Daily Papers

Few-shot models aim at making predictions using a minimal number of labeled examples from a given task. The main challenge in this area is the one-shot setting where only one element represents each class. We propose HyperShot - the fusion of kernels and hypernetwork paradigm. Compared to reference approaches that apply a gradient-based adjustment of the parameters, our model aims to switch the classification module parameters depending on the task's embedding. In practice, we utilize a hypernetwork, which takes the aggregated information from support data and returns the classifier's parameters handcrafted for the considered problem. Moreover, we introduce the kernel-based representation of the support examples delivered to hypernetwork to create the parameters of the classification module. Consequently, we rely on relations between embeddings of the support examples instead of direct feature values provided by the backbone models. Thanks to this approach, our model can adapt to highly different tasks.

Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes that closely resemble the input volume while, ideally, also being computationally and memory efficient. Meeting both these requirements remains a challenge. To this end, we propose an adaptive and exponentially weighted pooling method: adaPool. Our method learns a regional-specific fusion of two sets of pooling kernels that are based on the exponent of the Dice-Sorensen coefficient and the exponential maximum, respectively. AdaPool improves the preservation of detail on a range of tasks including image and video classification and object detection. A key property of adaPool is its bidirectional nature. In contrast to common pooling methods, the learned weights can also be used to upsample activation maps. We term this method adaUnPool. We evaluate adaUnPool on image and video super-resolution and frame interpolation. For benchmarking, we introduce Inter4K, a novel high-quality, high frame-rate video dataset. Our experiments demonstrate that adaPool systematically achieves better results across tasks and backbones, while introducing a minor additional computational and memory overhead.

In the study, we present AMFusionNet, an innovative approach to infrared and visible image fusion (IVIF), harnessing the power of multiple kernel sizes and attention mechanisms. By assimilating thermal details from infrared images with texture features from visible sources, our method produces images enriched with comprehensive information. Distinct from prevailing deep learning methodologies, our model encompasses a fusion mechanism powered by multiple convolutional kernels, facilitating the robust capture of a wide feature spectrum. Notably, we incorporate parallel attention mechanisms to emphasize and retain pivotal target details in the resultant images. Moreover, the integration of the multi-scale structural similarity (MS-SSIM) loss function refines network training, optimizing the model for IVIF task. Experimental results demonstrate that our method outperforms state-of-the-art algorithms in terms of quality and quantity. The performance metrics on publicly available datasets also show significant improvement

Since the breakthrough performance of AlexNet in 2012, convolutional neural networks (convnets) have grown into extremely powerful vision models. Deep learning researchers have used convnets to perform vision tasks with accuracy that was unachievable a decade ago. Confronted with the immense computation that convnets use, deep learning researchers also became interested in efficiency. However, the engineers who deployed efficient convnets soon realized that they were slower than the previous generation, despite using fewer operations. Many reverted to older models that ran faster. Hence researchers switched the objective of their search from arithmetic complexity to latency and produced a new wave of models that performed better. Paradoxically, these models also used more operations. Skepticism grew among researchers and engineers alike about the relevance of arithmetic complexity. Contrary to the prevailing view that latency and arithmetic complexity are irreconcilable, a simple formula relates both through computational efficiency. This insight enabled us to co-optimize the separate factors that determine latency. We observed that the degenerate conv2d layers that produce the best accuracy--complexity trade-off also use significant memory resources and have low computational efficiency. We devised block fusion algorithms to implement all the layers of a residual block in a single kernel, thereby creating temporal locality, avoiding communication, and reducing workspace size. Our ConvFirst model with block-fusion kernels has less arithmetic complexity and greater computational efficiency than baseline models and kernels, and ran approximately four times as fast as ConvNeXt. We also created novel tools, including efficiency gap plots and waterline analysis. Our unified approach to convnet efficiency envisions a new era of models and kernels that achieve greater accuracy at lower cost.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

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.

Fusion is a technique for merging multiple independently-trained neural networks in order to combine their capabilities. Past attempts have been restricted to the case of fully-connected, convolutional, and residual networks. In this paper, we present a systematic approach for fusing two or more transformer-based networks exploiting Optimal Transport to (soft-)align the various architectural components. We flesh out an abstraction for layer alignment, that can generalize to arbitrary architectures -- in principle -- and we apply this to the key ingredients of Transformers such as multi-head self-attention, layer-normalization, and residual connections, and we discuss how to handle them via various ablation studies. Furthermore, our method allows the fusion of models of different sizes (heterogeneous fusion), providing a new and efficient way for compression of Transformers. The proposed approach is evaluated on both image classification tasks via Vision Transformer and natural language modeling tasks using BERT. Our approach consistently outperforms vanilla fusion, and, after a surprisingly short finetuning, also outperforms the individual converged parent models. In our analysis, we uncover intriguing insights about the significant role of soft alignment in the case of Transformers. Our results showcase the potential of fusing multiple Transformers, thus compounding their expertise, in the budding paradigm of model fusion and recombination.

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings , we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression. The code is available at the following link, https://github.com/sidak/otfusion.

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a reproducing kernel Hilbert space (RKHS) defined by the NNGP contains only functions that can be approximated by the architecture. To achieve a certain approximation error the required number of neurons in each layer is defined by the RKHS norm of the target function. Moreover, the approximation can be constructed from a supervised dataset by a random multi-layer representation of an input vector, together with training of the last layer's weights. For a 2-layer NN and a domain equal to an n-1-dimensional sphere in {mathbb R}^n, we compare the number of neurons required by Barron's theorem and by the multi-layer features construction. We show that if eigenvalues of the integral operator of the NNGP decay slower than k^{-n-2{3}} where k is an order of an eigenvalue, then our theorem guarantees a more succinct neural network approximation than Barron's theorem. We also make some computational experiments to verify our theoretical findings. Our experiments show that realistic neural networks easily learn target functions even when both theorems do not give any guarantees.

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

Image harmonization aims to solve the visual inconsistency problem in composited images by adaptively adjusting the foreground pixels with the background as references. Existing methods employ local color transformation or region matching between foreground and background, which neglects powerful proximity prior and independently distinguishes fore-/back-ground as a whole part for harmonization. As a result, they still show a limited performance across varied foreground objects and scenes. To address this issue, we propose a novel Global-aware Kernel Network (GKNet) to harmonize local regions with comprehensive consideration of long-distance background references. Specifically, GKNet includes two parts, \ie, harmony kernel prediction and harmony kernel modulation branches. The former includes a Long-distance Reference Extractor (LRE) to obtain long-distance context and Kernel Prediction Blocks (KPB) to predict multi-level harmony kernels by fusing global information with local features. To achieve this goal, a novel Selective Correlation Fusion (SCF) module is proposed to better select relevant long-distance background references for local harmonization. The latter employs the predicted kernels to harmonize foreground regions with both local and global awareness. Abundant experiments demonstrate the superiority of our method for image harmonization over state-of-the-art methods, \eg, achieving 39.53dB PSNR that surpasses the best counterpart by +0.78dB uparrow; decreasing fMSE/MSE by 11.5\%downarrow/6.7\%downarrow compared with the SoTA method. Code will be available at https://github.com/XintianShen/GKNet{here}.

Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to wide neural networks in certain regimes. However, a key feature of DNNs is their ability to scale the model size and training data size independently, whereas in traditional kernel machines model size is tied to data size. Because of this coupling, scaling kernel machines to large data has been computationally challenging. In this paper, we provide a way forward for constructing large-scale general kernel models, which are a generalization of kernel machines that decouples the model and data, allowing training on large datasets. Specifically, we introduce EigenPro 3.0, an algorithm based on projected dual preconditioned SGD and show scaling to model and data sizes which have not been possible with existing kernel methods.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

We present a novel method for reconstructing a 3D implicit surface from a large-scale, sparse, and noisy point cloud. Our approach builds upon the recently introduced Neural Kernel Fields (NKF) representation. It enjoys similar generalization capabilities to NKF, while simultaneously addressing its main limitations: (a) We can scale to large scenes through compactly supported kernel functions, which enable the use of memory-efficient sparse linear solvers. (b) We are robust to noise, through a gradient fitting solve. (c) We minimize training requirements, enabling us to learn from any dataset of dense oriented points, and even mix training data consisting of objects and scenes at different scales. Our method is capable of reconstructing millions of points in a few seconds, and handling very large scenes in an out-of-core fashion. We achieve state-of-the-art results on reconstruction benchmarks consisting of single objects, indoor scenes, and outdoor scenes.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Contrastive learning is a powerful self-supervised learning method, but we have a limited theoretical understanding of how it works and why it works. In this paper, we prove that contrastive learning with the standard InfoNCE loss is equivalent to spectral clustering on the similarity graph. Using this equivalence as the building block, we extend our analysis to the CLIP model and rigorously characterize how similar multi-modal objects are embedded together. Motivated by our theoretical insights, we introduce the kernel mixture loss, incorporating novel kernel functions that outperform the standard Gaussian kernel on several vision datasets.

Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs 7x7 depthwise convolution. Although such depthwise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves 60% throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation. It is still unclear how to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e. small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely IncepitonNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves 1.6x higher training throughputs than ConvNeX-T, as well as attains 0.2% top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint. Code is available at https://github.com/sail-sg/inceptionnext.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output units (e.g. an O-class classifier), however, the eNTK on N inputs is of size NO times NO, taking O((NO)^2) memory and up to O((NO)^3) computation. Most existing applications have therefore used one of a handful of approximations yielding N times N kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits", converges to the true eNTK at initialization for any network with a wide final "readout" layer. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Lightweight direct Time-of-Flight (dToF) sensors are ideal for 3D sensing on mobile devices. However, due to the manufacturing constraints of compact devices and the inherent physical principles of imaging, dToF depth maps are sparse and noisy. In this paper, we propose a novel video depth completion method, called SVDC, by fusing the sparse dToF data with the corresponding RGB guidance. Our method employs a multi-frame fusion scheme to mitigate the spatial ambiguity resulting from the sparse dToF imaging. Misalignment between consecutive frames during multi-frame fusion could cause blending between object edges and the background, which results in a loss of detail. To address this, we introduce an adaptive frequency selective fusion (AFSF) module, which automatically selects convolution kernel sizes to fuse multi-frame features. Our AFSF utilizes a channel-spatial enhancement attention (CSEA) module to enhance features and generates an attention map as fusion weights. The AFSF ensures edge detail recovery while suppressing high-frequency noise in smooth regions. To further enhance temporal consistency, We propose a cross-window consistency loss to ensure consistent predictions across different windows, effectively reducing flickering. Our proposed SVDC achieves optimal accuracy and consistency on the TartanAir and Dynamic Replica datasets. Code is available at https://github.com/Lan1eve/SVDC.

Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as physics-informed simulators in which accurate forecasts in real time with a minimal lag are required. The present neural network designs include millions of parameters, which makes it difficult to install such complex models on devices that have limited memory. Compression techniques might be able to resolve these issues by decreasing the size of CNN models that are created by reducing the number of parameters that contribute to the complexity of the models. We propose a compressed tensor format of convolutional layer, a priori, before the training of the neural network. 3-way kernels or 2-way kernels in convolutional layers are replaced by one-way fiters. The overfitting phenomena will be reduced also. The time needed to make predictions or time required for training using the original Convolutional Neural Networks model would be cut significantly if there were fewer parameters to deal with. In this paper we present a method of a priori compressing convolutional neural networks for finite element (FE) predictions of physical data. Afterwards we validate our a priori compressed models on physical data from a FE model solving a 2D wave equation. We show that the proposed convolutinal compression technique achieves equivalent performance as classical convolutional layers with fewer trainable parameters and lower memory footprint.

Deep neural networks have made huge progress in the last few decades. However, as the real-world data often exhibits a long-tailed distribution, vanilla deep models tend to be heavily biased toward the majority classes. To address this problem, state-of-the-art methods usually adopt a mixture of experts (MoE) to focus on different parts of the long-tailed distribution. Experts in these methods are with the same model depth, which neglects the fact that different classes may have different preferences to be fit by models with different depths. To this end, we propose a novel MoE-based method called Self-Heterogeneous Integration with Knowledge Excavation (SHIKE). We first propose Depth-wise Knowledge Fusion (DKF) to fuse features between different shallow parts and the deep part in one network for each expert, which makes experts more diverse in terms of representation. Based on DKF, we further propose Dynamic Knowledge Transfer (DKT) to reduce the influence of the hardest negative class that has a non-negligible impact on the tail classes in our MoE framework. As a result, the classification accuracy of long-tailed data can be significantly improved, especially for the tail classes. SHIKE achieves the state-of-the-art performance of 56.3%, 60.3%, 75.4%, and 41.9% on CIFAR100-LT (IF100), ImageNet-LT, iNaturalist 2018, and Places-LT, respectively.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Data augmentation is a crucial component in unsupervised contrastive learning (CL). It determines how positive samples are defined and, ultimately, the quality of the learned representation. In this work, we open the door to new perspectives for CL by integrating prior knowledge, given either by generative models -- viewed as prior representations -- or weak attributes in the positive and negative sampling. To this end, we use kernel theory to propose a novel loss, called decoupled uniformity, that i) allows the integration of prior knowledge and ii) removes the negative-positive coupling in the original InfoNCE loss. We draw a connection between contrastive learning and conditional mean embedding theory to derive tight bounds on the downstream classification loss. In an unsupervised setting, we empirically demonstrate that CL benefits from generative models to improve its representation both on natural and medical images. In a weakly supervised scenario, our framework outperforms other unconditional and conditional CL approaches.

