Zhihui Zhu

Xili Dai, Mingyang Li, Pengyuan Zhai et al. · deepmind

Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be expressed by a linear combination of a few elements from a convolutional dictionary, are powerful tools for analyzing natural images with good theoretical interpretability and biological plausibility. However, such principled models have not demonstrated competitive performance when compared with empirically designed deep networks. This paper revisits the sparse convolutional modeling for image classification and bridges the gap between good empirical performance (of deep learning) and good interpretability (of sparse convolutional models). Our method uses differentiable optimization layers that are defined from convolutional sparse coding as drop-in replacements of standard convolutional layers in conventional deep neural networks. We show that such models have equally strong empirical performance on CIFAR-10, CIFAR-100, and ImageNet datasets when compared to conventional neural networks. By leveraging stable recovery property of sparse modeling, we further show that such models can be much more robust to input corruptions as well as adversarial perturbations in testing through a simple proper trade-off between sparse regularization and data reconstruction terms. Source code can be found at https://github.com/Delay-Xili/SDNet.

Jinxin Zhou, Xiao Li, Tianyu Ding et al. · deepmind

When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and (ii) cross-example within-class variability of last-layer activations collapses to zero. This phenomenon is called Neural Collapse (NC), which seems to take place regardless of the choice of loss functions. In this work, we justify NC under the mean squared error (MSE) loss, where recent empirical evidence shows that it performs comparably or even better than the de-facto cross-entropy loss. Under a simplified unconstrained feature model, we provide the first global landscape analysis for vanilla nonconvex MSE loss and show that the (only!) global minimizers are neural collapse solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. Furthermore, we justify the usage of rescaled MSE loss by probing the optimization landscape around the NC solutions, showing that the landscape can be improved by tuning the rescaling hyperparameters. Finally, our theoretical findings are experimentally verified on practical network architectures.

Jinxin Zhou, Chong You, Xiao Li et al. · deepmind

While cross entropy (CE) is the most commonly used loss to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is still a mystery, because there seem to be multiple factors affecting the answer, such as properties of the dataset, the choice of network architecture, and so on. This paper studies the choice of loss function by examining the last-layer features of deep networks, drawing inspiration from a recent line work showing that the global optimal solution of CE and mean-square-error (MSE) losses exhibits a Neural Collapse phenomenon. That is, for sufficiently large networks trained until convergence, (i) all features of the same class collapse to the corresponding class mean and (ii) the means associated with different classes are in a configuration where their pairwise distances are all equal and maximized. We extend such results and show through global solution and landscape analyses that a broad family of loss functions including commonly used label smoothing (LS) and focal loss (FL) exhibits Neural Collapse. Hence, all relevant losses(i.e., CE, LS, FL, MSE) produce equivalent features on training data. Based on the unconstrained feature model assumption, we provide either the global landscape analysis for LS loss or the local landscape analysis for FL loss and show that the (only!) global minimizers are neural collapse solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions either in the global scope for LS loss or in the local scope for FL loss near the optimal solution. The experiments further show that Neural Collapse features obtained from all relevant losses lead to largely identical performance on test data as well, provided that the network is sufficiently large and trained until convergence.

Can Yaras, Peng Wang, Wei Hu et al.

Over the past few years, an extensively studied phenomenon in training deep networks is the implicit bias of gradient descent towards parsimonious solutions. In this work, we investigate this phenomenon by narrowing our focus to deep linear networks. Through our analysis, we reveal a surprising "law of parsimony" in the learning dynamics when the data possesses low-dimensional structures. Specifically, we show that the evolution of gradient descent starting from orthogonal initialization only affects a minimal portion of singular vector spaces across all weight matrices. In other words, the learning process happens only within a small invariant subspace of each weight matrix, despite the fact that all weight parameters are updated throughout training. This simplicity in learning dynamics could have significant implications for both efficient training and a better understanding of deep networks. First, the analysis enables us to considerably improve training efficiency by taking advantage of the low-dimensional structure in learning dynamics. We can construct smaller, equivalent deep linear networks without sacrificing the benefits associated with the wider counterparts. Second, it allows us to better understand deep representation learning by elucidating the linear progressive separation and concentration of representations from shallow to deep layers. We also conduct numerical experiments to support our theoretical results. The code for our experiments can be found at https://github.com/cjyaras/lawofparsimony.

Jiachen Jiang, Jinxin Zhou, Peng Wang et al. · deepmind

Neural collapse provides an elegant mathematical characterization of learned last layer representations (a.k.a. features) and classifier weights in deep classification models. Such results not only provide insights but also motivate new techniques for improving practical deep models. However, most of the existing empirical and theoretical studies in neural collapse focus on the case that the number of classes is small relative to the dimension of the feature space. This paper extends neural collapse to cases where the number of classes are much larger than the dimension of feature space, which broadly occur for language models, retrieval systems, and face recognition applications. We show that the features and classifier exhibit a generalized neural collapse phenomenon, where the minimum one-vs-rest margins is maximized.We provide empirical study to verify the occurrence of generalized neural collapse in practical deep neural networks. Moreover, we provide theoretical study to show that the generalized neural collapse provably occurs under unconstrained feature model with spherical constraint, under certain technical conditions on feature dimension and number of classes.

Tianyu Ding, Luming Liang, Zhihui Zhu et al.

DNN-based frame interpolation, which generates intermediate frames from two consecutive frames, is often dependent on model architectures with a large number of features, preventing their deployment on systems with limited resources, such as mobile devices. We present a compression-driven network design for frame interpolation that leverages model pruning through sparsity-inducing optimization to greatly reduce the model size while attaining higher performance. Concretely, we begin by compressing the recently proposed AdaCoF model and demonstrating that a 10 times compressed AdaCoF performs similarly to its original counterpart, where different strategies for using layerwise sparsity information as a guide are comprehensively investigated under a variety of hyperparameter settings. We then enhance this compressed model by introducing a multi-resolution warping module, which improves visual consistency with multi-level details. As a result, we achieve a considerable performance gain with a quarter of the size of the original AdaCoF. In addition, our model performs favorably against other state-of-the-art approaches on a wide variety of datasets. We note that the suggested compression-driven framework is generic and can be easily transferred to other DNN-based frame interpolation algorithms. The source code is available at https://github.com/tding1/CDFI.

Peng Wang, Xiao Li, Can Yaras et al.

