzag Mamba with the Stochastic Interpolant framework to investigate the scalability of the model on large-resolution visual datasets, such as FacesHQ 1024times 1024 and UCF101, MultiModal-CelebA-HQ, and MS COCO 256times 256. Code will be released at https://taohu.me/zigma/

Reinforcement learning (RL) has improved guided image generation with diffusion models by directly optimizing rewards that capture image quality, aesthetics, and instruction following capabilities. However, the resulting generative policies inherit the same iterative sampling process of diffusion models that causes slow generation. To overcome this limitation, consistency models proposed learning a new class of generative models that directly map noise to data, resulting in a model that can generate an image in as few as one sampling iteration. In this work, to optimize text-to-image generative models for task specific rewards and enable fast training and inference, we propose a framework for fine-tuning consistency models via RL. Our framework, called Reinforcement Learning for Consistency Model (RLCM), frames the iterative inference process of a consistency model as an RL procedure. RLCM improves upon RL fine-tuned diffusion models on text-to-image generation capabilities and trades computation during inference time for sample quality. Experimentally, we show that RLCM can adapt text-to-image consistency models to objectives that are challenging to express with prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Comparing to RL finetuned diffusion models, RLCM trains significantly faster, improves the quality of the generation measured under the reward objectives, and speeds up the inference procedure by generating high quality images with as few as two inference steps. Our code is available at https://rlcm.owenoertell.com

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

The neural semi-Markov Conditional Random Field (semi-CRF) framework has demonstrated promise for event-based piano transcription. In this framework, all events (notes or pedals) are represented as closed time intervals tied to specific event types. The neural semi-CRF approach requires an interval scoring matrix that assigns a score for every candidate interval. However, designing an efficient and expressive architecture for scoring intervals is not trivial. This paper introduces a simple method for scoring intervals using scaled inner product operations that resemble how attention scoring is done in transformers. We show theoretically that, due to the special structure from encoding the non-overlapping intervals, under a mild condition, the inner product operations are expressive enough to represent an ideal scoring matrix that can yield the correct transcription result. We then demonstrate that an encoder-only structured non-hierarchical transformer backbone, operating only on a low-time-resolution feature map, is capable of transcribing piano notes and pedals with high accuracy and time precision. The experiment shows that our approach achieves the new state-of-the-art performance across all subtasks in terms of the F1 measure on the Maestro dataset.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN. Our implementation is available at https://github.com/hojonathanho/diffusion

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

Despite its success in image synthesis, we observe that diffusion probabilistic models (DPMs) often lack contextual reasoning ability to learn the relations among object parts in an image, leading to a slow learning process. To solve this issue, we propose a Masked Diffusion Transformer (MDT) that introduces a mask latent modeling scheme to explicitly enhance the DPMs' ability of contextual relation learning among object semantic parts in an image. During training, MDT operates on the latent space to mask certain tokens. Then, an asymmetric masking diffusion transformer is designed to predict masked tokens from unmasked ones while maintaining the diffusion generation process. Our MDT can reconstruct the full information of an image from its incomplete contextual input, thus enabling it to learn the associated relations among image tokens. Experimental results show that MDT achieves superior image synthesis performance, e.g. a new SoTA FID score on the ImageNet dataset, and has about 3x faster learning speed than the previous SoTA DiT. The source code is released at https://github.com/sail-sg/MDT.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Magnetic resonance imaging (MRI) is a common and life-saving medical imaging technique. However, acquiring high signal-to-noise ratio MRI scans requires long scan times, resulting in increased costs and patient discomfort, and decreased throughput. Thus, there is great interest in denoising MRI scans, especially for the subtype of diffusion MRI scans that are severely SNR-limited. While most prior MRI denoising methods are supervised in nature, acquiring supervised training datasets for the multitude of anatomies, MRI scanners, and scan parameters proves impractical. Here, we propose Denoising Diffusion Models for Denoising Diffusion MRI (DDM^2), a self-supervised denoising method for MRI denoising using diffusion denoising generative models. Our three-stage framework integrates statistic-based denoising theory into diffusion models and performs denoising through conditional generation. During inference, we represent input noisy measurements as a sample from an intermediate posterior distribution within the diffusion Markov chain. We conduct experiments on 4 real-world in-vivo diffusion MRI datasets and show that our DDM^2 demonstrates superior denoising performances ascertained with clinically-relevant visual qualitative and quantitative metrics.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