The democratization of machine learning systems has made the process of fine-tuning accessible to practitioners, leading to a wide range of open-source models fine-tuned on specialized tasks and datasets. Recent work has proposed to merge such models to combine their functionalities. However, prior approaches are usually restricted to models that are fine-tuned from the same base model. Furthermore, the final merged model is typically required to be of the same size as the original models. In this work, we propose a new two-step algorithm to merge models -- termed PLeaS -- which relaxes these constraints. First, leveraging the Permutation symmetries inherent in the two models, PLeaS partially matches nodes in each layer by maximizing alignment. Next, PLeaS computes the weights of the merged model as a layer-wise Least Squares solution to minimize the approximation error between the features of the merged model and the permuted features of the original models. PLeaS allows a practitioner to merge two models sharing the same architecture into a single performant model of a desired size, even when the two original models are fine-tuned from different base models. We also demonstrate how our method can be extended to address a challenging scenario where no data is available from the fine-tuning domains. We demonstrate our method to merge ResNet and ViT models trained with shared and different label spaces, and show improvement over the state-of-the-art merging methods of up to 15 percentage points for the same target compute while merging models trained on DomainNet and fine-grained classification tasks. Our code is open-sourced at https://github.com/SewoongLab/PLeaS-Merging .

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their specialized capabilities across different tasks and domains. Current model merging techniques focus on merging all available models simultaneously, with weight interpolation-based methods being the predominant approaches. However, these conventional approaches are not well-suited for scenarios where models become available sequentially, and they often suffer from high memory requirements and potential interference between tasks. In this study, we propose a training-free projection-based continual merging method that processes models sequentially through orthogonal projections of weight matrices and adaptive scaling mechanisms. Our method operates by projecting new parameter updates onto subspaces orthogonal to existing merged parameter updates while using an adaptive scaling mechanism to maintain stable parameter distances, enabling efficient sequential integration of task-specific knowledge. Our approach maintains constant memory complexity to the number of models, minimizes interference between tasks through orthogonal projections, and retains the performance of previously merged models through adaptive task vector scaling. Extensive experiments on CLIP-ViT models demonstrate that our method achieves a 5-8% average accuracy improvement while maintaining robust performance in different task orderings.

In this paper, we propose a learning-based image fragment pair-searching and -matching approach to solve the challenging restoration problem. Existing works use rule-based methods to match similar contour shapes or textures, which are always difficult to tune hyperparameters for extensive data and computationally time-consuming. Therefore, we propose a neural network that can effectively utilize neighbor textures with contour shape information to fundamentally improve performance. First, we employ a graph-based network to extract the local contour and texture features of fragments. Then, for the pair-searching task, we adopt a linear transformer-based module to integrate these local features and use contrastive loss to encode the global features of each fragment. For the pair-matching task, we design a weighted fusion module to dynamically fuse extracted local contour and texture features, and formulate a similarity matrix for each pair of fragments to calculate the matching score and infer the adjacent segment of contours. To faithfully evaluate our proposed network, we created a new image fragment dataset through an algorithm we designed that tears complete images into irregular fragments. The experimental results show that our proposed network achieves excellent pair-searching accuracy, reduces matching errors, and significantly reduces computational time. Details, sourcecode, and data are available in our supplementary material.

As the task of 2D-to-3D reconstruction has gained significant attention in various real-world scenarios, it becomes crucial to be able to generate high-quality point clouds. Despite the recent success of deep learning models in generating point clouds, there are still challenges in producing high-fidelity results due to the disparities between images and point clouds. While vision transformers (ViT) and diffusion models have shown promise in various vision tasks, their benefits for reconstructing point clouds from images have not been demonstrated yet. In this paper, we first propose a neat and powerful architecture called DiffPoint that combines ViT and diffusion models for the task of point cloud reconstruction. At each diffusion step, we divide the noisy point clouds into irregular patches. Then, using a standard ViT backbone that treats all inputs as tokens (including time information, image embeddings, and noisy patches), we train our model to predict target points based on input images. We evaluate DiffPoint on both single-view and multi-view reconstruction tasks and achieve state-of-the-art results. Additionally, we introduce a unified and flexible feature fusion module for aggregating image features from single or multiple input images. Furthermore, our work demonstrates the feasibility of applying unified architectures across languages and images to improve 3D reconstruction tasks.

Knowledge distillation~(KD) has proven to be a highly effective approach for enhancing model performance through a teacher-student training scheme. However, most existing distillation methods are designed under the assumption that the teacher and student models belong to the same model family, particularly the hint-based approaches. By using centered kernel alignment (CKA) to compare the learned features between heterogeneous teacher and student models, we observe significant feature divergence. This divergence illustrates the ineffectiveness of previous hint-based methods in cross-architecture distillation. To tackle the challenge in distilling heterogeneous models, we propose a simple yet effective one-for-all KD framework called OFA-KD, which significantly improves the distillation performance between heterogeneous architectures. Specifically, we project intermediate features into an aligned latent space such as the logits space, where architecture-specific information is discarded. Additionally, we introduce an adaptive target enhancement scheme to prevent the student from being disturbed by irrelevant information. Extensive experiments with various architectures, including CNN, Transformer, and MLP, demonstrate the superiority of our OFA-KD framework in enabling distillation between heterogeneous architectures. Specifically, when equipped with our OFA-KD, the student models achieve notable performance improvements, with a maximum gain of 8.0% on the CIFAR-100 dataset and 0.7% on the ImageNet-1K dataset. PyTorch code and checkpoints can be found at https://github.com/Hao840/OFAKD.

Neighborhood attention reduces the cost of self attention by restricting each token's attention span to its nearest neighbors. This restriction, parameterized by a window size and dilation factor, draws a spectrum of possible attention patterns between linear projection and self attention. Neighborhood attention, and more generally sliding window attention patterns, have long been bounded by infrastructure, particularly in higher-rank spaces (2-D and 3-D), calling for the development of custom kernels, which have been limited in either functionality, or performance, if not both. In this work, we first show that neighborhood attention can be represented as a batched GEMM problem, similar to standard attention, and implement it for 1-D and 2-D neighborhood attention. These kernels on average provide 895% and 272% improvement in full precision latency compared to existing naive kernels for 1-D and 2-D neighborhood attention respectively. We find certain inherent inefficiencies in all unfused neighborhood attention kernels that bound their performance and lower-precision scalability. We also developed fused neighborhood attention; an adaptation of fused dot-product attention kernels that allow fine-grained control over attention across different spatial axes. Known for reducing the quadratic time complexity of self attention to a linear complexity, neighborhood attention can now enjoy a reduced and constant memory footprint, and record-breaking half precision latency. We observe that our fused kernels successfully circumvent some of the unavoidable inefficiencies in unfused implementations. While our unfused GEMM-based kernels only improve half precision performance compared to naive kernels by an average of 496% and 113% in 1-D and 2-D problems respectively, our fused kernels improve naive kernels by an average of 1607% and 581% in 1-D and 2-D problems respectively.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

In standard Convolutional Neural Networks (CNNs), the receptive fields of artificial neurons in each layer are designed to share the same size. It is well-known in the neuroscience community that the receptive field size of visual cortical neurons are modulated by the stimulus, which has been rarely considered in constructing CNNs. We propose a dynamic selection mechanism in CNNs that allows each neuron to adaptively adjust its receptive field size based on multiple scales of input information. A building block called Selective Kernel (SK) unit is designed, in which multiple branches with different kernel sizes are fused using softmax attention that is guided by the information in these branches. Different attentions on these branches yield different sizes of the effective receptive fields of neurons in the fusion layer. Multiple SK units are stacked to a deep network termed Selective Kernel Networks (SKNets). On the ImageNet and CIFAR benchmarks, we empirically show that SKNet outperforms the existing state-of-the-art architectures with lower model complexity. Detailed analyses show that the neurons in SKNet can capture target objects with different scales, which verifies the capability of neurons for adaptively adjusting their receptive field sizes according to the input. The code and models are available at https://github.com/implus/SKNet.

Today's generative models are capable of synthesizing high-fidelity images, but each model specializes on a specific target domain. This raises the need for model merging: combining two or more pretrained generative models into a single unified one. In this work we tackle the problem of model merging, given two constraints that often come up in the real world: (1) no access to the original training data, and (2) without increasing the size of the neural network. To the best of our knowledge, model merging under these constraints has not been studied thus far. We propose a novel, two-stage solution. In the first stage, we transform the weights of all the models to the same parameter space by a technique we term model rooting. In the second stage, we merge the rooted models by averaging their weights and fine-tuning them for each specific domain, using only data generated by the original trained models. We demonstrate that our approach is superior to baseline methods and to existing transfer learning techniques, and investigate several applications.

Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, even fine-tuning the PLMs and doing inference are expensive, especially on edge devices with low computing power. Some general approaches (e.g. quantization and distillation) have been widely studied to reduce the compute/memory of PLM fine-tuning, while very few one-shot compression techniques are explored. In this paper, we investigate the neural tangent kernel (NTK)--which reveals the gradient descent dynamics of neural networks--of the multilayer perceptrons (MLP) modules in a PLM and propose to coin a lightweight PLM through NTK-approximating MLP fusion. To achieve this, we reconsider the MLP as a bundle of sub-MLPs, and cluster them into a given number of centroids, which can then be restored as a compressed MLP and surprisingly shown to well approximate the NTK of the original PLM. Extensive experiments of PLM fine-tuning on both natural language understanding (NLU) and generation (NLG) tasks are provided to verify the effectiveness of the proposed method MLP fusion. Our code is available at https://github.com/weitianxin/MLP_Fusion.

Pre-training models are an important tool in Natural Language Processing (NLP), while the BERT model is a classic pre-training model whose structure has been widely adopted by followers. It was even chosen as the reference model for the MLPerf training benchmark. The distributed training performance optimization of BERT models plays an important role in accelerating the solutions of most NLP tasks. BERT model often uses padding tensors as its inputs, leading to excessive redundant computations. Thus, removing these redundant computations is essential to improve the distributed training performance. This paper designs a new approach to train BERT models with variable-length inputs efficiently. Firstly, we propose a general structure for the variable-length BERT models, and accelerate the encoder layer via our grouped multi-stream FMHA (Fused Multi-Head Attention) method. Secondly, through data exchange, we address the unbalanced workload problem caused by the variable-length inputs, which overlaps highly with the training process. Finally, we optimize the overall performance of the BERT model, such as kernel fusion, and operator optimization. Our experimental results show that our highly optimized BERT model achieves state-of-the-art throughput and ranks first in MLPerf Training v2.0 within the same GPU configuration. The optimizations in this paper can be applied to more BERT-like models in our future works.

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice. A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which high bandwidth convolutional kernels of learnable kernel size can be learned at a fixed parameter cost. FlexNets model long-term dependencies without the use of pooling, achieve state-of-the-art performance on several sequential datasets, outperform recent works with learned kernel sizes, and are competitive with much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be deployed at higher resolutions than those seen during training. To avoid aliasing, we propose a novel kernel parameterization with which the frequency of the kernels can be analytically controlled. Our novel kernel parameterization shows higher descriptive power and faster convergence speed than existing parameterizations. This leads to important improvements in classification accuracy.

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

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a sudden increase in test accuracy, Grokking is also believed to be a beyond lazy-learning/Gaussian Process (GP) phenomenon involving feature learning. Here we apply a recent development in the theory of feature learning, the adaptive kernel approach, to two teacher-student models with cubic-polynomial and modular addition teachers. We provide analytical predictions on feature learning and Grokking properties of these models and demonstrate a mapping between Grokking and the theory of phase transitions. We show that after Grokking, the state of the DNN is analogous to the mixed phase following a first-order phase transition. In this mixed phase, the DNN generates useful internal representations of the teacher that are sharply distinct from those before the transition.

We present a method for making neural network predictions robust to shifts from the training data distribution. The proposed method is based on making predictions via a diverse set of cues (called 'middle domains') and ensembling them into one strong prediction. The premise of the idea is that predictions made via different cues respond differently to a distribution shift, hence one should be able to merge them into one robust final prediction. We perform the merging in a straightforward but principled manner based on the uncertainty associated with each prediction. The evaluations are performed using multiple tasks and datasets (Taskonomy, Replica, ImageNet, CIFAR) under a wide range of adversarial and non-adversarial distribution shifts which demonstrate the proposed method is considerably more robust than its standard learning counterpart, conventional deep ensembles, and several other baselines.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

This paper proposes the paradigm of large convolutional kernels in designing modern Convolutional Neural Networks (ConvNets). We establish that employing a few large kernels, instead of stacking multiple smaller ones, can be a superior design strategy. Our work introduces a set of architecture design guidelines for large-kernel ConvNets that optimize their efficiency and performance. We propose the UniRepLKNet architecture, which offers systematical architecture design principles specifically crafted for large-kernel ConvNets, emphasizing their unique ability to capture extensive spatial information without deep layer stacking. This results in a model that not only surpasses its predecessors with an ImageNet accuracy of 88.0%, an ADE20K mIoU of 55.6%, and a COCO box AP of 56.4% but also demonstrates impressive scalability and performance on various modalities such as time-series forecasting, audio, point cloud, and video recognition. These results indicate the universal modeling abilities of large-kernel ConvNets with faster inference speed compared with vision transformers. Our findings reveal that large-kernel ConvNets possess larger effective receptive fields and a higher shape bias, moving away from the texture bias typical of smaller-kernel CNNs. All codes and models are publicly available at https://github.com/AILab-CVC/UniRepLKNet promoting further research and development in the community.

Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the epsilon-neighbor kernel or the adjacency matrix of a graph. This work revisits the classical idea of spectrally transformed kernel regression (STKR), and provides a new class of general and scalable STKR estimators able to leverage unlabeled data. Intuitively, via spectral transformation, STKR exploits the data distribution for which unlabeled data can provide additional information. First, we show that STKR is a principled and general approach, by characterizing a universal type of "target smoothness", and proving that any sufficiently smooth function can be learned by STKR. Second, we provide scalable STKR implementations for the inductive setting and a general transformation function, while prior work is mostly limited to the transductive setting. Third, we derive statistical guarantees for two scenarios: STKR with a known polynomial transformation, and STKR with kernel PCA when the transformation is unknown. Overall, we believe that this work helps deepen our understanding of how to work with unlabeled data, and its generality makes it easier to inspire new methods.