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this work, we attempt to unveil this mystery by investigating the structures of intermediate features. Motivated by our empirical findings that linear layers mimic the roles of deep layers in nonlinear networks for feature learning, we explore how deep linear networks transform input data into output by investigating the output (i.e., features) of each layer after training in the context of multi-class classification problems. Toward this goal, we first define metrics to measure within-class compression and between-class discrimination of intermediate features, respectively. Through theoretical analysis of these two metrics, we show that the evolution of features follows a simple and quantitative pattern from shallow to deep layers when the input data is nearly orthogonal and the network weights are minimum-norm, balanced, and approximate low-rank: Each layer of the linear network progressively compresses within-class features at a geometric rate and discriminates between-class features at a linear rate with respect to the number of layers that data have passed through. To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks. Empirically, our extensive experiments not only validate our theoretical results numerically but also reveal a similar pattern in deep nonlinear networks which aligns well with recent empirical studies. Moreover, we demonstrate the practical implications of our results in transfer learning. Our code is available at https://github.com/Heimine/PNC_DLN.

Tianyi Chen, Luming Liang, Tianyu Ding et al.

The existing model compression methods via structured pruning typically require complicated multi-stage procedures. Each individual stage necessitates numerous engineering efforts and domain-knowledge from the end-users which prevent their wider applications onto broader scenarios. We propose the second generation of Only-Train-Once (OTOv2), which first automatically trains and compresses a general DNN only once from scratch to produce a more compact model with competitive performance without fine-tuning. OTOv2 is automatic and pluggable into various deep learning applications, and requires almost minimal engineering efforts from the users. Methodologically, OTOv2 proposes two major improvements: (i) Autonomy: automatically exploits the dependency of general DNNs, partitions the trainable variables into Zero-Invariant Groups (ZIGs), and constructs the compressed model; and (ii) Dual Half-Space Projected Gradient (DHSPG): a novel optimizer to more reliably solve structured-sparsity problems. Numerically, we demonstrate the generality and autonomy of OTOv2 on a variety of model architectures such as VGG, ResNet, CARN, ConvNeXt, DenseNet and StackedUnets, the majority of which cannot be handled by other methods without extensive handcrafting efforts. Together with benchmark datasets including CIFAR10/100, DIV2K, Fashion-MNIST, SVNH and ImageNet, its effectiveness is validated by performing competitively or even better than the state-of-the-arts. The source code is available at https://github.com/tianyic/only_train_once.

Xiao Li, Sheng Liu, Jinxin Zhou et al.

With the ever-increasing complexity of large-scale pre-trained models coupled with a shortage of labeled data for downstream training, transfer learning has become the primary approach in many fields, including natural language processing, computer vision, and multi-modal learning. Despite recent progress, the fine-tuning process for large-scale pre-trained models in vision still mostly relies on trial and error. This work investigates the relationship between neural collapse (NC) and transfer learning for classification problems. NC is an intriguing while prevalent phenomenon that has been recently discovered in terms of the final-layer features and linear classifiers of trained neural networks. Specifically, during the terminal phase of training, NC implies that the variability of the features within each class diminishes to zero, while the means of features between classes are maximally and equally distanced. In this work, we examine the NC attributes of pre-trained models on both downstream and source data for transfer learning, and we find strong correlation between feature collapse and downstream performance. In particular, we discovered a systematic pattern that emerges when linear probing pre-trained models on downstream training data: the more feature collapse of pre-trained models on downstream training data, the higher the transfer accuracy. Additionally, we also studied the relationship between NC and transfer accuracy on the source data. Moreover, these findings allow us to develop a principled, parameter-efficient fine-tuning method that employs skip-connection to induce the last-layer feature collapse on downstream data. Our proposed fine-tuning methods deliver good performances while reducing fine-tuning parameters by at least 90% and mitigating overfitting in situations especially when the downstream data is scarce.

Can Yaras, Peng Wang, Zhihui Zhu et al.

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More specifically, for the output features of the penultimate layer, for each class the within-class features converge to their means, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's classifier. As feature normalization in the last layer becomes a common practice in modern representation learning, in this work we theoretically justify the neural collapse phenomenon for normalized features. Based on an unconstrained feature model, we simplify the empirical loss function in a multi-class classification task into a nonconvex optimization problem over the Riemannian manifold by constraining all features and classifiers over the sphere. In this context, we analyze the nonconvex landscape of the Riemannian optimization problem over the product of spheres, showing a benign global landscape in the sense that the only global minimizers are the neural collapse solutions while all other critical points are strict saddles with negative curvature. Experimental results on practical deep networks corroborate our theory and demonstrate that better representations can be learned faster via feature normalization.

Zhen Qin, Alexander Lidiak, Zhexuan Gong et al.

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for representing a matrix from a set of selected rows and columns-is an efficient method for constructing a tensor train decomposition of a tensor from few of its entries. While tensor train cross approximation has achieved remarkable performance in practical applications, its theoretical analysis, in particular regarding the error of the approximation, is so far lacking. To our knowledge, existing results only provide element-wise approximation accuracy guarantees, which lead to a very loose bound when extended to the entire tensor. In this paper, we bridge this gap by providing accuracy guarantees in terms of the entire tensor for both exact and noisy measurements. Our results illustrate how the choice of selected subtensors affects the quality of the cross approximation and that the approximation error caused by model error and/or measurement error may not grow exponentially with the order of the tensor. These results are verified by numerical experiments, and may have important implications for the usefulness of cross approximations for high-order tensors, such as those encountered in the description of quantum many-body states.

Xiao Li, Zhihui Zhu, Qiuwei Li et al.

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the symmetric NMF is not as easy as for its nonsymmetric counterpart, since the latter admits the splitting property that allows state-of-the-art alternating-type algorithms. To overcome this issue, we first split the decision variable and transform the symmetric NMF to a penalized nonsymmetric one, paving the way for designing efficient alternating-type algorithms. We then show that solving the penalized nonsymmetric reformulation returns a solution to the original symmetric NMF. Moreover, we design a family of alternating-type algorithms and show that they all admit strong convergence guarantee: the generated sequence of iterates is convergent and converges at least sublinearly to a critical point of the original symmetric NMF. Finally, we conduct experiments on both synthetic data and real image clustering to support our theoretical results and demonstrate the performance of the alternating-type algorithms.

Lijun Ding, Zhen Qin, Liwei Jiang et al.

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a rank-overspecified factored representation of the matrix variable, where the global optimal solutions overfit and do not correspond to the underlying ground truth. We then solve the associated nonconvex problem using gradient descent with small random initialization. We show that as long as the measurement operators satisfy the restricted isometry property (RIP) with its rank parameter scaling with the rank of the ground-truth matrix rather than scaling with the overspecified matrix rank, gradient descent iterations are on a particular trajectory towards the ground-truth matrix and achieve nearly information-theoretically optimal recovery when it is stopped appropriately. We then propose an efficient stopping strategy based on the common hold-out method and show that it detects a nearly optimal estimator provably. Moreover, experiments show that the proposed validation approach can also be efficiently used for image restoration with deep image prior, which over-parameterizes an image with a deep network.