While Neural Radiance Fields (NeRFs) have demonstrated exceptional quality, their protracted training duration remains a limitation. Generalizable and MVS-based NeRFs, although capable of mitigating training time, often incur tradeoffs in quality. This paper presents a novel approach called BoostMVSNeRFs to enhance the rendering quality of MVS-based NeRFs in large-scale scenes. We first identify limitations in MVS-based NeRF methods, such as restricted viewport coverage and artifacts due to limited input views. Then, we address these limitations by proposing a new method that selects and combines multiple cost volumes during volume rendering. Our method does not require training and can adapt to any MVS-based NeRF methods in a feed-forward fashion to improve rendering quality. Furthermore, our approach is also end-to-end trainable, allowing fine-tuning on specific scenes. We demonstrate the effectiveness of our method through experiments on large-scale datasets, showing significant rendering quality improvements in large-scale scenes and unbounded outdoor scenarios. We release the source code of BoostMVSNeRFs at https://su-terry.github.io/BoostMVSNeRFs/.

Creating high quality and realistic materials in computer graphics is a challenging and time-consuming task, which requires great expertise. In this paper, we present MatFuse, a novel unified approach that harnesses the generative power of diffusion models (DM) to simplify the creation of SVBRDF maps. Our DM-based pipeline integrates multiple sources of conditioning, such as color palettes, sketches, and pictures, enabling fine-grained control and flexibility in material synthesis. This design allows for the combination of diverse information sources (e.g., sketch + image embedding), enhancing creative possibilities in line with the principle of compositionality. We demonstrate the generative capabilities of the proposed method under various conditioning settings; on the SVBRDF estimation task, we show that our method yields performance comparable to state-of-the-art approaches, both qualitatively and quantitatively.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Generalizable Neural Radiance Fields (GNeRF) are one of the most promising real-world solutions for novel view synthesis, thanks to their cross-scene generalization capability and thus the possibility of instant rendering on new scenes. While adversarial robustness is essential for real-world applications, little study has been devoted to understanding its implication on GNeRF. We hypothesize that because GNeRF is implemented by conditioning on the source views from new scenes, which are often acquired from the Internet or third-party providers, there are potential new security concerns regarding its real-world applications. Meanwhile, existing understanding and solutions for neural networks' adversarial robustness may not be applicable to GNeRF, due to its 3D nature and uniquely diverse operations. To this end, we present NeRFool, which to the best of our knowledge is the first work that sets out to understand the adversarial robustness of GNeRF. Specifically, NeRFool unveils the vulnerability patterns and important insights regarding GNeRF's adversarial robustness. Built upon the above insights gained from NeRFool, we further develop NeRFool+, which integrates two techniques capable of effectively attacking GNeRF across a wide range of target views, and provide guidelines for defending against our proposed attacks. We believe that our NeRFool/NeRFool+ lays the initial foundation for future innovations in developing robust real-world GNeRF solutions. Our codes are available at: https://github.com/GATECH-EIC/NeRFool.

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds (1fs=10^{-15}s). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of 10^{5} - 10^{6}:fs. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such algorithms leveraging recent advances in convex analysis and optimization methods involving Bregman divergences, namely the Bregman--Moreau envelopes and the Bregman proximity operators, and in the Langevin Monte Carlo algorithms reminiscent of mirror descent. The proposed algorithms extend existing Langevin Monte Carlo algorithms in two aspects -- the ability to sample nonsmooth distributions with mirror descent-like algorithms, and the use of the more general Bregman--Moreau envelope in place of the Moreau envelope as a smooth approximation of the nonsmooth part of the potential. A particular case of the proposed scheme is reminiscent of the Bregman proximal gradient algorithm. The efficiency of the proposed methodology is illustrated with various sampling tasks at which existing Langevin Monte Carlo methods are known to perform poorly.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

Research on geospatial foundation models (GFMs) has become a trending topic in geospatial artificial intelligence (AI) research due to their potential for achieving high generalizability and domain adaptability, reducing model training costs for individual researchers. Unlike large language models, such as ChatGPT, constructing visual foundation models for image analysis, particularly in remote sensing, encountered significant challenges such as formulating diverse vision tasks into a general problem framework. This paper evaluates the recently released NASA-IBM GFM Prithvi for its predictive performance on high-level image analysis tasks across multiple benchmark datasets. Prithvi was selected because it is one of the first open-source GFMs trained on time-series of high-resolution remote sensing imagery. A series of experiments were designed to assess Prithvi's performance as compared to other pre-trained task-specific AI models in geospatial image analysis. New strategies, including band adaptation, multi-scale feature generation, and fine-tuning techniques, are introduced and integrated into an image analysis pipeline to enhance Prithvi's domain adaptation capability and improve model performance. In-depth analyses reveal Prithvi's strengths and weaknesses, offering insights for both improving Prithvi and developing future visual foundation models for geospatial tasks.