Sequence Parallel (SP) serves as a prevalent strategy to handle long sequences that exceed the memory limit of a single GPU. However, existing SP methods do not take advantage of linear attention features, resulting in sub-optimal parallelism efficiency and usability for linear attention-based language models. In this paper, we introduce Linear Attention Sequence Parallel (LASP), an efficient SP method tailored to linear attention-based language models. Specifically, we design an efficient point-to-point communication mechanism to leverage the right-product kernel trick of linear attention, which sharply decreases the communication overhead of SP. We also enhance the practical efficiency of LASP by performing kernel fusion and intermediate state caching, making the implementation of LASP hardware-friendly on GPU clusters. Furthermore, we meticulously ensure the compatibility of sequence-level LASP with all types of batch-level data parallel methods, which is vital for distributed training on large clusters with long sequences and large batches. We conduct extensive experiments on two linear attention-based models with varying sequence lengths and GPU cluster sizes. LASP scales sequence length up to 4096K using 128 A100 80G GPUs on 1B models, which is 8 times longer than existing SP methods while being significantly faster. The code is available at https://github.com/OpenNLPLab/LASP.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

Efficiently supporting long context length is crucial for Transformer models. The quadratic complexity of the self-attention computation plagues traditional Transformers. Sliding window-based static sparse attention mitigates the problem by limiting the attention scope of the input tokens, reducing the theoretical complexity from quadratic to linear. Although the sparsity induced by window attention is highly structured, it does not align perfectly with the microarchitecture of the conventional accelerators, leading to suboptimal implementation. In response, we propose a dataflow-aware FPGA-based accelerator design, SWAT, that efficiently leverages the sparsity to achieve scalable performance for long input. The proposed microarchitecture is based on a design that maximizes data reuse by using a combination of row-wise dataflow, kernel fusion optimization, and an input-stationary design considering the distributed memory and computation resources of FPGA. Consequently, it achieves up to 22times and 5.7times improvement in latency and energy efficiency compared to the baseline FPGA-based accelerator and 15times energy efficiency compared to GPU-based solution.

Pose estimation plays a critical role in human-centered vision applications. However, it is difficult to deploy state-of-the-art HRNet-based pose estimation models on resource-constrained edge devices due to the high computational cost (more than 150 GMACs per frame). In this paper, we study efficient architecture design for real-time multi-person pose estimation on edge. We reveal that HRNet's high-resolution branches are redundant for models at the low-computation region via our gradual shrinking experiments. Removing them improves both efficiency and performance. Inspired by this finding, we design LitePose, an efficient single-branch architecture for pose estimation, and introduce two simple approaches to enhance the capacity of LitePose, including Fusion Deconv Head and Large Kernel Convs. Fusion Deconv Head removes the redundancy in high-resolution branches, allowing scale-aware feature fusion with low overhead. Large Kernel Convs significantly improve the model's capacity and receptive field while maintaining a low computational cost. With only 25% computation increment, 7x7 kernels achieve +14.0 mAP better than 3x3 kernels on the CrowdPose dataset. On mobile platforms, LitePose reduces the latency by up to 5.0x without sacrificing performance, compared with prior state-of-the-art efficient pose estimation models, pushing the frontier of real-time multi-person pose estimation on edge. Our code and pre-trained models are released at https://github.com/mit-han-lab/litepose.

Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

Merging has become a widespread way to cheaply combine individual models into a single model that inherits their capabilities and attains better performance. This popularity has spurred rapid development of many new merging methods, which are typically validated in disparate experimental settings and frequently differ in the assumptions made about model architecture, data availability, and computational budget. In this work, we characterize the relative merits of different merging methods by evaluating them in a shared experimental setting and precisely identifying the practical requirements of each method. Specifically, our setting focuses on using merging for compositional generalization of capabilities in image classification, image generation, and natural language processing. Additionally, we measure the computational costs of different merging methods as well as how they perform when scaling the number of models being merged. Taken together, our results clarify the state of the field of model merging and provide a comprehensive and rigorous experimental setup to test new methods.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

This study addresses the issue of fusing infrared and visible images that appear differently for object detection. Aiming at generating an image of high visual quality, previous approaches discover commons underlying the two modalities and fuse upon the common space either by iterative optimization or deep networks. These approaches neglect that modality differences implying the complementary information are extremely important for both fusion and subsequent detection task. This paper proposes a bilevel optimization formulation for the joint problem of fusion and detection, and then unrolls to a target-aware Dual Adversarial Learning (TarDAL) network for fusion and a commonly used detection network. The fusion network with one generator and dual discriminators seeks commons while learning from differences, which preserves structural information of targets from the infrared and textural details from the visible. Furthermore, we build a synchronized imaging system with calibrated infrared and optical sensors, and collect currently the most comprehensive benchmark covering a wide range of scenarios. Extensive experiments on several public datasets and our benchmark demonstrate that our method outputs not only visually appealing fusion but also higher detection mAP than the state-of-the-art approaches.

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

Recent advances in vision transformers (ViTs) have demonstrated the advantage of global modeling capabilities, prompting widespread integration of large-kernel convolutions for enlarging the effective receptive field (ERF). However, the quadratic scaling of parameter count and computational complexity (FLOPs) with respect to kernel size poses significant efficiency and optimization challenges. This paper introduces RecConv, a recursive decomposition strategy that efficiently constructs multi-frequency representations using small-kernel convolutions. RecConv establishes a linear relationship between parameter growth and decomposing levels which determines the effective kernel size ktimes 2^ell for a base kernel k and ell levels of decomposition, while maintaining constant FLOPs regardless of the ERF expansion. Specifically, RecConv achieves a parameter expansion of only ell+2 times and a maximum FLOPs increase of 5/3 times, compared to the exponential growth (4^ell) of standard and depthwise convolutions. RecNeXt-M3 outperforms RepViT-M1.1 by 1.9 AP^{box} on COCO with similar FLOPs. This innovation provides a promising avenue towards designing efficient and compact networks across various modalities. Codes and models can be found at https://github.com/suous/RecNeXt.

Large-kernel convolutional neural networks (ConvNets) have recently received extensive research attention, but there are two unresolved and critical issues that demand further investigation. 1) The architectures of existing large-kernel ConvNets largely follow the design principles of conventional ConvNets or transformers, while the architectural design for large-kernel ConvNets remains under-addressed. 2) As transformers have dominated multiple modalities, it remains to be investigated whether ConvNets also have a strong universal perception ability in domains beyond vision. In this paper, we contribute from two aspects. 1) We propose four architectural guidelines for designing large-kernel ConvNets, the core of which is to exploit the essential characteristics of large kernels that distinguish them from small kernels - they can see wide without going deep. Following such guidelines, our proposed large-kernel ConvNet shows leading performance in image recognition. For example, our models achieve an ImageNet accuracy of 88.0%, ADE20K mIoU of 55.6%, and COCO box AP of 56.4%, demonstrating better performance and higher speed than a number of recently proposed powerful competitors. 2) We discover that large kernels are the key to unlocking the exceptional performance of ConvNets in domains where they were originally not proficient. With certain modality-related preprocessing approaches, the proposed model achieves state-of-the-art performance on time-series forecasting and audio recognition tasks even without modality-specific customization to the architecture. Code and all the models at https://github.com/AILab-CVC/UniRepLKNet.

Mammalian brains handle complex reasoning tasks in a gestalt manner by integrating information from regions of the brain that are specialised to individual sensory modalities. This allows for improved robustness and better generalisation ability. In contrast, deep neural networks are usually designed to process one particular information stream and susceptible to various types of adversarial perturbations. While many methods exist for detecting and defending against adversarial attacks, they do not generalise across a range of attacks and negatively affect performance on clean, unperturbed data. We developed a fusion model using a combination of background and foreground features extracted in parallel from Places-CNN and Imagenet-CNN. We tested the benefits of the fusion approach on preserving adversarial robustness for human perceivable (e.g., Gaussian blur) and network perceivable (e.g., gradient-based) attacks for CIFAR-10 and MS COCO data sets. For gradient based attacks, our results show that fusion allows for significant improvements in classification without decreasing performance on unperturbed data and without need to perform adversarial retraining. Our fused model revealed improvements for Gaussian blur type perturbations as well. The increase in performance from fusion approach depended on the variability of the image contexts; larger increases were seen for classes of images with larger differences in their contexts. We also demonstrate the effect of regularization to bias the classifier decision in the presence of a known adversary. We propose that this biologically inspired approach to integrate information across multiple modalities provides a new way to improve adversarial robustness that can be complementary to current state of the art approaches.

Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

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.

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f_theta (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function f_theta follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

Infrared and visible image fusion is a powerful technique that combines complementary information from different modalities for downstream semantic perception tasks. Existing learning-based methods show remarkable performance, but are suffering from the inherent vulnerability of adversarial attacks, causing a significant decrease in accuracy. In this work, a perception-aware fusion framework is proposed to promote segmentation robustness in adversarial scenes. We first conduct systematic analyses about the components of image fusion, investigating the correlation with segmentation robustness under adversarial perturbations. Based on these analyses, we propose a harmonized architecture search with a decomposition-based structure to balance standard accuracy and robustness. We also propose an adaptive learning strategy to improve the parameter robustness of image fusion, which can learn effective feature extraction under diverse adversarial perturbations. Thus, the goals of image fusion (i.e., extracting complementary features from source modalities and defending attack) can be realized from the perspectives of architectural and learning strategies. Extensive experimental results demonstrate that our scheme substantially enhances the robustness, with gains of 15.3% mIOU of segmentation in the adversarial scene, compared with advanced competitors. The source codes are available at https://github.com/LiuZhu-CV/PAIF.

The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of discarding residual learning by employing large implicit kernels to achieve full context interaction at each layer of the network. To accomplish it, we introduce coordinate-based implicit MLPs as a slow network to generate hyper-kernels for another fast convolutional network. To get context-varying weights for fast dynamic encoding, we propose a HyperZ{cdotZ{cdot}W} operator that connects hyper-kernels (W) and hidden activations (Z) through simple elementwise multiplication, followed by convolution of Z using the context-dependent W. Based on this design, we present a novel Terminator architecture that integrates hyper-kernels of different sizes to produce multi-branch hidden representations for enhancing the feature extraction capability of each layer. Additionally, a bottleneck layer is employed to compress the concatenated channels, allowing only valuable information to propagate to the subsequent layers. Notably, our model incorporates several innovative components and exhibits excellent properties, such as introducing local feedback error for updating the slow network, stable zero-mean features, faster training convergence, and fewer model parameters. Extensive experimental results on pixel-level 1D and 2D image classification benchmarks demonstrate the superior performance of our architecture.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

This paper focuses on solving a fault detection problem using multivariate time series of vibration signals collected from planetary gearboxes in a test rig. Various traditional machine learning and deep learning methods have been proposed for multivariate time-series classification, including distance-based, functional data-oriented, feature-driven, and convolution kernel-based methods. Recent studies have shown using convolution kernel-based methods like ROCKET, and 1D convolutional neural networks with ResNet and FCN, have robust performance for multivariate time-series data classification. We propose an ensemble of three convolution kernel-based methods and show its efficacy on this fault detection problem by outperforming other approaches and achieving an accuracy of more than 98.8\%.

We tackle the problem of single-image Human Mesh Recovery (HMR). Previous approaches are mostly based on a single crop. In this paper, we shift the single-crop HMR to a novel multiple-crop HMR paradigm. Cropping a human from image multiple times by shifting and scaling the original bounding box is feasible in practice, easy to implement, and incurs neglectable cost, but immediately enriches available visual details. With multiple crops as input, we manage to leverage the relation among these crops to extract discriminative features and reduce camera ambiguity. Specifically, (1) we incorporate a contrastive learning scheme to enhance the similarity between features extracted from crops of the same human. (2) We also propose a crop-aware fusion scheme to fuse the features of multiple crops for regressing the target mesh. (3) We compute local cameras for all the input crops and build a camera-consistency loss between the local cameras, which reward us with less ambiguous cameras. Based on the above innovations, our proposed method outperforms previous approaches as demonstrated by the extensive experiments.

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Merging various task-specific Transformer-based models trained on different tasks into a single unified model can execute all the tasks concurrently. Previous methods, exemplified by task arithmetic, have been proven to be both effective and scalable. Existing methods have primarily focused on seeking a static optimal solution within the original model parameter space. A notable challenge is mitigating the interference between parameters of different models, which can substantially deteriorate performance. In this paper, we propose to merge most of the parameters while upscaling the MLP of the Transformer layers to a weight-ensembling mixture of experts (MoE) module, which can dynamically integrate shared and task-specific knowledge based on the input, thereby providing a more flexible solution that can adapt to the specific needs of each instance. Our key insight is that by identifying and separating shared knowledge and task-specific knowledge, and then dynamically integrating them, we can mitigate the parameter interference problem to a great extent. We conduct the conventional multi-task model merging experiments and evaluate the generalization and robustness of our method. The results demonstrate the effectiveness of our method and provide a comprehensive understanding of our method. The code is available at https://anonymous.4open.science/r/weight-ensembling_MoE-67C9/

Generalized Few-shot Semantic Segmentation (GFSS) extends Few-shot Semantic Segmentation (FSS) to simultaneously segment unseen classes and seen classes during evaluation. Previous works leverage additional branch or prototypical aggregation to eliminate the constrained setting of FSS. However, representation division and embedding prejudice, which heavily results in poor performance of GFSS, have not been synthetical considered. We address the aforementioned problems by jointing the prototypical kernel learning and open-set foreground perception. Specifically, a group of learnable kernels is proposed to perform segmentation with each kernel in charge of a stuff class. Then, we explore to merge the prototypical learning to the update of base-class kernels, which is consistent with the prototype knowledge aggregation of few-shot novel classes. In addition, a foreground contextual perception module cooperating with conditional bias based inference is adopted to perform class-agnostic as well as open-set foreground detection, thus to mitigate the embedding prejudice and prevent novel targets from being misclassified as background. Moreover, we also adjust our method to the Class Incremental Few-shot Semantic Segmentation (CIFSS) which takes the knowledge of novel classes in a incremental stream. Extensive experiments on PASCAL-5i and COCO-20i datasets demonstrate that our method performs better than previous state-of-the-art.