Jiachen Jiang, Huminhao Zhu, Zhihui Zhu

LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges. We introduce SMCEvolve, which recasts program search as sampling from a reward-tilted target distribution and approximates it with a Sequential Monte Carlo (SMC) sampler. From this view, three core mechanisms emerge as principled components: adaptive parent resampling, mixture of mutation with acceptance, and automatic convergence control. We further provide a finite-sample complexity analysis that bounds the LLM-call budget required to reach a target approximation error. Across math, algorithm efficiency, symbolic regression, and end-to-end ML research benchmarks, SMCEvolve surpasses state-of-the-art evolving systems while using fewer LLM calls under self-determined termination. The code is available at https://github.com/kongwanbianjinyu/SMCEvolve.

Jinxin Zhou, Tianyu Ding, Tianyi Chen et al.

We present DREAM, a novel training framework representing Diffusion Rectification and Estimation Adaptive Models, requiring minimal code changes (just three lines) yet significantly enhancing the alignment of training with sampling in diffusion models. DREAM features two components: diffusion rectification, which adjusts training to reflect the sampling process, and estimation adaptation, which balances perception against distortion. When applied to image super-resolution (SR), DREAM adeptly navigates the tradeoff between minimizing distortion and preserving high image quality. Experiments demonstrate DREAM's superiority over standard diffusion-based SR methods, showing a $2$ to $3\times $ faster training convergence and a $10$ to $20\times$ reduction in sampling steps to achieve comparable results. We hope DREAM will inspire a rethinking of diffusion model training paradigms.

Zhen Qin, Jiachen Jiang, Zhihui Zhu

Transformer models have become foundational across a wide range of scientific and engineering domains due to their strong empirical performance. A key capability underlying their success is in-context learning (ICL): when presented with a short prompt from an unseen task, transformers can perform per-token and next-token predictions without any parameter updates. Recent theoretical efforts have begun to uncover the mechanisms behind this phenomenon, particularly in supervised regression settings. However, these analyses predominantly assume stationary task distributions, which overlook a broad class of real-world scenarios where the target function varies over time. In this work, we bridge this gap by providing a theoretical analysis of ICL under non-stationary regression problems. We study how the gated linear attention (GLA) mechanism adapts to evolving input-output relationships and rigorously characterize its advantages over standard linear attention in this dynamic setting. To model non-stationarity, we adopt a first-order autoregressive process and show that GLA achieves lower training and testing errors by adaptively modulating the influence of past inputs -- effectively implementing a learnable recency bias. Our theoretical findings are further supported by empirical results, which validate the benefits of gating mechanisms in non-stationary ICL tasks.

Xiang Zhuang, Chenyi Zhou, Kehua Feng et al.

Artificial intelligence has demonstrated remarkable capability in predicting scientific properties, yet scientific discovery remains an inherently physical, long-horizon pursuit governed by experimental cycles. Most current computational approaches are misaligned with this reality, framing discovery as isolated, task-specific predictions rather than continuous interaction with the physical world. Here, we argue for embodied science, a paradigm that reframes scientific discovery as a closed loop tightly coupling agentic reasoning with physical execution. We propose a unified Perception-Language-Action-Discovery (PLAD) framework, wherein embodied agents perceive experimental environments, reason over scientific knowledge, execute physical interventions, and internalize outcomes to drive subsequent exploration. By grounding computational reasoning in robust physical feedback, this approach bridges the gap between digital prediction and empirical validation, offering a roadmap for autonomous discovery systems in the life and chemical sciences.

Mingyang Rao, Kehua Feng, Zhihui Zhu et al.

While Large Language Models (LLMs) have revolutionized scientific text processing, they exhibit a significant capability gap when interpreting chemical reaction diagrams. We identify two fundamental bottlenecks restricting current systems: a Visual Deficit, where generic vision encoders struggle to resolve the strict topological connectivity of dense molecular graphs, and a Semantic Disconnect, where standard linear strings, such as SMILES, fail to effectively activate the model's latent chemical reasoning. To bridge these gaps, we propose the Chemical Visual Activation (ChemVA) framework, which employs a Visual Anchor mechanism to ground functional groups via hybrid-granularity detection, followed by a semantic alignment approach that translates visual features into entity names to maximize knowledge activation in LLMs. We evaluate our approach on OCRD-Bench, a newly constructed dataset featuring dense visual-semantic contexts and comprehensive reaction coverage to evaluate the full spectrum from recognition to reasoning. Extensive experiments on OCRD-Bench demonstrate that ChemVA achieves 92.0% structural recognition accuracy. By bridging visual and semantic bottlenecks, our framework delivers a consistent performance gain of approximately 20 percentage points across 9 diverse LLMs, enabling open-weight models to rival proprietary SOTA systems in complex chemical reasoning tasks.

Zhen Qin, Xuwei Tan, Zhihui Zhu

Enforcing orthonormal or isometric property for the weight matrices has been shown to enhance the training of deep neural networks by mitigating gradient exploding/vanishing and increasing the robustness of the learned networks. However, despite its practical performance, the theoretical analysis of orthonormality in neural networks is still lacking; for example, how orthonormality affects the convergence of the training process. In this letter, we aim to bridge this gap by providing convergence analysis for training orthonormal deep linear neural networks. Specifically, we show that Riemannian gradient descent with an appropriate initialization converges at a linear rate for training orthonormal deep linear neural networks with a class of loss functions. Unlike existing works that enforce orthonormal weight matrices for all the layers, our approach excludes this requirement for one layer, which is crucial to establish the convergence guarantee. Our results shed light on how increasing the number of hidden layers can impact the convergence speed. Experimental results validate our theoretical analysis.

Tianyi Chen, Tianyu Ding, Zhihui Zhu et al.

Compressing a predefined deep neural network (DNN) into a compact sub-network with competitive performance is crucial in the efficient machine learning realm. This topic spans various techniques, from structured pruning to neural architecture search, encompassing both pruning and erasing operators perspectives. Despite advancements, existing methods suffers from complex, multi-stage processes that demand substantial engineering and domain knowledge, limiting their broader applications. We introduce the third-generation Only-Train-Once (OTOv3), which first automatically trains and compresses a general DNN through pruning and erasing operations, creating a compact and competitive sub-network without the need of fine-tuning. OTOv3 simplifies and automates the training and compression process, minimizes the engineering efforts required from users. It offers key technological advancements: (i) automatic search space construction for general DNNs based on dependency graph analysis; (ii) Dual Half-Space Projected Gradient (DHSPG) and its enhanced version with hierarchical search (H2SPG) to reliably solve (hierarchical) structured sparsity problems and ensure sub-network validity; and (iii) automated sub-network construction using solutions from DHSPG/H2SPG and dependency graphs. Our empirical results demonstrate the efficacy of OTOv3 across various benchmarks in structured pruning and neural architecture search. OTOv3 produces sub-networks that match or exceed the state-of-the-arts. The source code will be available at https://github.com/tianyic/only_train_once.