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.80, inception score (IS) from 80.4 to 356.4, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper, we conduct an in-depth investigation of the representation power of DPMs, and propose a novel knowledge transfer method that leverages the knowledge acquired by generative DPMs for recognition tasks. Our study begins by examining the feature space of DPMs, revealing that DPMs are inherently denoising autoencoders that balance the representation learning with regularizing model capacity. To this end, we introduce a novel knowledge transfer paradigm named RepFusion. Our paradigm extracts representations at different time steps from off-the-shelf DPMs and dynamically employs them as supervision for student networks, in which the optimal time is determined through reinforcement learning. We evaluate our approach on several image classification, semantic segmentation, and landmark detection benchmarks, and demonstrate that it outperforms state-of-the-art methods. Our results uncover the potential of DPMs as a powerful tool for representation learning and provide insights into the usefulness of generative models beyond sample generation. The code is available at https://github.com/Adamdad/Repfusion.

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/

We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution of real molecules. Then, we follow the neural empirical Bayes framework [Saremi and Hyvarinen, 2019] and generate molecules in two steps: (i) sample noisy density grids from a smooth distribution via underdamped Langevin Markov chain Monte Carlo, and (ii) recover the ``clean'' molecule by denoising the noisy grid with a single step. Our method, VoxMol, generates molecules in a fundamentally different way than the current state of the art (i.e., diffusion models applied to atom point clouds). It differs in terms of the data representation, the noise model, the network architecture and the generative modeling algorithm. VoxMol achieves comparable results to state of the art on unconditional 3D molecule generation while being simpler to train and faster to generate molecules.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Diffusion models, such as Stable Diffusion, have made significant strides in visual generation, yet their paradigm remains fundamentally different from autoregressive language models, complicating the development of unified language-vision models. Recent efforts like LlamaGen have attempted autoregressive image generation using discrete VQVAE tokens, but the large number of tokens involved renders this approach inefficient and slow. In this work, we present Meissonic, which elevates non-autoregressive masked image modeling (MIM) text-to-image to a level comparable with state-of-the-art diffusion models like SDXL. By incorporating a comprehensive suite of architectural innovations, advanced positional encoding strategies, and optimized sampling conditions, Meissonic substantially improves MIM's performance and efficiency. Additionally, we leverage high-quality training data, integrate micro-conditions informed by human preference scores, and employ feature compression layers to further enhance image fidelity and resolution. Our model not only matches but often exceeds the performance of existing models like SDXL in generating high-quality, high-resolution images. Extensive experiments validate Meissonic's capabilities, demonstrating its potential as a new standard in text-to-image synthesis. We release a model checkpoint capable of producing 1024 times 1024 resolution images.

The recent use of diffusion prior, enhanced by pre-trained text-image models, has markedly elevated the performance of image super-resolution (SR). To alleviate the huge computational cost required by pixel-based diffusion SR, latent-based methods utilize a feature encoder to transform the image and then implement the SR image generation in a compact latent space. Nevertheless, there are two major issues that limit the performance of latent-based diffusion. First, the compression of latent space usually causes reconstruction distortion. Second, huge computational cost constrains the parameter scale of the diffusion model. To counteract these issues, we first propose a frequency compensation module that enhances the frequency components from latent space to pixel space. The reconstruction distortion (especially for high-frequency information) can be significantly decreased. Then, we propose to use Sample-Space Mixture of Experts (SS-MoE) to achieve more powerful latent-based SR, which steadily improves the capacity of the model without a significant increase in inference costs. These carefully crafted designs contribute to performance improvements in largely explored 4x blind super-resolution benchmarks and extend to large magnification factors, i.e., 8x image SR benchmarks. The code is available at https://github.com/amandaluof/moe_sr.