Sliding Window Sum algorithms have been successfully used for training and inference of Deep Neural Networks. We have shown before how both pooling and convolution 1-D primitives could be expressed as sliding sums and evaluated by the compute kernels with a shared structure. In this paper, we present an extensive study of the Sliding Window convolution technique as a more efficient alternative to the commonly used General Matrix Multiplication (GEMM) based convolution in Deep Neural Networks (DNNs). The Sliding Window technique addresses the memory bloating problem and demonstrates a significant speedup in 2-D convolution. We explore the performance of this technique on a range of implementations, including custom kernels for specific filter sizes. Our results suggest that the Sliding Window computation kernels can outperform GEMM-based convolution on a CPU and even on dedicated hardware accelerators. This could promote a wider adoption of AI on low-power and low-memory devices without the need for specialized hardware. We also discuss the compatibility of model compression methods and optimized network architectures with the Sliding Window technique, encouraging further research in these areas.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distributions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distributions. The mixtures are fitted, via online-EM methods, to the optimal kernel through minimisation of the Kullback-Leibler divergence between the auxiliary target and instrumental distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimisation problem for the whole particle sample, yielding an algorithm with only linear complexity. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space models.

Effective fusion of multi-scale features is crucial for improving speaker verification performance. While most existing methods aggregate multi-scale features in a layer-wise manner via simple operations, such as summation or concatenation. This paper proposes a novel architecture called Enhanced Res2Net (ERes2Net), which incorporates both local and global feature fusion techniques to improve the performance. The local feature fusion (LFF) fuses the features within one single residual block to extract the local signal. The global feature fusion (GFF) takes acoustic features of different scales as input to aggregate global signal. To facilitate effective feature fusion in both LFF and GFF, an attentional feature fusion module is employed in the ERes2Net architecture, replacing summation or concatenation operations. A range of experiments conducted on the VoxCeleb datasets demonstrate the superiority of the ERes2Net in speaker verification. Code has been made publicly available at https://github.com/alibaba-damo-academy/3D-Speaker.

We abstract the features (i.e. learned representations) of multi-modal data into 1) uni-modal features, which can be learned from uni-modal training, and 2) paired features, which can only be learned from cross-modal interactions. Multi-modal models are expected to benefit from cross-modal interactions on the basis of ensuring uni-modal feature learning. However, recent supervised multi-modal late-fusion training approaches still suffer from insufficient learning of uni-modal features on each modality. We prove that this phenomenon does hurt the model's generalization ability. To this end, we propose to choose a targeted late-fusion learning method for the given supervised multi-modal task from Uni-Modal Ensemble(UME) and the proposed Uni-Modal Teacher(UMT), according to the distribution of uni-modal and paired features. We demonstrate that, under a simple guiding strategy, we can achieve comparable results to other complex late-fusion or intermediate-fusion methods on various multi-modal datasets, including VGG-Sound, Kinetics-400, UCF101, and ModelNet40.

Multispectral images (e.g. visible and infrared) may be particularly useful when detecting objects with the same model in different environments (e.g. day/night outdoor scenes). To effectively use the different spectra, the main technical problem resides in the information fusion process. In this paper, we propose a new halfway feature fusion method for neural networks that leverages the complementary/consistency balance existing in multispectral features by adding to the network architecture, a particular module that cyclically fuses and refines each spectral feature. We evaluate the effectiveness of our fusion method on two challenging multispectral datasets for object detection. Our results show that implementing our Cyclic Fuse-and-Refine module in any network improves the performance on both datasets compared to other state-of-the-art multispectral object detection methods.

We develop a multiexposure image fusion method based on texture features, which exploits the edge preserving and intraregion smoothing property of nonlinear diffusion filters based on partial differential equations (PDE). With the captured multiexposure image series, we first decompose images into base layers and detail layers to extract sharp details and fine details, respectively. The magnitude of the gradient of the image intensity is utilized to encourage smoothness at homogeneous regions in preference to inhomogeneous regions. Then, we have considered texture features of the base layer to generate a mask (i.e., decision mask) that guides the fusion of base layers in multiresolution fashion. Finally, well-exposed fused image is obtained that combines fused base layer and the detail layers at each scale across all the input exposures. Proposed algorithm skipping complex High Dynamic Range Image (HDRI) generation and tone mapping steps to produce detail preserving image for display on standard dynamic range display devices. Moreover, our technique is effective for blending flash/no-flash image pair and multifocus images, that is, images focused on different targets.

Learning holistic computational representations in physical, chemical or biological systems requires the ability to process information from different distributions and modalities within the same model. Thus, the demand for multimodal machine learning models has sharply risen for modalities that go beyond vision and language, such as sequences, graphs, time series, or tabular data. While there are many available multimodal fusion and alignment approaches, most of them require end-to-end training, scale quadratically with the number of modalities, cannot handle cases of high modality imbalance in the training set, or are highly topology-specific, making them too restrictive for many biomedical learning tasks. This paper presents Multimodal Lego (MM-Lego), a modular and general-purpose fusion and model merging framework to turn any set of encoders into a competitive multimodal model with no or minimal fine-tuning. We achieve this by introducing a wrapper for unimodal encoders that enforces lightweight dimensionality assumptions between modalities and harmonises their representations by learning features in the frequency domain to enable model merging with little signal interference. We show that MM-Lego 1) can be used as a model merging method which achieves competitive performance with end-to-end fusion models without any fine-tuning, 2) can operate on any unimodal encoder, and 3) is a model fusion method that, with minimal fine-tuning, achieves state-of-the-art results on six benchmarked multimodal biomedical tasks.

In recent years, analysis of remote sensing data has benefited immensely from borrowing techniques from the broader field of computer vision, such as the use of shared models pre-trained on large and diverse datasets. However, satellite imagery has unique features that are not accounted for in traditional computer vision, such as the existence of multiple revisits of the same location. Here, we explore the best way to use revisits in the framework of fine-tuning pre-trained remote sensing models. We focus on an applied research question of relevance to climate change mitigation -- power substation segmentation -- that is representative of applied uses of pre-trained models more generally. Through extensive tests of different multi-temporal input schemes across diverse model architectures, we find that fusing representations from multiple revisits in the model latent space is superior to other methods of using revisits, including as a form of data augmentation. We also find that a SWIN Transformer-based architecture performs better than U-nets and ViT-based models. We verify the generality of our results on a separate building density estimation task.

COMpression with Bayesian Implicit NEural Representations (COMBINER) is a recent data compression method that addresses a key inefficiency of previous Implicit Neural Representation (INR)-based approaches: it avoids quantization and enables direct optimization of the rate-distortion performance. However, COMBINER still has significant limitations: 1) it uses factorized priors and posterior approximations that lack flexibility; 2) it cannot effectively adapt to local deviations from global patterns in the data; and 3) its performance can be susceptible to modeling choices and the variational parameters' initializations. Our proposed method, Robust and Enhanced COMBINER (RECOMBINER), addresses these issues by 1) enriching the variational approximation while retaining a low computational cost via a linear reparameterization of the INR weights, 2) augmenting our INRs with learnable positional encodings that enable them to adapt to local details and 3) splitting high-resolution data into patches to increase robustness and utilizing expressive hierarchical priors to capture dependency across patches. We conduct extensive experiments across several data modalities, showcasing that RECOMBINER achieves competitive results with the best INR-based methods and even outperforms autoencoder-based codecs on low-resolution images at low bitrates. Our PyTorch implementation is available at https://github.com/cambridge-mlg/RECOMBINER/.

Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper, we investigate the key characteristics of task matrices -- weight update matrices applied to a pre-trained model -- that enable effective merging. We show that alignment between singular components of task-specific and merged matrices strongly correlates with performance improvement over the pre-trained model. Based on this, we propose an isotropic merging framework that flattens the singular value spectrum of task matrices, enhances alignment, and reduces the performance gap. Additionally, we incorporate both common and task-specific subspaces to further improve alignment and performance. Our proposed approach achieves state-of-the-art performance across multiple scenarios, including various sets of tasks and model scales. This work advances the understanding of model merging dynamics, offering an effective methodology to merge models without requiring additional training. Code is available at https://github.com/danielm1405/iso-merging .

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to ell_2 regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

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.

Malware has become a formidable threat as it has been growing exponentially in number and sophistication, thus, it is imperative to have a solution that is easy to implement, reliable, and effective. While recent research has introduced deep learning multi-feature fusion algorithms, they lack a proper explanation. In this work, we investigate the power of fusing Convolutional Neural Network models trained on different modalities of a malware executable. We are proposing a novel multimodal fusion algorithm, leveraging three different visual malware features: Grayscale Image, Entropy Graph, and SimHash Image, with which we conducted exhaustive experiments independently on each feature and combinations of all three of them using fusion operators such as average, maximum, add, and concatenate for effective malware detection and classification. The proposed strategy has a detection rate of 1.00 (on a scale of 0-1) in identifying malware in the given dataset. We explained its interpretability with visualization techniques such as t-SNE and Grad-CAM. Experimental results show the model works even for a highly imbalanced dataset. We also assessed the effectiveness of the proposed method on obfuscated malware and achieved state-of-the-art results. The proposed methodology is more reliable as our findings prove VGG16 model can detect and classify malware in a matter of seconds in real-time.

Text-to-image diffusion models have made significant advances in generating and editing high-quality images. As a result, numerous approaches have explored the ability of diffusion model features to understand and process single images for downstream tasks, e.g., classification, semantic segmentation, and stylization. However, significantly less is known about what these features reveal across multiple, different images and objects. In this work, we exploit Stable Diffusion (SD) features for semantic and dense correspondence and discover that with simple post-processing, SD features can perform quantitatively similar to SOTA representations. Interestingly, the qualitative analysis reveals that SD features have very different properties compared to existing representation learning features, such as the recently released DINOv2: while DINOv2 provides sparse but accurate matches, SD features provide high-quality spatial information but sometimes inaccurate semantic matches. We demonstrate that a simple fusion of these two features works surprisingly well, and a zero-shot evaluation using nearest neighbors on these fused features provides a significant performance gain over state-of-the-art methods on benchmark datasets, e.g., SPair-71k, PF-Pascal, and TSS. We also show that these correspondences can enable interesting applications such as instance swapping in two images.

Recent research on remote sensing object detection has largely focused on improving the representation of oriented bounding boxes but has overlooked the unique prior knowledge presented in remote sensing scenarios. Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, and the long-range context required by different types of objects can vary. In this paper, we take these priors into account and propose the Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To the best of our knowledge, this is the first time that large and selective kernel mechanisms have been explored in the field of remote sensing object detection. Without bells and whistles, LSKNet sets new state-of-the-art scores on standard benchmarks, i.e., HRSC2016 (98.46\% mAP), DOTA-v1.0 (81.85\% mAP) and FAIR1M-v1.0 (47.87\% mAP). Based on a similar technique, we rank 2nd place in 2022 the Greater Bay Area International Algorithm Competition. Code is available at https://github.com/zcablii/Large-Selective-Kernel-Network.

Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks. Recent research, exemplified by task arithmetic, highlights that this multi-task model can be derived through arithmetic operations on task vectors. Nevertheless, current merging techniques frequently resolve potential conflicts among parameters from task-specific models by evaluating individual attributes, such as the parameters' magnitude or sign, overlooking their collective impact on the overall functionality of the model. In this work, we propose the CONtinuous relaxation of disCRETE (Concrete) subspace learning method to identify a common low-dimensional subspace and utilize its shared information to track the interference problem without sacrificing much performance. Specifically, we model the problem as a bi-level optimization problem and introduce a meta-learning framework to find the Concrete subspace mask through gradient-based techniques. At the upper level, we focus on learning a shared Concrete mask to identify the subspace, while at the inner level, model merging is performed to maximize the performance of the merged model. We conduct extensive experiments on both vision domain and language domain, and the results demonstrate the effectiveness of our method. The code is available at https://github.com/tanganke/subspace_fusion

We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal circumstances, via a likelihood-ratio hypothesis test. The model is based on a modern implementation of kernel methods, nonparametric algorithms that can learn any continuous function given enough data. The resulting approach is efficient and agnostic to the type of anomaly that may be present in the data. Our study demonstrates the effectiveness of this strategy on multivariate data from drift tube chamber muon detectors.

Layer-wise model fusion via optimal transport, named OTFusion, applies soft neuron association for unifying different pre-trained networks to save computational resources. While enjoying its success, OTFusion requires the input networks to have the same number of layers. To address this issue, we propose a novel model fusion framework, named CLAFusion, to fuse neural networks with a different number of layers, which we refer to as heterogeneous neural networks, via cross-layer alignment. The cross-layer alignment problem, which is an unbalanced assignment problem, can be solved efficiently using dynamic programming. Based on the cross-layer alignment, our framework balances the number of layers of neural networks before applying layer-wise model fusion. Our experiments indicate that CLAFusion, with an extra finetuning process, improves the accuracy of residual networks on the CIFAR10, CIFAR100, and Tiny-ImageNet datasets. Furthermore, we explore its practical usage for model compression and knowledge distillation when applying to the teacher-student setting.

There has been significant progress in Masked Image Modeling (MIM). Existing MIM methods can be broadly categorized into two groups based on the reconstruction target: pixel-based and tokenizer-based approaches. The former offers a simpler pipeline and lower computational cost, but it is known to be biased toward high-frequency details. In this paper, we provide a set of empirical studies to confirm this limitation of pixel-based MIM and propose a new method that explicitly utilizes low-level features from shallow layers to aid pixel reconstruction. By incorporating this design into our base method, MAE, we reduce the wasted modeling capability of pixel-based MIM, improving its convergence and achieving non-trivial improvements across various downstream tasks. To the best of our knowledge, we are the first to systematically investigate multi-level feature fusion for isotropic architectures like the standard Vision Transformer (ViT). Notably, when applied to a smaller model (e.g., ViT-S), our method yields significant performance gains, such as 1.2\% on fine-tuning, 2.8\% on linear probing, and 2.6\% on semantic segmentation. Code and models are available at https://github.com/open-mmlab/mmpretrain.