Shunyang Luo, Peibei Cao, Zhihui Zhu et al.

Reward models (RMs) are central to aligning large language models, yet their practical effectiveness hinges on generalization to unseen prompts and shifting distributions. Most existing RM evaluations rely on static, pre-annotated preference datasets, which provide limited coverage and often fail to faithfully assess generalization in open-world settings. We introduce Pairwise Maximum Discrepancy Competition (PMDC), a dynamic and annotation-efficient framework for evaluating RM generalization using a large, unlabeled, open-domain prompt pool. PMDC actively selects prompt--response pairs that maximize disagreement between two RMs, yielding a compact set of highly contentious test cases. These cases are adjudicated by an oracle, and the resulting outcomes are aggregated via a Bradley--Terry model to produce a global ranking and pairwise win-rate landscape of RMs. We apply PMDC to re-evaluate 10 representative RMs and observe substantial rank reshuffling compared with conventional benchmarks. Qualitative analyses further uncover systematic generalization failures, providing valuable insights for improving reward modeling.

Yuqi Tang, Jing Yu, Zichang Su et al.

Clinical diagnosis begins with doctor-patient interaction, during which physicians iteratively gather information, determine examination and refine differential diagnosis through patients' response. This dynamic clinical-reasoning process is poorly represented by existing LLM benchmarks that focus on static question-answering. To mitigate these gaps, recent methods explore dynamic medical frameworks involving interactive clinical dialogues. Although effective, they often rely on limited, contamination-prone datasets and lack granular, multi-level evaluation. In this work, we propose ClinDEF, a dynamic framework for assessing clinical reasoning in LLMs through simulated diagnostic dialogues. Grounded in a disease knowledge graph, our method dynamically generates patient cases and facilitates multi-turn interactions between an LLM-based doctor and an automated patient agent. Our evaluation protocol goes beyond diagnostic accuracy by incorporating fine-grained efficiency analysis and rubric-based assessment of diagnostic quality. Experiments show that ClinDEF effectively exposes critical clinical reasoning gaps in state-of-the-art LLMs, offering a more nuanced and clinically meaningful evaluation paradigm.

Xinyi Ling, Hanwen Du, Zhihui Zhu et al.

E-commerce platforms are rich in multimodal data, featuring a variety of images that depict product details. However, this raises an important question: do these images always enhance product understanding, or can they sometimes introduce redundancy or degrade performance? Existing datasets are limited in both scale and design, making it difficult to systematically examine this question. To this end, we introduce EcomMMMU, an e-commerce multimodal multitask understanding dataset with 406,190 samples and 8,989,510 images. EcomMMMU is comprised of multi-image visual-language data designed with 8 essential tasks and a specialized VSS subset to benchmark the capability of multimodal large language models (MLLMs) to effectively utilize visual content. Analysis on EcomMMMU reveals that product images do not consistently improve performance and can, in some cases, degrade it. This indicates that MLLMs may struggle to effectively leverage rich visual content for e-commerce tasks. Building on these insights, we propose SUMEI, a data-driven method that strategically utilizes multiple images via predicting visual utilities before using them for downstream tasks. Comprehensive experiments demonstrate the effectiveness and robustness of SUMEI. The data and code are available through https://github.com/ninglab/EcomMMMU.

Tianyu Ding, Jinxin Zhou, Tianyi Chen et al.

Existing angle-based contour descriptors suffer from lossy representation for non-starconvex shapes. By and large, this is the result of the shape being registered with a single global inner center and a set of radii corresponding to a polar coordinate parameterization. In this paper, we propose AdaContour, an adaptive contour descriptor that uses multiple local representations to desirably characterize complex shapes. After hierarchically encoding object shapes in a training set and constructing a contour matrix of all subdivided regions, we compute a robust low-rank robust subspace and approximate each local contour by linearly combining the shared basis vectors to represent an object. Experiments show that AdaContour is able to represent shapes more accurately and robustly than other descriptors while retaining effectiveness. We validate AdaContour by integrating it into off-the-shelf detectors to enable instance segmentation which demonstrates faithful performance. The code is available at https://github.com/tding1/AdaContour.

Tianyi Chen, Bo Ji, Tianyu Ding et al.

Structured pruning is a commonly used technique in deploying deep neural networks (DNNs) onto resource-constrained devices. However, the existing pruning methods are usually heuristic, task-specified, and require an extra fine-tuning procedure. To overcome these limitations, we propose a framework that compresses DNNs into slimmer architectures with competitive performances and significant FLOPs reductions by Only-Train-Once (OTO). OTO contains two keys: (i) we partition the parameters of DNNs into zero-invariant groups, enabling us to prune zero groups without affecting the output; and (ii) to promote zero groups, we then formulate a structured-sparsity optimization problem and propose a novel optimization algorithm, Half-Space Stochastic Projected Gradient (HSPG), to solve it, which outperforms the standard proximal methods on group sparsity exploration and maintains comparable convergence. To demonstrate the effectiveness of OTO, we train and compress full models simultaneously from scratch without fine-tuning for inference speedup and parameter reduction, and achieve state-of-the-art results on VGG16 for CIFAR10, ResNet50 for CIFAR10 and Bert for SQuAD and competitive result on ResNet50 for ImageNet. The source code is available at https://github.com/tianyic/only_train_once.

Tianyu Ding, Luming Liang, Zhihui Zhu et al.

DNN-based frame interpolation--that generates the intermediate frames given two consecutive frames--typically relies on heavy model architectures with a huge number of features, preventing them from being deployed on systems with limited resources, e.g., mobile devices. We propose a compression-driven network design for frame interpolation (CDFI), that leverages model pruning through sparsity-inducing optimization to significantly reduce the model size while achieving superior performance. Concretely, we first compress the recently proposed AdaCoF model and show that a 10X compressed AdaCoF performs similarly as its original counterpart; then we further improve this compressed model by introducing a multi-resolution warping module, which boosts visual consistencies with multi-level details. As a consequence, we achieve a significant performance gain with only a quarter in size compared with the original AdaCoF. Moreover, our model performs favorably against other state-of-the-arts in a broad range of datasets. Finally, the proposed compression-driven framework is generic and can be easily transferred to other DNN-based frame interpolation algorithm. Our source code is available at https://github.com/tding1/CDFI.