This paper presents Diffusion Forcing, a new training paradigm where a diffusion model is trained to denoise a set of tokens with independent per-token noise levels. We apply Diffusion Forcing to sequence generative modeling by training a causal next-token prediction model to generate one or several future tokens without fully diffusing past ones. Our approach is shown to combine the strengths of next-token prediction models, such as variable-length generation, with the strengths of full-sequence diffusion models, such as the ability to guide sampling to desirable trajectories. Our method offers a range of additional capabilities, such as (1) rolling-out sequences of continuous tokens, such as video, with lengths past the training horizon, where baselines diverge and (2) new sampling and guiding schemes that uniquely profit from Diffusion Forcing's variable-horizon and causal architecture, and which lead to marked performance gains in decision-making and planning tasks. In addition to its empirical success, our method is proven to optimize a variational lower bound on the likelihoods of all subsequences of tokens drawn from the true joint distribution. Project website: https://boyuan.space/diffusion-forcing/

AI is revolutionizing MRI along the acquisition and processing chain. Advanced AI frameworks have been developed to apply AI in various successive tasks, such as image reconstruction, quantitative parameter map estimation, and image segmentation. Existing frameworks are often designed to perform tasks independently or are focused on specific models or datasets, limiting generalization. We introduce ATOMMIC, an open-source toolbox that streamlines AI applications for accelerated MRI reconstruction and analysis. ATOMMIC implements several tasks using DL networks and enables MultiTask Learning (MTL) to perform related tasks integrated, targeting generalization in the MRI domain. We first review the current state of AI frameworks for MRI through a comprehensive literature search and by parsing 12,479 GitHub repositories. We benchmark 25 DL models on eight publicly available datasets to present distinct applications of ATOMMIC on accelerated MRI reconstruction, image segmentation, quantitative parameter map estimation, and joint accelerated MRI reconstruction and image segmentation utilizing MTL. Our findings demonstrate that ATOMMIC is the only MTL framework with harmonized complex-valued and real-valued data support. Evaluations on single tasks show that physics-based models, which enforce data consistency by leveraging the physical properties of MRI, outperform other models in reconstructing highly accelerated acquisitions. Physics-based models that produce high reconstruction quality can accurately estimate quantitative parameter maps. When high-performing reconstruction models are combined with robust segmentation networks utilizing MTL, performance is improved in both tasks. ATOMMIC facilitates MRI reconstruction and analysis by standardizing workflows, enhancing data interoperability, integrating unique features like MTL, and effectively benchmarking DL models.

Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the Controlled Monte Carlo Diffusion sampler (CMCD) for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. On the way, we clarify the relationship between the EM-algorithm and iterative proportional fitting (IPF) for Schr{\"o}dinger bridges, deriving as well a regularised objective that bypasses the iterative bottleneck of standard IPF-updates. Finally, we show that CMCD has a strong foundation in the Jarzinsky and Crooks identities from statistical physics, and that it convincingly outperforms competing approaches across a wide array of experiments.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

This review paper is intended for the 2nd edition of the Handbook of Markov chain Monte Carlo. We provide an introduction to approximate inference techniques as Bayesian computation methods applied to deep learning models. We organize the chapter by presenting popular computational methods for Bayesian neural networks and deep generative models, explaining their unique challenges in posterior inference as well as the solutions.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed-generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal.

Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can be inaccurate, increasing the need for Uncertainty Quantification (UQ). Bayesian modeling provides the mathematical framework for UQ, but classical Bayesian methods based on Markov chain Monte Carlo (MCMC) are computationally intractable for NN potentials. By training graph NN potentials for coarse-grained systems of liquid water and alanine dipeptide, we demonstrate here that scalable Bayesian UQ via stochastic gradient MCMC (SG-MCMC) yields reliable uncertainty estimates for MD observables. We show that cold posteriors can reduce the required training data size and that for reliable UQ, multiple Markov chains are needed. Additionally, we find that SG-MCMC and the Deep Ensemble method achieve comparable results, despite shorter training and less hyperparameter tuning of the latter. We show that both methods can capture aleatoric and epistemic uncertainty reliably, but not systematic uncertainty, which needs to be minimized by adequate modeling to obtain accurate credible intervals for MD observables. Our results represent a step towards accurate UQ that is of vital importance for trustworthy NN potential-based MD simulations required for decision-making in practice.

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of 1-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.