Deep models have achieved significant process on single image super-resolution (SISR) tasks, in particular large models with large kernel (3times3 or more). However, the heavy computational footprint of such models prevents their deployment in real-time, resource-constrained environments. Conversely, 1times1 convolutions bring substantial computational efficiency, but struggle with aggregating local spatial representations, an essential capability to SISR models. In response to this dichotomy, we propose to harmonize the merits of both 3times3 and 1times1 kernels, and exploit a great potential for lightweight SISR tasks. Specifically, we propose a simple yet effective fully 1times1 convolutional network, named Shift-Conv-based Network (SCNet). By incorporating a parameter-free spatial-shift operation, it equips the fully 1times1 convolutional network with powerful representation capability while impressive computational efficiency. Extensive experiments demonstrate that SCNets, despite its fully 1times1 convolutional structure, consistently matches or even surpasses the performance of existing lightweight SR models that employ regular convolutions.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs). Despite the introduction of linear-complexity variant, applying attention to a large number of grid points can result in instability and is still expensive to compute. In this work, we propose Factorized Transformer(FactFormer), which is based on an axial factorized kernel integral. Concretely, we introduce a learnable projection operator that decomposes the input function into multiple sub-functions with one-dimensional domain. These sub-functions are then evaluated and used to compute the instance-based kernel with an axial factorized scheme. We showcase that the proposed model is able to simulate 2D Kolmogorov flow on a 256 by 256 grid and 3D smoke buoyancy on a 64 by 64 by 64 grid with good accuracy and efficiency. In addition, we find out that with the factorization scheme, the attention matrices enjoy a more compact spectrum than full softmax-free attention matrices.

With the rapid advancement of Internet technology, the threat of malware to computer systems and network security has intensified. Malware affects individual privacy and security and poses risks to critical infrastructures of enterprises and nations. The increasing quantity and complexity of malware, along with its concealment and diversity, challenge traditional detection techniques. Static detection methods struggle against variants and packed malware, while dynamic methods face high costs and risks that limit their application. Consequently, there is an urgent need for novel and efficient malware detection techniques to improve accuracy and robustness. This study first employs the minhash algorithm to convert binary files of malware into grayscale images, followed by the extraction of global and local texture features using GIST and LBP algorithms. Additionally, the study utilizes IDA Pro to decompile and extract opcode sequences, applying N-gram and tf-idf algorithms for feature vectorization. The fusion of these features enables the model to comprehensively capture the behavioral characteristics of malware. In terms of model construction, a CNN-BiLSTM fusion model is designed to simultaneously process image features and opcode sequences, enhancing classification performance. Experimental validation on multiple public datasets demonstrates that the proposed method significantly outperforms traditional detection techniques in terms of accuracy, recall, and F1 score, particularly in detecting variants and obfuscated malware with greater stability. The research presented in this paper offers new insights into the development of malware detection technologies, validating the effectiveness of feature and model fusion, and holds promising application prospects.

An important and unsolved problem in computer vision is to ensure that the algorithms are robust to changes in image domains. We address this problem in the scenario where we have access to images from the target domains but no annotations. Motivated by the challenges of the OOD-CV benchmark where we encounter real world Out-of-Domain (OOD) nuisances and occlusion, we introduce a novel Bayesian approach to OOD robustness for object classification. Our work extends Compositional Neural Networks (CompNets), which have been shown to be robust to occlusion but degrade badly when tested on OOD data. We exploit the fact that CompNets contain a generative head defined over feature vectors represented by von Mises-Fisher (vMF) kernels, which correspond roughly to object parts, and can be learned without supervision. We obverse that some vMF kernels are similar between different domains, while others are not. This enables us to learn a transitional dictionary of vMF kernels that are intermediate between the source and target domains and train the generative model on this dictionary using the annotations on the source domain, followed by iterative refinement. This approach, termed Unsupervised Generative Transition (UGT), performs very well in OOD scenarios even when occlusion is present. UGT is evaluated on different OOD benchmarks including the OOD-CV dataset, several popular datasets (e.g., ImageNet-C [9]), artificial image corruptions (including adding occluders), and synthetic-to-real domain transfer, and does well in all scenarios outperforming SOTA alternatives (e.g. up to 10% top-1 accuracy on Occluded OOD-CV dataset).

Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abundance of training data, is vulnerable to out-of-distribution blurs and images. To address this challenge, we suggest a dataset-free deep residual prior for the kernel induced error (termed as residual) expressed by a customized untrained deep neural network, which allows us to flexibly adapt to different blurs and images in real scenarios. By organically integrating the respective strengths of deep priors and hand-crafted priors, we propose an unsupervised semi-blind deblurring model which recovers the latent image from the blurry image and inaccurate blur kernel. To tackle the formulated model, an efficient alternating minimization algorithm is developed. Extensive experiments demonstrate the favorable performance of the proposed method as compared to data-driven and model-driven methods in terms of image quality and the robustness to the kernel error.

Convolutional layers are one of the basic building blocks of modern deep neural networks. One fundamental assumption is that convolutional kernels should be shared for all examples in a dataset. We propose conditionally parameterized convolutions (CondConv), which learn specialized convolutional kernels for each example. Replacing normal convolutions with CondConv enables us to increase the size and capacity of a network, while maintaining efficient inference. We demonstrate that scaling networks with CondConv improves the performance and inference cost trade-off of several existing convolutional neural network architectures on both classification and detection tasks. On ImageNet classification, our CondConv approach applied to EfficientNet-B0 achieves state-of-the-art performance of 78.3% accuracy with only 413M multiply-adds. Code and checkpoints for the CondConv Tensorflow layer and CondConv-EfficientNet models are available at: https://github.com/tensorflow/tpu/tree/master/models/official/efficientnet/condconv.

Structural pruning of neural networks conventionally relies on identifying and discarding less important neurons, a practice often resulting in significant accuracy loss that necessitates subsequent fine-tuning efforts. This paper introduces a novel approach named Intra-Fusion, challenging this prevailing pruning paradigm. Unlike existing methods that focus on designing meaningful neuron importance metrics, Intra-Fusion redefines the overlying pruning procedure. Through utilizing the concepts of model fusion and Optimal Transport, we leverage an agnostically given importance metric to arrive at a more effective sparse model representation. Notably, our approach achieves substantial accuracy recovery without the need for resource-intensive fine-tuning, making it an efficient and promising tool for neural network compression. Additionally, we explore how fusion can be added to the pruning process to significantly decrease the training time while maintaining competitive performance. We benchmark our results for various networks on commonly used datasets such as CIFAR-10, CIFAR-100, and ImageNet. More broadly, we hope that the proposed Intra-Fusion approach invigorates exploration into a fresh alternative to the predominant compression approaches. Our code is available here: https://github.com/alexandertheus/Intra-Fusion.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.

Convolutional neural networks (CNNs) have been the consensus for medical image segmentation tasks. However, they suffer from the limitation in modeling long-range dependencies and spatial correlations due to the nature of convolution operation. Although transformers were first developed to address this issue, they fail to capture low-level features. In contrast, it is demonstrated that both local and global features are crucial for dense prediction, such as segmenting in challenging contexts. In this paper, we propose HiFormer, a novel method that efficiently bridges a CNN and a transformer for medical image segmentation. Specifically, we design two multi-scale feature representations using the seminal Swin Transformer module and a CNN-based encoder. To secure a fine fusion of global and local features obtained from the two aforementioned representations, we propose a Double-Level Fusion (DLF) module in the skip connection of the encoder-decoder structure. Extensive experiments on various medical image segmentation datasets demonstrate the effectiveness of HiFormer over other CNN-based, transformer-based, and hybrid methods in terms of computational complexity, and quantitative and qualitative results. Our code is publicly available at: https://github.com/amirhossein-kz/HiFormer

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.

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

Generative Adversarial Networks (GANs) can generate near photo realistic images in narrow domains such as human faces. Yet, modeling complex distributions of datasets such as ImageNet and COCO-Stuff remains challenging in unconditional settings. In this paper, we take inspiration from kernel density estimation techniques and introduce a non-parametric approach to modeling distributions of complex datasets. We partition the data manifold into a mixture of overlapping neighborhoods described by a datapoint and its nearest neighbors, and introduce a model, called instance-conditioned GAN (IC-GAN), which learns the distribution around each datapoint. Experimental results on ImageNet and COCO-Stuff show that IC-GAN significantly improves over unconditional models and unsupervised data partitioning baselines. Moreover, we show that IC-GAN can effortlessly transfer to datasets not seen during training by simply changing the conditioning instances, and still generate realistic images. Finally, we extend IC-GAN to the class-conditional case and show semantically controllable generation and competitive quantitative results on ImageNet; while improving over BigGAN on ImageNet-LT. Code and trained models to reproduce the reported results are available at https://github.com/facebookresearch/ic_gan.

State space models (SSMs) have high performance on long sequence modeling but require sophisticated initialization techniques and specialized implementations for high quality and runtime performance. We study whether a simple alternative can match SSMs in performance and efficiency: directly learning long convolutions over the sequence. We find that a key requirement to achieving high performance is keeping the convolution kernels smooth. We find that simple interventions--such as squashing the kernel weights--result in smooth kernels and recover SSM performance on a range of tasks including the long range arena, image classification, language modeling, and brain data modeling. Next, we develop FlashButterfly, an IO-aware algorithm to improve the runtime performance of long convolutions. FlashButterfly appeals to classic Butterfly decompositions of the convolution to reduce GPU memory IO and increase FLOP utilization. FlashButterfly speeds up convolutions by 2.2times, and allows us to train on Path256, a challenging task with sequence length 64K, where we set state-of-the-art by 29.1 points while training 7.2times faster than prior work. Lastly, we introduce an extension to FlashButterfly that learns the coefficients of the Butterfly decomposition, increasing expressivity without increasing runtime. Using this extension, we outperform a Transformer on WikiText103 by 0.2 PPL with 30% fewer parameters.

Variational inference (VI) seeks to approximate a target distribution pi by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates pi by minimizing the Kullback-Leibler (KL) divergence to pi over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when pi is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when pi is only log-smooth.

Multi-modality image fusion is a technique that combines information from different sensors or modalities, enabling the fused image to retain complementary features from each modality, such as functional highlights and texture details. However, effective training of such fusion models is challenging due to the scarcity of ground truth fusion data. To tackle this issue, we propose the Equivariant Multi-Modality imAge fusion (EMMA) paradigm for end-to-end self-supervised learning. Our approach is rooted in the prior knowledge that natural imaging responses are equivariant to certain transformations. Consequently, we introduce a novel training paradigm that encompasses a fusion module, a pseudo-sensing module, and an equivariant fusion module. These components enable the net training to follow the principles of the natural sensing-imaging process while satisfying the equivariant imaging prior. Extensive experiments confirm that EMMA yields high-quality fusion results for infrared-visible and medical images, concurrently facilitating downstream multi-modal segmentation and detection tasks. The code is available at https://github.com/Zhaozixiang1228/MMIF-EMMA.

Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its latent functions. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness and the interpretability of MTGP. Specifically, we express the interaction as a product of function interaction and coefficient interaction. The function interaction is modeled by using cross convolution of latent functions. The coefficient interaction between the LMCs is described as a cross coregionalization term. We validate that considering the interactions can promote knowledge transferring in MTGP and compare our approach with some state-of-the-art MTGPs on both synthetic- and real-world datasets.

In recent years, the use of large convolutional kernels has become popular in designing convolutional neural networks due to their ability to capture long-range dependencies and provide large receptive fields. However, the increase in kernel size also leads to a quadratic growth in the number of parameters, resulting in heavy computation and memory requirements. To address this challenge, we propose a neighborhood attention (NA) module that upgrades the standard convolution with a self-attention mechanism. The NA module efficiently extracts long-range dependencies in a sliding window pattern, thereby achieving similar performance to large convolutional kernels but with fewer parameters. Building upon the NA module, we propose a lightweight single image super-resolution (SISR) network named TCSR. Additionally, we introduce an enhanced feed-forward network (EFFN) in TCSR to improve the SISR performance. EFFN employs a parameter-free spatial-shift operation for efficient feature aggregation. Our extensive experiments and ablation studies demonstrate that TCSR outperforms existing lightweight SISR methods and achieves state-of-the-art performance. Our codes are available at https://github.com/Aitical/TCSR.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.

Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the development of approximating the self-attention at linear complexity. However, an in-depth analysis in this work reveals that existing methods are either theoretically flawed or empirically ineffective for visual recognition. We identify that their limitations are rooted in the inheritance of softmax-based self-attention during approximations, that is, normalizing the scaled dot-product between token feature vectors using the softmax function. As preserving the softmax operation challenges any subsequent linearization efforts. By this insight, a family of Softmax-Free Transformers (SOFT) are proposed. Specifically, a Gaussian kernel function is adopted to replace the dot-product similarity, enabling a full self-attention matrix to be approximated under low-rank matrix decomposition. For computational robustness, we estimate the Moore-Penrose inverse using an iterative Newton-Raphson method in the forward process only, while calculating its theoretical gradients only once in the backward process. To further expand applicability (e.g., dense prediction tasks), an efficient symmetric normalization technique is introduced. Extensive experiments on ImageNet, COCO, and ADE20K show that our SOFT significantly improves the computational efficiency of existing ViT variants. With linear complexity, much longer token sequences are permitted by SOFT, resulting in superior trade-off between accuracy and complexity. Code and models are available at https://github.com/fudan-zvg/SOFT.

We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear features without fussiness. Our merging thus benefits from past work that can optimize for either goal individually, yet typically by sacrificing the other. The new possibility of combining any two distributions using different distance field functions and their parameters also allows us to produce a vast range of stippling styles, which we demonstrate as well.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters.