Zhen Qin, Michael B. Wakin, Zhihui Zhu

In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which enforces orthonormality among most of the factors. To ensure the orthonormal structure, we utilize the Riemannian gradient descent (RGD) for optimizing those factors over the Stiefel manifold. We first delve into the TT factorization problem and establish the local linear convergence of RGD. Notably, the rate of convergence only experiences a linear decline as the tensor order increases. We then study the sensing problem that aims to recover a TT format tensor from linear measurements. Assuming the sensing operator satisfies the restricted isometry property (RIP), we show that with a proper initialization, which could be obtained through spectral initialization, RGD also converges to the ground-truth tensor at a linear rate. Furthermore, we expand our analysis to encompass scenarios involving Gaussian noise in the measurements. We prove that RGD can reliably recover the ground truth at a linear rate, with the recovery error exhibiting only polynomial growth in relation to the tensor order. We conduct various experiments to validate our theoretical findings.

Yichen Gao, Altay Unal, Akshay Rangamani et al.

While numerous machine unlearning (MU) methods have recently been developed with promising results in erasing the influence of forgotten data, classes, or concepts, they are also highly vulnerable-for example, simple fine-tuning can inadvertently reintroduce erased concepts. In this paper, we address this contradiction by examining the internal representations of unlearned models, in contrast to prior work that focuses primarily on output-level behavior. Our analysis shows that many state-of-the-art MU methods appear successful mainly due to a misalignment between last-layer features and the classifier, a phenomenon we call feature-classifier misalignment. In fact, hidden features remain highly discriminative, and simple linear probing can recover near-original accuracy. Assuming neural collapse in the original model, we further demonstrate that adjusting only the classifier can achieve negligible forget accuracy while preserving retain accuracy, and we corroborate this with experiments using classifier-only fine-tuning. Motivated by these findings, we propose MU methods based on a class-mean features (CMF) classifier, which explicitly enforces alignment between features and classifiers. Experiments on standard benchmarks show that CMF-based unlearning reduces forgotten information in representations while maintaining high retain accuracy, highlighting the need for faithful representation-level evaluation of MU.

Xiao Li, Zekai Zhang, Xiang Li et al.

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal representation dynamics, where the quality of learned features peaks at an intermediate noise level. In this work, we conduct a comprehensive theoretical and empirical investigation of this phenomenon. Leveraging the inherent low-dimensionality structure of image data, we theoretically demonstrate that the unimodal dynamic emerges when the diffusion model successfully captures the underlying data distribution. The unimodality arises from an interplay between denoising strength and class confidence across noise scales. Empirically, we further show that, in classification tasks, the presence of unimodal dynamics reliably reflects the generalization of the diffusion model: it emerges when the model generates novel images and gradually transitions to a monotonically decreasing curve as the model begins to memorize the training data.

Jiachen Jiang, Yuxin Dong, Jinxin Zhou et al.

In-context learning (ICL) enables large language models (LLMs) to adapt to new tasks without weight updates by learning from demonstration sequences. While ICL shows strong empirical performance, its internal representational mechanisms are not yet well understood. In this work, we conduct a statistical geometric analysis of ICL representations to investigate how task-specific information is captured across layers. Our analysis reveals an intriguing phenomenon, which we term *Layerwise Compression-Expression*: early layers progressively produce compact and discriminative representations that encode task information from the input demonstrations, while later layers express these representations to incorporate the query and generate the prediction. This phenomenon is observed consistently across diverse tasks and a range of contemporary LLM architectures. We demonstrate that it has important implications for ICL performance -- improving with model size and the number of demonstrations -- and for robustness in the presence of noisy examples. To further understand the effect of the compact task representation, we propose a bias-variance decomposition and provide a theoretical analysis showing how attention mechanisms contribute to reducing both variance and bias, thereby enhancing performance as the number of demonstrations increases. Our findings reveal an intriguing layerwise dynamic in ICL, highlight how structured representations emerge within LLMs, and showcase that analyzing internal representations can facilitate a deeper understanding of model behavior.

Huminhao Zhu, Fangyikang Wang, Tianyu Ding et al.

Training with synthetic data is becoming increasingly inevitable as synthetic content proliferates across the web, driven by the remarkable performance of recent deep generative models. This reliance on synthetic data can also be intentional, as seen in Rectified Flow models, whose Reflow method iteratively uses self-generated data to straighten the flow and improve sampling efficiency. However, recent studies have shown that repeatedly training on self-generated samples can lead to model collapse (MC), where performance degrades over time. Despite this, most recent work on MC either focuses on empirical observations or analyzes regression problems and maximum likelihood objectives, leaving a rigorous theoretical analysis of reflow methods unexplored. In this paper, we aim to fill this gap by providing both theoretical analysis and practical solutions for addressing MC in diffusion/flow models. We begin by studying Denoising Autoencoders and prove performance degradation when DAEs are iteratively trained on their own outputs. To the best of our knowledge, we are the first to rigorously analyze model collapse in DAEs and, by extension, in diffusion models and Rectified Flow. Our analysis and experiments demonstrate that rectified flow also suffers from MC, leading to potential performance degradation in each reflow step. Additionally, we prove that incorporating real data can prevent MC during recursive DAE training, supporting the recent trend of using real data as an effective approach for mitigating MC. Building on these insights, we propose a novel Real-data Augmented Reflow and a series of improved variants, which seamlessly integrate real data into Reflow training by leveraging reverse flow. Empirical evaluations on standard image benchmarks confirm that RA Reflow effectively mitigates model collapse, preserving high-quality sample generation even with fewer sampling steps.

Xinyi Ling, Hanwen Du, Bo Peng et al.

Leveraging multimodal data to drive breakthroughs in e-commerce applications through Multimodal Foundation Models (MFMs) is gaining increasing attention from the research community. However, there are significant challenges that hinder the optimal use of multimodal e-commerce data by foundation models: (1) the scarcity of large-scale, high-quality multimodal benchmark datasets; and (2) the lack of effective multimodal information integration methods. To address these challenges, in this paper, we introduce MMECInstruct, the first-ever, large-scale, and high-quality multimodal instruction dataset for e-commerce. We also develop CASLIE, a simple, lightweight, yet effective framework for integrating multimodal information for e-commerce. Leveraging MMECInstruct, we fine-tune a series of e-commerce MFMs within CASLIE, denoted as CASLIE models. Our comprehensive evaluation demonstrates that CASLIE models substantially outperform 5 categories of advanced baseline models in the in-domain evaluation. Moreover, CASLIE models show strong generalizability to out-of-domain settings. MMECInstruct and CASLIE models are publicly accessible through https://ninglab.github.io/CASLIE/.