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in R^d, where in addition to the m independent and labeled samples from the true distribution, a set of n (usually with ngg m) out of domain and unlabeled samples are given as well. Using only the labeled data, it is known that the generalization error can be bounded by proptoleft(d/mright)^{1/2}. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared to ERM. Our results underscore two significant insights: 1) out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the ``cluster assumption", and 2) the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

Convolutions (Convs) and multi-head self-attentions (MHSAs) are typically considered alternatives to each other for building vision backbones. Although some works try to integrate both, they apply the two operators simultaneously at the finest pixel granularity. With Convs responsible for per-pixel feature extraction already, the question is whether we still need to include the heavy MHSAs at such a fine-grained level. In fact, this is the root cause of the scalability issue w.r.t. the input resolution for vision transformers. To address this important problem, we propose in this work to use MSHAs and Convs in parallel at different granularity levels instead. Specifically, in each layer, we use two different ways to represent an image: a fine-grained regular grid and a coarse-grained set of semantic slots. We apply different operations to these two representations: Convs to the grid for local features, and MHSAs to the slots for global features. A pair of fully differentiable soft clustering and dispatching modules is introduced to bridge the grid and set representations, thus enabling local-global fusion. Through extensive experiments on various vision tasks, we empirically verify the potential of the proposed integration scheme, named GLMix: by offloading the burden of fine-grained features to light-weight Convs, it is sufficient to use MHSAs in a few (e.g., 64) semantic slots to match the performance of recent state-of-the-art backbones, while being more efficient. Our visualization results also demonstrate that the soft clustering module produces a meaningful semantic grouping effect with only IN1k classification supervision, which may induce better interpretability and inspire new weakly-supervised semantic segmentation approaches. Code will be available at https://github.com/rayleizhu/GLMix.

Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task subspace'' in which models are matched before being merged. We connect the task subspace of a given model to its loss landscape and formalize how this approach to model merging can be seen as solving a linear system of equations. While past work has generally been limited to linear systems that have a closed-form solution, we consider using the conjugate gradient method to find a solution. We show that using the conjugate gradient method can outperform closed-form solutions, enables merging via linear systems that are otherwise intractable to solve, and flexibly allows choosing from a wide variety of initializations and estimates for the ''task subspace''. We ultimately demonstrate that our merging framework called ''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-art results in multitask and intermediate-task model merging. We release all of the code and checkpoints used in our work at https://github.com/r-three/mats.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

We present MVD-Fusion: a method for single-view 3D inference via generative modeling of multi-view-consistent RGB-D images. While recent methods pursuing 3D inference advocate learning novel-view generative models, these generations are not 3D-consistent and require a distillation process to generate a 3D output. We instead cast the task of 3D inference as directly generating mutually-consistent multiple views and build on the insight that additionally inferring depth can provide a mechanism for enforcing this consistency. Specifically, we train a denoising diffusion model to generate multi-view RGB-D images given a single RGB input image and leverage the (intermediate noisy) depth estimates to obtain reprojection-based conditioning to maintain multi-view consistency. We train our model using large-scale synthetic dataset Obajverse as well as the real-world CO3D dataset comprising of generic camera viewpoints. We demonstrate that our approach can yield more accurate synthesis compared to recent state-of-the-art, including distillation-based 3D inference and prior multi-view generation methods. We also evaluate the geometry induced by our multi-view depth prediction and find that it yields a more accurate representation than other direct 3D inference approaches.

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

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Bird's eye view (BEV) representation is a new perception formulation for autonomous driving, which is based on spatial fusion. Further, temporal fusion is also introduced in BEV representation and gains great success. In this work, we propose a new method that unifies both spatial and temporal fusion and merges them into a unified mathematical formulation. The unified fusion could not only provide a new perspective on BEV fusion but also brings new capabilities. With the proposed unified spatial-temporal fusion, our method could support long-range fusion, which is hard to achieve in conventional BEV methods. Moreover, the BEV fusion in our work is temporal-adaptive and the weights of temporal fusion are learnable. In contrast, conventional methods mainly use fixed and equal weights for temporal fusion. Besides, the proposed unified fusion could avoid information lost in conventional BEV fusion methods and make full use of features. Extensive experiments and ablation studies on the NuScenes dataset show the effectiveness of the proposed method and our method gains the state-of-the-art performance in the map segmentation task.

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and real-world benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches -- models attaining sub-quadratic attention complexity can utilize a notion of sparsity or a low-rank approximation of inputs to reduce the number of attended keys; other ways to reduce complexity include locality-sensitive hashing, key pooling, additional memory to store information in compacted or hybridization with other architectures, such as CNN. Often based on a strong mathematical basis, kernelized approaches allow for the approximation of attention with linear complexity while retaining high accuracy. Therefore, in the present paper, we aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. But both attention and multi-layer perceptions (MLPs) in ViTs are not efficient enough due to dense multiplications, resulting in costly training and inference. To this end, we propose to reparameterize the pre-trained ViT with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed ShiftAddViT, which aims for end-to-end inference speedups on GPUs without the need of training from scratch. Specifically, all MatMuls among queries, keys, and values are reparameterized by additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized by shift kernels. We utilize TVM to implement and optimize those customized kernels for practical hardware deployment on GPUs. We find that such a reparameterization on (quadratic or linear) attention maintains model accuracy, while inevitably leading to accuracy drops when being applied to MLPs. To marry the best of both worlds, we further propose a new mixture of experts (MoE) framework to reparameterize MLPs by taking multiplication or its primitives as experts, e.g., multiplication and shift, and designing a new latency-aware load-balancing loss. Such a loss helps to train a generic router for assigning a dynamic amount of input tokens to different experts according to their latency. In principle, the faster experts run, the larger amount of input tokens are assigned. Extensive experiments consistently validate the effectiveness of our proposed ShiftAddViT, achieving up to 5.18\times$ latency reductions on GPUs and 42.9%$ energy savings, while maintaining comparable accuracy as original or efficient ViTs.

There still remains an extreme performance gap between Vision Transformers (ViTs) and Convolutional Neural Networks (CNNs) when training from scratch on small datasets, which is concluded to the lack of inductive bias. In this paper, we further consider this problem and point out two weaknesses of ViTs in inductive biases, that is, the spatial relevance and diverse channel representation. First, on spatial aspect, objects are locally compact and relevant, thus fine-grained feature needs to be extracted from a token and its neighbors. While the lack of data hinders ViTs to attend the spatial relevance. Second, on channel aspect, representation exhibits diversity on different channels. But the scarce data can not enable ViTs to learn strong enough representation for accurate recognition. To this end, we propose Dynamic Hybrid Vision Transformer (DHVT) as the solution to enhance the two inductive biases. On spatial aspect, we adopt a hybrid structure, in which convolution is integrated into patch embedding and multi-layer perceptron module, forcing the model to capture the token features as well as their neighboring features. On channel aspect, we introduce a dynamic feature aggregation module in MLP and a brand new "head token" design in multi-head self-attention module to help re-calibrate channel representation and make different channel group representation interacts with each other. The fusion of weak channel representation forms a strong enough representation for classification. With this design, we successfully eliminate the performance gap between CNNs and ViTs, and our DHVT achieves a series of state-of-the-art performance with a lightweight model, 85.68% on CIFAR-100 with 22.8M parameters, 82.3% on ImageNet-1K with 24.0M parameters. Code is available at https://github.com/ArieSeirack/DHVT.

Recently, 3D Gaussian Splatting, as a novel 3D representation, has garnered attention for its fast rendering speed and high rendering quality. However, this comes with high memory consumption, e.g., a well-trained Gaussian field may utilize three million Gaussian primitives and over 700 MB of memory. We credit this high memory footprint to the lack of consideration for the relationship between primitives. In this paper, we propose a memory-efficient Gaussian field named SUNDAE with spectral pruning and neural compensation. On one hand, we construct a graph on the set of Gaussian primitives to model their relationship and design a spectral down-sampling module to prune out primitives while preserving desired signals. On the other hand, to compensate for the quality loss of pruning Gaussians, we exploit a lightweight neural network head to mix splatted features, which effectively compensates for quality losses while capturing the relationship between primitives in its weights. We demonstrate the performance of SUNDAE with extensive results. For example, SUNDAE can achieve 26.80 PSNR at 145 FPS using 104 MB memory while the vanilla Gaussian splatting algorithm achieves 25.60 PSNR at 160 FPS using 523 MB memory, on the Mip-NeRF360 dataset. Codes are publicly available at https://runyiyang.github.io/projects/SUNDAE/.

We present Mantis Shrimp, a multi-survey deep learning model for photometric redshift estimation that fuses ultra-violet (GALEX), optical (PanSTARRS), and infrared (UnWISE) imagery. Machine learning is now an established approach for photometric redshift estimation, with generally acknowledged higher performance in areas with a high density of spectroscopically identified galaxies over template-based methods. Multiple works have shown that image-based convolutional neural networks can outperform tabular-based color/magnitude models. In comparison to tabular models, image models have additional design complexities: it is largely unknown how to fuse inputs from different instruments which have different resolutions or noise properties. The Mantis Shrimp model estimates the conditional density estimate of redshift using cutout images. The density estimates are well calibrated and the point estimates perform well in the distribution of available spectroscopically confirmed galaxies with (bias = 1e-2), scatter (NMAD = 2.44e-2) and catastrophic outlier rate (eta=17.53%). We find that early fusion approaches (e.g., resampling and stacking images from different instruments) match the performance of late fusion approaches (e.g., concatenating latent space representations), so that the design choice ultimately is left to the user. Finally, we study how the models learn to use information across bands, finding evidence that our models successfully incorporates information from all surveys. The applicability of our model to the analysis of large populations of galaxies is limited by the speed of downloading cutouts from external servers; however, our model could be useful in smaller studies such as generating priors over redshift for stellar population synthesis.

Does the dominant approach to learn representations (as a side effect of optimizing an expected cost for a single training distribution) remain a good approach when we are dealing with multiple distributions? Our thesis is that such scenarios are better served by representations that are richer than those obtained with a single optimization episode. We support this thesis with simple theoretical arguments and with experiments utilizing an apparently na\"{\i}ve ensembling technique: concatenating the representations obtained from multiple training episodes using the same data, model, algorithm, and hyper-parameters, but different random seeds. These independently trained networks perform similarly. Yet, in a number of scenarios involving new distributions, the concatenated representation performs substantially better than an equivalently sized network trained with a single training run. This proves that the representations constructed by multiple training episodes are in fact different. Although their concatenation carries little additional information about the training task under the training distribution, it becomes substantially more informative when tasks or distributions change. Meanwhile, a single training episode is unlikely to yield such a redundant representation because the optimization process has no reason to accumulate features that do not incrementally improve the training performance.

The primary goal of knowledge distillation (KD) is to encapsulate the information of a model learned from a teacher network into a student network, with the latter being more compact than the former. Existing work, e.g., using Kullback-Leibler divergence for distillation, may fail to capture important structural knowledge in the teacher network and often lacks the ability for feature generalization, particularly in situations when teacher and student are built to address different classification tasks. We propose Wasserstein Contrastive Representation Distillation (WCoRD), which leverages both primal and dual forms of Wasserstein distance for KD. The dual form is used for global knowledge transfer, yielding a contrastive learning objective that maximizes the lower bound of mutual information between the teacher and the student networks. The primal form is used for local contrastive knowledge transfer within a mini-batch, effectively matching the distributions of features between the teacher and the student networks. Experiments demonstrate that the proposed WCoRD method outperforms state-of-the-art approaches on privileged information distillation, model compression and cross-modal transfer.

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (cf. Mallinar et al. 2022).

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the classic k-means algorithm, leading to efficient algorithms that approximate k-means clusters using axis-aligned decision trees. However, interpretable variants of k-means have limited applicability in practice, where more flexible clustering methods are often needed to obtain useful partitions of the data. In this work, we investigate interpretable kernel clustering, and propose algorithms that construct decision trees to approximate the partitions induced by kernel k-means, a nonlinear extension of k-means. We further build on previous work on explainable k-means and demonstrate how a suitable choice of features allows preserving interpretability without sacrificing approximation guarantees on the interpretable model.

Contrastive loss is a powerful approach for representation learning, where larger batch sizes enhance performance by providing more negative samples to better distinguish between similar and dissimilar data. However, scaling batch sizes is constrained by the quadratic growth in GPU memory consumption, primarily due to the full instantiation of the similarity matrix. To address this, we propose a tile-based computation strategy that partitions the contrastive loss calculation into arbitrary small blocks, avoiding full materialization of the similarity matrix. Furthermore, we introduce a multi-level tiling strategy to leverage the hierarchical structure of distributed systems, employing ring-based communication at the GPU level to optimize synchronization and fused kernels at the CUDA core level to reduce I/O overhead. Experimental results show that the proposed method scales batch sizes to unprecedented levels. For instance, it enables contrastive training of a CLIP-ViT-L/14 model with a batch size of 4M or 12M using 8 or 32 A800 80GB without sacrificing any accuracy. Compared to SOTA memory-efficient solutions, it achieves a two-order-of-magnitude reduction in memory while maintaining comparable speed. The code will be made publicly available.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Diffusion models have been widely used for conditional data cross-modal generation tasks such as text-to-image and text-to-video. However, state-of-the-art models still fail to align the generated visual concepts with high-level semantics in a language such as object count, spatial relationship, etc. We approach this problem from a multimodal data fusion perspective and investigate how different fusion strategies can affect vision-language alignment. We discover that compared to the widely used early fusion of conditioning text in a pretrained image feature space, a specially designed intermediate fusion can: (i) boost text-to-image alignment with improved generation quality and (ii) improve training and inference efficiency by reducing low-rank text-to-image attention calculations. We perform experiments using a text-to-image generation task on the MS-COCO dataset. We compare our intermediate fusion mechanism with the classic early fusion mechanism on two common conditioning methods on a U-shaped ViT backbone. Our intermediate fusion model achieves a higher CLIP Score and lower FID, with 20% reduced FLOPs, and 50% increased training speed compared to a strong U-ViT baseline with an early fusion.

Blending multiple convolutional kernels is proved advantageous in neural architecture design. However, current two-stage neural architecture search methods are mainly limited to single-path search spaces. How to efficiently search models of multi-path structures remains a difficult problem. In this paper, we are motivated to train a one-shot multi-path supernet to accurately evaluate the candidate architectures. Specifically, we discover that in the studied search spaces, feature vectors summed from multiple paths are nearly multiples of those from a single path. Such disparity perturbs the supernet training and its ranking ability. Therefore, we propose a novel mechanism called Shadow Batch Normalization (SBN) to regularize the disparate feature statistics. Extensive experiments prove that SBNs are capable of stabilizing the optimization and improving ranking performance. We call our unified multi-path one-shot approach as MixPath, which generates a series of models that achieve state-of-the-art results on ImageNet.

In this paper, we propose a recurrent framework for Joint Unsupervised LEarning (JULE) of deep representations and image clusters. In our framework, successive operations in a clustering algorithm are expressed as steps in a recurrent process, stacked on top of representations output by a Convolutional Neural Network (CNN). During training, image clusters and representations are updated jointly: image clustering is conducted in the forward pass, while representation learning in the backward pass. Our key idea behind this framework is that good representations are beneficial to image clustering and clustering results provide supervisory signals to representation learning. By integrating two processes into a single model with a unified weighted triplet loss and optimizing it end-to-end, we can obtain not only more powerful representations, but also more precise image clusters. Extensive experiments show that our method outperforms the state-of-the-art on image clustering across a variety of image datasets. Moreover, the learned representations generalize well when transferred to other tasks.

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer (KAT), a novel architecture that replaces MLP layers with Kolmogorov-Arnold Network (KAN) layers to enhance the expressiveness and performance of the model. Integrating KANs into transformers, however, is no easy feat, especially when scaled up. Specifically, we identify three key challenges: (C1) Base function. The standard B-spline function used in KANs is not optimized for parallel computing on modern hardware, resulting in slower inference speeds. (C2) Parameter and Computation Inefficiency. KAN requires a unique function for each input-output pair, making the computation extremely large. (C3) Weight initialization. The initialization of weights in KANs is particularly challenging due to their learnable activation functions, which are critical for achieving convergence in deep neural networks. To overcome the aforementioned challenges, we propose three key solutions: (S1) Rational basis. We replace B-spline functions with rational functions to improve compatibility with modern GPUs. By implementing this in CUDA, we achieve faster computations. (S2) Group KAN. We share the activation weights through a group of neurons, to reduce the computational load without sacrificing performance. (S3) Variance-preserving initialization. We carefully initialize the activation weights to make sure that the activation variance is maintained across layers. With these designs, KAT scales effectively and readily outperforms traditional MLP-based transformers.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

Multi-task learning (MTL) compresses the information from multiple tasks into a unified backbone to improve computational efficiency and generalization. Recent work directly merges multiple independently trained models to perform MTL instead of collecting their raw data for joint training, greatly expanding the application scenarios of MTL. However, by visualizing the representation distribution of existing model merging schemes, we find that the merged model often suffers from the dilemma of representation bias. That is, there is a significant discrepancy in the representation distribution between the merged and individual models, resulting in poor performance of merged MTL. In this paper, we propose a representation surgery solution called "Surgery" to reduce representation bias in the merged model. Specifically, Surgery is a lightweight task-specific module that takes the representation of the merged model as input and attempts to output the biases contained in the representation from the merged model. We then designed an unsupervised optimization objective that updates the Surgery module by minimizing the distance between the merged model's representation and the individual model's representation. Extensive experiments demonstrate significant MTL performance improvements when our Surgery module is applied to state-of-the-art (SOTA) model merging schemes.

The study explores the synergistic combination of Synthetic Aperture Radar (SAR) and Visible-Near Infrared-Short Wave Infrared (VNIR-SWIR) imageries for land use/land cover (LULC) classification. Image fusion, employing Bayesian fusion, merges SAR texture bands with VNIR-SWIR imageries. The research aims to investigate the impact of this fusion on LULC classification. Despite the popularity of random forests for supervised classification, their limitations, such as suboptimal performance with fewer features and accuracy stagnation, are addressed. To overcome these issues, ensembles of random forests (RFE) are created, introducing random rotations using the Forest-RC algorithm. Three rotation approaches: principal component analysis (PCA), sparse random rotation (SRP) matrix, and complete random rotation (CRP) matrix are employed. Sentinel-1 SAR data and Sentinel-2 VNIR-SWIR data from the IIT-Kanpur region constitute the training datasets, including SAR, SAR with texture, VNIR-SWIR, VNIR-SWIR with texture, and fused VNIR-SWIR with texture. The study evaluates classifier efficacy, explores the impact of SAR and VNIR-SWIR fusion on classification, and significantly enhances the execution speed of Bayesian fusion code. The SRP-based RFE outperforms other ensembles for the first two datasets, yielding average overall kappa values of 61.80% and 68.18%, while the CRP-based RFE excels for the last three datasets with average overall kappa values of 95.99%, 96.93%, and 96.30%. The fourth dataset achieves the highest overall kappa of 96.93%. Furthermore, incorporating texture with SAR bands results in a maximum overall kappa increment of 10.00%, while adding texture to VNIR-SWIR bands yields a maximum increment of approximately 3.45%.

Unsupervised Domain Adaptation (UDA) is the task of bridging the domain gap between a labeled source domain, e.g., synthetic data, and an unlabeled target domain. We observe that current UDA methods show inferior results on fine structures and tend to oversegment objects with ambiguous appearance. To address these shortcomings, we propose to leverage geometric information, i.e., depth predictions, as depth discontinuities often coincide with segmentation boundaries. We show that naively incorporating depth into current UDA methods does not fully exploit the potential of this complementary information. To this end, we present MICDrop, which learns a joint feature representation by masking image encoder features while inversely masking depth encoder features. With this simple yet effective complementary masking strategy, we enforce the use of both modalities when learning the joint feature representation. To aid this process, we propose a feature fusion module to improve both global as well as local information sharing while being robust to errors in the depth predictions. We show that our method can be plugged into various recent UDA methods and consistently improve results across standard UDA benchmarks, obtaining new state-of-the-art performances.

In this paper, we introduce a new approach for high-quality multi-exposure image fusion (MEF). We show that the fusion weights of an exposure can be encoded into a 1D lookup table (LUT), which takes pixel intensity value as input and produces fusion weight as output. We learn one 1D LUT for each exposure, then all the pixels from different exposures can query 1D LUT of that exposure independently for high-quality and efficient fusion. Specifically, to learn these 1D LUTs, we involve attention mechanism in various dimensions including frame, channel and spatial ones into the MEF task so as to bring us significant quality improvement over the state-of-the-art (SOTA). In addition, we collect a new MEF dataset consisting of 960 samples, 155 of which are manually tuned by professionals as ground-truth for evaluation. Our network is trained by this dataset in an unsupervised manner. Extensive experiments are conducted to demonstrate the effectiveness of all the newly proposed components, and results show that our approach outperforms the SOTA in our and another representative dataset SICE, both qualitatively and quantitatively. Moreover, our 1D LUT approach takes less than 4ms to run a 4K image on a PC GPU. Given its high quality, efficiency and robustness, our method has been shipped into millions of Android mobiles across multiple brands world-wide. Code is available at: https://github.com/Hedlen/MEFLUT.

Recent works in volume rendering, e.g. NeRF and 3D Gaussian Splatting (3DGS), significantly advance the rendering quality and efficiency with the help of the learned implicit neural radiance field or 3D Gaussians. Rendering on top of an explicit representation, the vanilla 3DGS and its variants deliver real-time efficiency by optimizing the parametric model with single-view supervision per iteration during training which is adopted from NeRF. Consequently, certain views are overfitted, leading to unsatisfying appearance in novel-view synthesis and imprecise 3D geometries. To solve aforementioned problems, we propose a new 3DGS optimization method embodying four key novel contributions: 1) We transform the conventional single-view training paradigm into a multi-view training strategy. With our proposed multi-view regulation, 3D Gaussian attributes are further optimized without overfitting certain training views. As a general solution, we improve the overall accuracy in a variety of scenarios and different Gaussian variants. 2) Inspired by the benefit introduced by additional views, we further propose a cross-intrinsic guidance scheme, leading to a coarse-to-fine training procedure concerning different resolutions. 3) Built on top of our multi-view regulated training, we further propose a cross-ray densification strategy, densifying more Gaussian kernels in the ray-intersect regions from a selection of views. 4) By further investigating the densification strategy, we found that the effect of densification should be enhanced when certain views are distinct dramatically. As a solution, we propose a novel multi-view augmented densification strategy, where 3D Gaussians are encouraged to get densified to a sufficient number accordingly, resulting in improved reconstruction accuracy.

Recent advancements in both representation learning and function learning have demonstrated substantial promise across diverse domains of artificial intelligence. However, the effective integration of these paradigms poses a significant challenge, particularly in cases where users must manually decide whether to apply a representation learning or function learning model based on dataset characteristics. To address this issue, we introduce MLP-KAN, a unified method designed to eliminate the need for manual model selection. By integrating Multi-Layer Perceptrons (MLPs) for representation learning and Kolmogorov-Arnold Networks (KANs) for function learning within a Mixture-of-Experts (MoE) architecture, MLP-KAN dynamically adapts to the specific characteristics of the task at hand, ensuring optimal performance. Embedded within a transformer-based framework, our work achieves remarkable results on four widely-used datasets across diverse domains. Extensive experimental evaluation demonstrates its superior versatility, delivering competitive performance across both deep representation and function learning tasks. These findings highlight the potential of MLP-KAN to simplify the model selection process, offering a comprehensive, adaptable solution across various domains. Our code and weights are available at https://github.com/DLYuanGod/MLP-KAN.

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely unexplored. Our study attempts to reveal the star operation's ability to map inputs into high-dimensional, non-linear feature spaces -- akin to kernel tricks -- without widening the network. We further introduce StarNet, a simple yet powerful prototype, demonstrating impressive performance and low latency under compact network structure and efficient budget. Like stars in the sky, the star operation appears unremarkable but holds a vast universe of potential. Our work encourages further exploration across tasks, with codes available at https://github.com/ma-xu/Rewrite-the-Stars.

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Image Retrieval is a fundamental task of obtaining images similar to the query one from a database. A common image retrieval practice is to firstly retrieve candidate images via similarity search using global image features and then re-rank the candidates by leveraging their local features. Previous learning-based studies mainly focus on either global or local image representation learning to tackle the retrieval task. In this paper, we abandon the two-stage paradigm and seek to design an effective single-stage solution by integrating local and global information inside images into compact image representations. Specifically, we propose a Deep Orthogonal Local and Global (DOLG) information fusion framework for end-to-end image retrieval. It attentively extracts representative local information with multi-atrous convolutions and self-attention at first. Components orthogonal to the global image representation are then extracted from the local information. At last, the orthogonal components are concatenated with the global representation as a complementary, and then aggregation is performed to generate the final representation. The whole framework is end-to-end differentiable and can be trained with image-level labels. Extensive experimental results validate the effectiveness of our solution and show that our model achieves state-of-the-art image retrieval performances on Revisited Oxford and Paris datasets.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

There is an emerging effort to combine the two popular 3D frameworks using Multi-View Stereo (MVS) and Neural Implicit Surfaces (NIS) with a specific focus on the few-shot / sparse view setting. In this paper, we introduce a novel integration scheme that combines the multi-view stereo with neural signed distance function representations, which potentially overcomes the limitations of both methods. MVS uses per-view depth estimation and cross-view fusion to generate accurate surfaces, while NIS relies on a common coordinate volume. Based on this strategy, we propose to construct per-view cost frustum for finer geometry estimation, and then fuse cross-view frustums and estimate the implicit signed distance functions to tackle artifacts that are due to noise and holes in the produced surface reconstruction. We further apply a cascade frustum fusion strategy to effectively captures global-local information and structural consistency. Finally, we apply cascade sampling and a pseudo-geometric loss to foster stronger integration between the two architectures. Extensive experiments demonstrate that our method reconstructs robust surfaces and outperforms existing state-of-the-art methods.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Automatic organ segmentation is an important yet challenging problem for medical image analysis. The pancreas is an abdominal organ with very high anatomical variability. This inhibits previous segmentation methods from achieving high accuracies, especially compared to other organs such as the liver, heart or kidneys. In this paper, we present a probabilistic bottom-up approach for pancreas segmentation in abdominal computed tomography (CT) scans, using multi-level deep convolutional networks (ConvNets). We propose and evaluate several variations of deep ConvNets in the context of hierarchical, coarse-to-fine classification on image patches and regions, i.e. superpixels. We first present a dense labeling of local image patches via P{-}ConvNet and nearest neighbor fusion. Then we describe a regional ConvNet (R_1{-}ConvNet) that samples a set of bounding boxes around each image superpixel at different scales of contexts in a "zoom-out" fashion. Our ConvNets learn to assign class probabilities for each superpixel region of being pancreas. Last, we study a stacked R_2{-}ConvNet leveraging the joint space of CT intensities and the P{-}ConvNet dense probability maps. Both 3D Gaussian smoothing and 2D conditional random fields are exploited as structured predictions for post-processing. We evaluate on CT images of 82 patients in 4-fold cross-validation. We achieve a Dice Similarity Coefficient of 83.6pm6.3% in training and 71.8pm10.7% in testing.

Existing techniques for model inversion typically rely on hard-to-tune regularizers, such as total variation or feature regularization, which must be individually calibrated for each network in order to produce adequate images. In this work, we introduce Plug-In Inversion, which relies on a simple set of augmentations and does not require excessive hyper-parameter tuning. Under our proposed augmentation-based scheme, the same set of augmentation hyper-parameters can be used for inverting a wide range of image classification models, regardless of input dimensions or the architecture. We illustrate the practicality of our approach by inverting Vision Transformers (ViTs) and Multi-Layer Perceptrons (MLPs) trained on the ImageNet dataset, tasks which to the best of our knowledge have not been successfully accomplished by any previous works.