Jiachen Jiang, Tianyu Ding, Zhihui Zhu

LLM-driven evolutionary systems have shown promise for automated science discovery, yet existing approaches such as AlphaEvolve rely on full-code histories that are context-inefficient and potentially provide weak evolutionary guidance. In this work, we first formalize the evolutionary agents as a general Expectation-Maximization framework, where the language model samples candidate programs (E-step) and the system updates the control context based on evaluation feedback (M-step). Under this view, constructing context via full-code snapshots constitutes a suboptimal M-step, as redundant implement details dilutes core algorithmic ideas, making it difficult to provide clear inspirations for evolution. To address this, we propose DeltaEvolve, a momentum-driven evolutionary framework that replaces full-code history with structured semantic delta capturing how and why modifications between successive nodes affect performance. As programs are often decomposable, semantic delta usually contains many effective components which are transferable and more informative to drive improvement. By organizing semantic delta through multi-level database and progressive disclosure mechanism, input tokens are further reduced. Empirical evaluations on tasks across diverse scientific domains show that our framework can discover better solution with less token consumption over full-code-based evolutionary agents.

Zhen Qin, Michael B. Wakin, Zhihui Zhu

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number of entries in a tensor grows exponentially with the order. Consequently, they are widely used in signal recovery and data analysis across domains such as signal processing, machine learning, and quantum physics. A computationally and memory-efficient approach to these problems is to optimize directly over the factors using local search algorithms such as gradient descent, a strategy known as the factorization approach in matrix and tensor optimization. However, the resulting optimization problems are highly nonconvex due to the multiplicative interactions between factors, posing significant challenges for convergence analysis and recovery guarantees. In this paper, we present a unified framework for the factorization approach to solving various tensor decomposition problems. Specifically, by leveraging the canonical form of tensor decompositions--where most factors are constrained to be orthonormal to mitigate scaling ambiguity--we apply Riemannian gradient descent (RGD) to optimize these orthonormal factors on the Stiefel manifold. Under a mild condition on the loss function, we establish a Riemannian regularity condition for the factorized objective and prove that RGD converges to the ground-truth tensor at a linear rate when properly initialized. Notably, both the initialization requirement and the convergence rate scale polynomially rather than exponentially with $N$, improving upon existing results for Tucker and tensor-train format tensors.

Yuxin Dong, Jiachen Jiang, Zhihui Zhu et al.

Task vectors offer a compelling mechanism for accelerating inference in in-context learning (ICL) by distilling task-specific information into a single, reusable representation. Despite their empirical success, the underlying principles governing their emergence and functionality remain unclear. This work proposes the Linear Combination Conjecture, positing that task vectors act as single in-context demonstrations formed through linear combinations of the original ones. We provide both theoretical and empirical support for this conjecture. First, we show that task vectors naturally emerge in linear transformers trained on triplet-formatted prompts through loss landscape analysis. Next, we predict the failure of task vectors on representing high-rank mappings and confirm this on practical LLMs. Our findings are further validated through saliency analyses and parameter visualization, suggesting an enhancement of task vectors by injecting multiple ones into few-shot prompts. Together, our results advance the understanding of task vectors and shed light on the mechanisms underlying ICL in transformer-based models.

Xudong Zhu, Jiachen Jiang, Mohammad Mahdi Khalili et al.

Self-reflection -- the ability of a large language model (LLM) to revisit, evaluate, and revise its own reasoning -- has recently emerged as a powerful behavior enabled by reinforcement learning with verifiable rewards (RLVR). While self-reflection correlates with improved reasoning accuracy, its origin and underlying mechanisms remain poorly understood. In this work, {\it we first show that self-reflection is not exclusive to RLVR fine-tuned models: it already emerges, albeit rarely, in pretrained models}. To probe this latent ability, we introduce Reflection-Inducing Probing, a method that injects reflection-triggering reasoning traces from fine-tuned models into pretrained models. This intervention raises self-reflection frequency of Qwen2.5 from 0.6\% to 18.6\%, revealing a hidden capacity for reflection. Moreover, our analysis of internal representations shows that both pretrained and fine-tuned models maintain hidden states that distinctly separate self-reflective from non-reflective contexts. Leveraging this observation, {\it we then construct a self-reflection vector, a direction in activation space associated with self-reflective reasoning}. By manipulating this vector, we enable bidirectional control over the self-reflective behavior for both pretrained and fine-tuned models. Experiments across multiple reasoning benchmarks show that enhancing these vectors improves reasoning performance by up to 12\%, while suppressing them reduces computational cost, providing a flexible mechanism to navigate the trade-off between reasoning quality and efficiency without requiring additional training. Our findings further our understanding of self-reflection and support a growing body of work showing that understanding model internals can enable precise behavioral control.

Zhen Qin, Jinxin Zhou, Zhihui Zhu

Transformer models have emerged as fundamental tools across various scientific and engineering disciplines, owing to their outstanding performance in diverse applications. Despite this empirical success, the theoretical foundations of Transformers remain relatively underdeveloped, particularly in understanding their training dynamics. Existing research predominantly examines isolated components--such as self-attention mechanisms and feedforward networks--without thoroughly investigating the interdependencies between these components, especially when residual connections are present. In this paper, we aim to bridge this gap by analyzing the convergence behavior of a structurally complete yet single-layer Transformer, comprising self-attention, a feedforward network, and residual connections. We demonstrate that, under appropriate initialization, gradient descent exhibits a linear convergence rate, where the convergence speed is determined by the minimum and maximum singular values of the output matrix from the attention layer. Moreover, our analysis reveals that residual connections serve to ameliorate the ill-conditioning of this output matrix, an issue stemming from the low-rank structure imposed by the softmax operation, thereby promoting enhanced optimization stability. We also extend our theoretical findings to a multi-layer Transformer architecture, confirming the linear convergence rate of gradient descent under suitable initialization. Empirical results corroborate our theoretical insights, illustrating the beneficial role of residual connections in promoting convergence stability.