Blind image deconvolution (BID) is a classic yet challenging problem in the field of image processing. Recent advances in deep image prior (DIP) have motivated a series of DIP-based approaches, demonstrating remarkable success in BID. However, due to the high non-convexity of the inherent optimization process, these methods are notorious for their sensitivity to the initialized kernel. To alleviate this issue and further improve their performance, we propose a new framework for BID that better considers the prior modeling and the initialization for blur kernels, leveraging a deep generative model. The proposed approach pre-trains a generative adversarial network-based kernel generator that aptly characterizes the kernel priors and a kernel initializer that facilitates a well-informed initialization for the blur kernel through latent space encoding. With the pre-trained kernel generator and initializer, one can obtain a high-quality initialization of the blur kernel, and enable optimization within a compact latent kernel manifold. Such a framework results in an evident performance improvement over existing DIP-based BID methods. Extensive experiments on different datasets demonstrate the effectiveness of the proposed method.

We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are fixed beforehand, the EIM is a nonlinear approximation method which constructs interpolation points and basis which are adapted to the kernel under consideration. The basis functions are obtained using evaluations of the kernel itself. We restrict ourselves to translation-invariant kernels, for which a modified version of the EIM approximation can be used in a multilevel FMM context; we call the obtained algorithm Empirical Interpolation Fast Multipole Method (EIFMM). An important feature of the EIFMM is a built-in error estimation of the interpolation error made by the low-rank approximation of the far-field behavior of the kernel: the algorithm selects the optimal number of interpolation points required to ensure a given accuracy for the result, leading to important gains for inhomogeneous kernels.

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for general optimizers as well, including Adam -- albeit with a nonlinear notion of "kernel." We derive the corresponding "neural tangent" and "maximal update" limits for any architecture. Two foundational advances underlie the above results: 1) A new Tensor Program language, NEXORT, that can express how adaptive optimizers process gradients into updates. 2) The introduction of bra-ket notation to drastically simplify expressions and calculations in Tensor Programs. This work summarizes and generalizes all previous results in the Tensor Programs series of papers.

Dataset distillation methods have achieved remarkable success in distilling a large dataset into a small set of representative samples. However, they are not designed to produce a distilled dataset that can be effectively used for facilitating self-supervised pre-training. To this end, we propose a novel problem of distilling an unlabeled dataset into a set of small synthetic samples for efficient self-supervised learning (SSL). We first prove that a gradient of synthetic samples with respect to a SSL objective in naive bilevel optimization is biased due to the randomness originating from data augmentations or masking. To address this issue, we propose to minimize the mean squared error (MSE) between a model's representations of the synthetic examples and their corresponding learnable target feature representations for the inner objective, which does not introduce any randomness. Our primary motivation is that the model obtained by the proposed inner optimization can mimic the self-supervised target model. To achieve this, we also introduce the MSE between representations of the inner model and the self-supervised target model on the original full dataset for outer optimization. Lastly, assuming that a feature extractor is fixed, we only optimize a linear head on top of the feature extractor, which allows us to reduce the computational cost and obtain a closed-form solution of the head with kernel ridge regression. We empirically validate the effectiveness of our method on various applications involving transfer learning.

Kernel continual learning by derakhshani2021kernel has recently emerged as a strong continual learner due to its non-parametric ability to tackle task interference and catastrophic forgetting. Unfortunately its success comes at the expense of an explicit memory to store samples from past tasks, which hampers scalability to continual learning settings with a large number of tasks. In this paper, we introduce generative kernel continual learning, which explores and exploits the synergies between generative models and kernels for continual learning. The generative model is able to produce representative samples for kernel learning, which removes the dependence on memory in kernel continual learning. Moreover, as we replay only on the generative model, we avoid task interference while being computationally more efficient compared to previous methods that need replay on the entire model. We further introduce a supervised contrastive regularization, which enables our model to generate even more discriminative samples for better kernel-based classification performance. We conduct extensive experiments on three widely-used continual learning benchmarks that demonstrate the abilities and benefits of our contributions. Most notably, on the challenging SplitCIFAR100 benchmark, with just a simple linear kernel we obtain the same accuracy as kernel continual learning with variational random features for one tenth of the memory, or a 10.1\% accuracy gain for the same memory budget.

Solid results from Transformers have made them prevailing architectures in various natural language and vision tasks. As a default component in Transformers, Layer Normalization (LN) normalizes activations within each token to boost the robustness. However, LN requires on-the-fly statistics calculation in inference as well as division and square root operations, leading to inefficiency on hardware. What is more, replacing LN with other hardware-efficient normalization schemes (e.g., Batch Normalization) results in inferior performance, even collapse in training. We find that this dilemma is caused by abnormal behaviors of activation statistics, including large fluctuations over iterations and extreme outliers across layers. To tackle these issues, we propose Unified Normalization (UN), which can speed up the inference by being fused with other linear operations and achieve comparable performance on par with LN. UN strives to boost performance by calibrating the activation and gradient statistics with a tailored fluctuation smoothing strategy. Meanwhile, an adaptive outlier filtration strategy is applied to avoid collapse in training whose effectiveness is theoretically proved and experimentally verified in this paper. We demonstrate that UN can be an efficient drop-in alternative to LN by conducting extensive experiments on language and vision tasks. Besides, we evaluate the efficiency of our method on GPU. Transformers equipped with UN enjoy about 31% inference speedup and nearly 18% memory reduction. Code will be released at https://github.com/hikvision-research/Unified-Normalization.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Coronary microvascular disease constitutes a substantial risk to human health. Employing computer-aided analysis and diagnostic systems, medical professionals can intervene early in disease progression, with 3D vessel segmentation serving as a crucial component. Nevertheless, conventional U-Net architectures tend to yield incoherent and imprecise segmentation outcomes, particularly for small vessel structures. While models with attention mechanisms, such as Transformers and large convolutional kernels, demonstrate superior performance, their extensive computational demands during training and inference lead to increased time complexity. In this study, we leverage Fourier domain learning as a substitute for multi-scale convolutional kernels in 3D hierarchical segmentation models, which can reduce computational expenses while preserving global receptive fields within the network. Furthermore, a zero-parameter frequency domain fusion method is designed to improve the skip connections in U-Net architecture. Experimental results on a public dataset and an in-house dataset indicate that our novel Fourier transformation-based network achieves remarkable dice performance (84.37\% on ASACA500 and 80.32\% on ImageCAS) in tubular vessel segmentation tasks and substantially reduces computational requirements without compromising global receptive fields.

In this paper, we construct a mixture of neural operators (MoNOs) between function spaces whose complexity is distributed over a network of expert neural operators (NOs), with each NO satisfying parameter scaling restrictions. Our main result is a distributed universal approximation theorem guaranteeing that any Lipschitz non-linear operator between L^2([0,1]^d) spaces can be approximated uniformly over the Sobolev unit ball therein, to any given varepsilon>0 accuracy, by an MoNO while satisfying the constraint that: each expert NO has a depth, width, and rank of O(varepsilon^{-1}). Naturally, our result implies that the required number of experts must be large, however, each NO is guaranteed to be small enough to be loadable into the active memory of most computers for reasonable accuracies varepsilon. During our analysis, we also obtain new quantitative expression rates for classical NOs approximating uniformly continuous non-linear operators uniformly on compact subsets of L^2([0,1]^d).

Dot-product attention mechanism plays a crucial role in modern deep architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact computation of this model incurs quadratic time and memory complexities in sequence length, hindering the training of long-sequence models. Critical bottlenecks are due to the computation of partition functions in the denominator of softmax function as well as the multiplication of the softmax matrix with the matrix of values. Our key observation is that the former can be reduced to a variant of the kernel density estimation (KDE) problem, and an efficient KDE solver can be further utilized to accelerate the latter via subsampling-based fast matrix products. Our proposed KDEformer can approximate the attention in sub-quadratic time with provable spectral norm bounds, while all prior results merely provide entry-wise error bounds. Empirically, we verify that KDEformer outperforms other attention approximations in terms of accuracy, memory, and runtime on various pre-trained models. On BigGAN image generation, we achieve better generative scores than the exact computation with over 4times speedup. For ImageNet classification with T2T-ViT, KDEformer shows over 18times speedup while the accuracy drop is less than 0.5%.

Convolutional Neural Networks (CNNs) have revolutionized image classification by extracting spatial features and enabling state-of-the-art accuracy in vision-based tasks. The squeeze and excitation network proposed module gathers channelwise representations of the input. Multilayer perceptrons (MLP) learn global representation from the data and in most image classification models used to learn extracted features of the image. In this paper, we introduce a novel aggregated multilayer perceptron, a multi-branch dense layer, within the Squeeze excitation residual module designed to surpass the performance of existing architectures. Our approach leverages a combination of squeeze excitation network module with dense layers. This fusion enhances the network's ability to capture channel-wise patterns and have global knowledge, leading to a better feature representation. This proposed model has a negligible increase in parameters when compared to SENet. We conduct extensive experiments on benchmark datasets to validate the model and compare them with established architectures. Experimental results demonstrate a remarkable increase in the classification accuracy of the proposed model.

Infrared and visible image fusion aims to integrate comprehensive information from multiple sources to achieve superior performances on various practical tasks, such as detection, over that of a single modality. However, most existing methods directly combined the texture details and object contrast of different modalities, ignoring the dynamic changes in reality, which diminishes the visible texture in good lighting conditions and the infrared contrast in low lighting conditions. To fill this gap, we propose a dynamic image fusion framework with a multi-modal gated mixture of local-to-global experts, termed MoE-Fusion, to dynamically extract effective and comprehensive information from the respective modalities. Our model consists of a Mixture of Local Experts (MoLE) and a Mixture of Global Experts (MoGE) guided by a multi-modal gate. The MoLE performs specialized learning of multi-modal local features, prompting the fused images to retain the local information in a sample-adaptive manner, while the MoGE focuses on the global information that complements the fused image with overall texture detail and contrast. Extensive experiments show that our MoE-Fusion outperforms state-of-the-art methods in preserving multi-modal image texture and contrast through the local-to-global dynamic learning paradigm, and also achieves superior performance on detection tasks. Our code will be available: https://github.com/SunYM2020/MoE-Fusion.

Typical deep visual recognition models are capable of performing the one task they were trained on. In this paper, we tackle the extremely difficult problem of combining completely distinct models with different initializations, each solving a separate task, into one multi-task model without any additional training. Prior work in model merging permutes one model to the space of the other then adds them together. While this works for models trained on the same task, we find that this fails to account for the differences in models trained on disjoint tasks. Thus, we introduce "ZipIt!", a general method for merging two arbitrary models of the same architecture that incorporates two simple strategies. First, in order to account for features that aren't shared between models, we expand the model merging problem to additionally allow for merging features within each model by defining a general "zip" operation. Second, we add support for partially zipping the models up until a specified layer, naturally creating a multi-head model. We find that these two changes combined account for a staggering 20-60% improvement over prior work, making the merging of models trained on disjoint tasks feasible.

We investigate methods for combining multiple self-supervised tasks--i.e., supervised tasks where data can be collected without manual labeling--in order to train a single visual representation. First, we provide an apples-to-apples comparison of four different self-supervised tasks using the very deep ResNet-101 architecture. We then combine tasks to jointly train a network. We also explore lasso regularization to encourage the network to factorize the information in its representation, and methods for "harmonizing" network inputs in order to learn a more unified representation. We evaluate all methods on ImageNet classification, PASCAL VOC detection, and NYU depth prediction. Our results show that deeper networks work better, and that combining tasks--even via a naive multi-head architecture--always improves performance. Our best joint network nearly matches the PASCAL performance of a model pre-trained on ImageNet classification, and matches the ImageNet network on NYU depth prediction.

We consider the problem of contextual kernel bandits with stochastic contexts, where the underlying reward function belongs to a known Reproducing Kernel Hilbert Space (RKHS). We study this problem under the additional constraint of joint differential privacy, where the agents needs to ensure that the sequence of query points is differentially private with respect to both the sequence of contexts and rewards. We propose a novel algorithm that improves upon the state of the art and achieves an error rate of Oleft(frac{gamma_T{T}} + gamma_T{T varepsilon}right) after T queries for a large class of kernel families, where gamma_T represents the effective dimensionality of the kernel and varepsilon > 0 is the privacy parameter. Our results are based on a novel estimator for the reward function that simultaneously enjoys high utility along with a low-sensitivity to observed rewards and contexts, which is crucial to obtain an order optimal learning performance with improved dependence on the privacy parameter.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks but also highlights the substantial role of deep learning in advancing quantum machine learning.

Vision Transformers (ViTs) and MLPs signal further efforts on replacing hand-wired features or inductive biases with general-purpose neural architectures. Existing works empower the models by massive data, such as large-scale pre-training and/or repeated strong data augmentations, and still report optimization-related problems (e.g., sensitivity to initialization and learning rates). Hence, this paper investigates ViTs and MLP-Mixers from the lens of loss geometry, intending to improve the models' data efficiency at training and generalization at inference. Visualization and Hessian reveal extremely sharp local minima of converged models. By promoting smoothness with a recently proposed sharpness-aware optimizer, we substantially improve the accuracy and robustness of ViTs and MLP-Mixers on various tasks spanning supervised, adversarial, contrastive, and transfer learning (e.g., +5.3\% and +11.0\% top-1 accuracy on ImageNet for ViT-B/16 and Mixer-B/16, respectively, with the simple Inception-style preprocessing). We show that the improved smoothness attributes to sparser active neurons in the first few layers. The resultant ViTs outperform ResNets of similar size and throughput when trained from scratch on ImageNet without large-scale pre-training or strong data augmentations. Model checkpoints are available at https://github.com/google-research/vision_transformer.