Zhen Qin, Zhihui Zhu

Tensor train (TT) decomposition represents an $N$-order tensor using $O(N)$ matrices (i.e., factors) of small dimensions, achieved through products among these factors. Due to its compact representation, TT decomposition has found wide applications, including various tensor recovery problems in signal processing and quantum information. In this paper, we study the problem of reconstructing a TT format tensor from measurements that are contaminated by outliers with arbitrary values. Given the vulnerability of smooth formulations to corruptions, we use an $\ell_1$ loss function to enhance robustness against outliers. We first establish the $\ell_1/\ell_2$-restricted isometry property (RIP) for Gaussian measurement operators, demonstrating that the information in the TT format tensor can be preserved using a number of measurements that grows linearly with $N$. We also prove the sharpness property for the $\ell_1$ loss function optimized over TT format tensors. Building on the $\ell_1/\ell_2$-RIP and sharpness property, we then propose two complementary methods to recover the TT format tensor from the corrupted measurements: the projected subgradient method (PSubGM), which optimizes over the entire tensor, and the factorized Riemannian subgradient method (FRSubGM), which optimizes directly over the factors. Compared to PSubGM, the factorized approach FRSubGM significantly reduces the memory cost at the expense of a slightly slower convergence rate. Nevertheless, we show that both methods, with diminishing step sizes, converge linearly to the ground-truth tensor given an appropriate initialization, which can be obtained by a truncated spectral method.

Jiachen Jiang, Tianyu Ding, Ke Zhang et al.

All-in-one image restoration seeks to recover high-quality images from various types of degradation using a single model, without prior knowledge of the corruption source. However, existing methods often struggle to effectively and efficiently handle multiple degradation types. We present Cat-AIR, a novel \textbf{C}ontent \textbf{A}nd \textbf{T}ask-aware framework for \textbf{A}ll-in-one \textbf{I}mage \textbf{R}estoration. Cat-AIR incorporates an alternating spatial-channel attention mechanism that adaptively balances the local and global information for different tasks. Specifically, we introduce cross-layer channel attentions and cross-feature spatial attentions that allocate computations based on content and task complexity. Furthermore, we propose a smooth learning strategy that allows for seamless adaptation to new restoration tasks while maintaining performance on existing ones. Extensive experiments demonstrate that Cat-AIR achieves state-of-the-art results across a wide range of restoration tasks, requiring fewer FLOPs than previous methods, establishing new benchmarks for efficient all-in-one image restoration.

Jiachen Jiang, Jinxin Zhou, Bo Peng et al.

Achieving better alignment between vision embeddings and Large Language Models (LLMs) is crucial for enhancing the abilities of Multimodal LLMs (MLLMs), particularly for recent models that rely on powerful pretrained vision encoders and LLMs. A common approach to connect the pretrained vision encoder and LLM is through a projector applied after the vision encoder. However, the projector is often trained to enable the LLM to generate captions, and hence the mechanism by which LLMs understand each vision token remains unclear. In this work, we first investigate the role of the projector in compressing vision embeddings and aligning them with word embeddings. We show that the projector significantly compresses visual information, removing redundant details while preserving essential elements necessary for the LLM to understand visual content. We then examine patch-level alignment -- the alignment between each vision patch and its corresponding semantic words -- and propose a *multi-semantic alignment hypothesis*. Our analysis indicates that the projector trained by caption loss improves patch-level alignment but only to a limited extent, resulting in weak and coarse alignment. To address this issue, we propose *patch-aligned training* to efficiently enhance patch-level alignment. Our experiments show that patch-aligned training (1) achieves stronger compression capability and improved patch-level alignment, enabling the MLLM to generate higher-quality captions, (2) improves the MLLM's performance by 16% on referring expression grounding tasks, 4% on question-answering tasks, and 3% on modern instruction-following benchmarks when using the same supervised fine-tuning (SFT) setting. The proposed method can be easily extended to other multimodal models.

Jinxin Zhou, Jiachen Jiang, Zhihui Zhu

Extending CLIP models to semantic segmentation remains challenging due to the misalignment between their image-level pre-training objectives and the pixel-level visual understanding required for dense prediction. While prior efforts have achieved encouraging results by reorganizing the final layer and features, they often inherit the global alignment bias of preceding layers, leading to suboptimal segmentation performance. In this work, we propose LHT-CLIP, a novel training-free framework that systematically exploits the visual discriminability of CLIP across layer, head, and token levels. Through comprehensive analysis, we reveal three key insights: (i) the final layers primarily strengthen image-text alignment with sacrifice of visual discriminability (e.g., last 3 layers in ViT-B/16 and 8 layers in ViT-L/14), partly due to the emergence of anomalous tokens; (ii) a subset of attention heads (e.g., 10 out of 144 in ViT-B/16) display consistently strong visual discriminability across datasets; (iii) abnormal tokens display sparse and consistent activation pattern compared to normal tokens. Based on these findings, we propose three complementary techniques: semantic-spatial reweighting, selective head enhancement, and abnormal token replacement to effectively restore visual discriminability and improve segmentation performance without any additional training, auxiliary pre-trained networks, or extensive hyperparameter tuning. Extensive experiments on 8 common semantic segmentation benchmarks demonstrate that LHT-CLIP achieves state-of-the-art performance across diverse scenarios, highlighting its effectiveness and practicality for real-world deployment.

Hancheng Min, Zhihui Zhu, René Vidal

Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at the last layer of a trained neural network. Prior works on the theoretical understandings of NC have focused on analyzing the optimization landscape of matrix-factorization-like problems by considering the last-layer features as unconstrained free optimization variables and showing that their global minima exhibit NC. In this paper, we show that gradient flow on a two-layer ReLU network for classifying orthogonally separable data provably exhibits NC, thereby advancing prior results in two ways: First, we relax the assumption of unconstrained features, showing the effect of data structure and nonlinear activations on NC characterizations. Second, we reveal the role of the implicit bias of the training dynamics in facilitating the emergence of NC.

Kehua Feng, Keyan Ding, Zhihui Zhu et al.

While chain-of-thought (CoT) distillation from advanced large language models (LLMs) has proven effective in general reasoning tasks, it struggles in scientific domains where even advanced models often produce incorrect or superficial reasoning due to high complexity and specialized knowledge requirements. Directly distilling from such flawed outputs results in low-quality training data and limits the performance of smaller student models. To overcome this, we propose CoT-Evo, an evolutionary CoT distillation framework. It begins by constructing a diverse pool of reasoning trajectories from multiple LLM thinkers, enriches them with automatically retrieved domain knowledge, and iteratively refines the trajectories using novelty-driven selection, reflective recombination and mutation. The refinement is guided by a fitness function that evaluates answer correctness, coherence, and effective knowledge utilization. This results in a high-quality CoT dataset tailored for scientific reasoning. We employ this evolved dataset to fine-tune a compact model, which achieves state-of-the-art performance on scientific reasoning benchmarks. Our work establishes a scalable approach to synthesizing high-fidelity scientific reasoning data from diverse and fallible LLMs.

Jiachen Jiang, Zhen Qin, Zhihui Zhu

Channel equalization is fundamental for mitigating distortions such as frequency-selective fading and inter-symbol interference. Unlike standard supervised learning approaches that require costly retraining or fine-tuning for each new task, in-context learning (ICL) adapts to new channels at inference time with only a few examples. However, existing ICL-based equalizers are primarily developed for and evaluated on static channels within the context window. Indeed, to our knowledge, prior principled analyses and theoretical studies of ICL focus exclusively on the stationary setting, where the function remains fixed within the context. In this paper, we investigate the ability of ICL to address non-stationary problems through the lens of time-varying channel equalization. We employ a principled framework for designing efficient attention mechanisms with improved adaptivity in non-stationary tasks, leveraging algorithms from adaptive signal processing to guide better designs. For example, new attention variants can be derived from the Least Mean Square (LMS) adaptive algorithm, a Least Root Mean Square (LRMS) formulation for enhanced robustness, or multi-step gradient updates for improved long-term tracking. Experimental results demonstrate that ICL holds strong promise for non-stationary MIMO equalization, and that attention mechanisms inspired by classical adaptive algorithms can substantially enhance adaptability and performance in dynamic environments. Our findings may provide critical insights for developing next-generation wireless foundation models with stronger adaptability and robustness.

Xudong Zhu, Mohammad Mahdi Khalili, Zhihui Zhu

Sparse autoencoders (SAEs) have emerged as powerful techniques for interpretability of large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the $\ell_0$ sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method, a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

Jiachen Jiang, Jinxin Zhou, Zhihui Zhu

Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such as those based on Centered Kernel Alignment (CKA), rely on statistical properties of the representations for a set of data points. In this paper, we focus on transformer models and study the similarity of representations between the hidden layers of individual transformers. In this context, we show that a simple sample-wise cosine similarity metric is capable of capturing the similarity and aligns with the complicated CKA. Our experimental results on common transformers reveal that representations across layers are positively correlated, with similarity increasing when layers get closer. We provide a theoretical justification for this phenomenon under the geodesic curve assumption for the learned transformer. We then show that an increase in representation similarity implies an increase in predicted probability when directly applying the last-layer classifier to any hidden layer representation. We then propose an aligned training method to improve the effectiveness of shallow layer by enhancing the similarity between internal representations, with trained models that enjoy the following properties: (1) more early saturation events, (2) layer-wise accuracies monotonically increase and reveal the minimal depth needed for the given task, (3) when served as multi-exit models, they achieve on-par performance with standard multi-exit architectures which consist of additional classifiers designed for early exiting in shallow layers. To our knowledge, our work is the first to show that one common classifier is sufficient for multi-exit models. We conduct experiments on both vision and NLP tasks to demonstrate the performance of the proposed aligned training.

Zhen Qin, Zhihui Zhu

Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor complexity poses challenges for storage and computation in ToT regression. To overcome this hurdle, tensor decompositions have been introduced, with the tensor train (TT)-based ToT model proving efficient in practice due to reduced memory requirements, enhanced computational efficiency, and decreased sampling complexity. Despite these practical benefits, a disparity exists between theoretical analysis and real-world performance. In this paper, we delve into the theoretical and algorithmic aspects of the TT-based ToT regression model. Assuming the regression operator satisfies the restricted isometry property (RIP), we conduct an error analysis for the solution to a constrained least-squares optimization problem. This analysis includes upper error bound and minimax lower bound, revealing that such error bounds polynomially depend on the order $N+M$. To efficiently find solutions meeting such error bounds, we propose two optimization algorithms: the iterative hard thresholding (IHT) algorithm (employing gradient descent with TT-singular value decomposition (TT-SVD)) and the factorization approach using the Riemannian gradient descent (RGD) algorithm. When RIP is satisfied, spectral initialization facilitates proper initialization, and we establish the linear convergence rate of both IHT and RGD.

Peng Wang, Huikang Liu, Druv Pai et al.

The maximal coding rate reduction (MCR$^2$) objective for learning structured and compact deep representations is drawing increasing attention, especially after its recent usage in the derivation of fully explainable and highly effective deep network architectures. However, it lacks a complete theoretical justification: only the properties of its global optima are known, and its global landscape has not been studied. In this work, we give a complete characterization of the properties of all its local and global optima, as well as other types of critical points. Specifically, we show that each (local or global) maximizer of the MCR$^2$ problem corresponds to a low-dimensional, discriminative, and diverse representation, and furthermore, each critical point of the objective is either a local maximizer or a strict saddle point. Such a favorable landscape makes MCR$^2$ a natural choice of objective for learning diverse and discriminative representations via first-order optimization methods. To validate our theoretical findings, we conduct extensive experiments on both synthetic and real data sets.

Xi Chen, Zhihui Zhu, Andrew Perrault

The reward signal plays a central role in defining the desired behaviors of agents in reinforcement learning (RL). Rewards collected from realistic environments could be perturbed, corrupted, or noisy due to an adversary, sensor error, or because they come from subjective human feedback. Thus, it is important to construct agents that can learn under such rewards. Existing methodologies for this problem make strong assumptions, including that the perturbation is known in advance, clean rewards are accessible, or that the perturbation preserves the optimal policy. We study a new, more general, class of unknown perturbations, and introduce a distributional reward critic framework for estimating reward distributions and perturbations during training. Our proposed methods are compatible with any RL algorithm. Despite their increased generality, we show that they achieve comparable or better rewards than existing methods in a variety of environments, including those with clean rewards. Under the challenging and generalized perturbations we study, we win/tie the highest return in 44/48 tested settings (compared to 11/48 for the best baseline). Our results broaden and deepen our ability to perform RL in reward-perturbed environments.

Sheng Liu, Zhihui Zhu, Qing Qu et al.

Recently, over-parameterized deep networks, with increasingly more network parameters than training samples, have dominated the performances of modern machine learning. However, when the training data is corrupted, it has been well-known that over-parameterized networks tend to overfit and do not generalize. In this work, we propose a principled approach for robust training of over-parameterized deep networks in classification tasks where a proportion of training labels are corrupted. The main idea is yet very simple: label noise is sparse and incoherent with the network learned from clean data, so we model the noise and learn to separate it from the data. Specifically, we model the label noise via another sparse over-parameterization term, and exploit implicit algorithmic regularizations to recover and separate the underlying corruptions. Remarkably, when trained using such a simple method in practice, we demonstrate state-of-the-art test accuracy against label noise on a variety of real datasets. Furthermore, our experimental results are corroborated by theory on simplified linear models, showing that exact separation between sparse noise and low-rank data can be achieved under incoherent conditions. The work opens many interesting directions for improving over-parameterized models by using sparse over-parameterization and implicit regularization.