Zhouchen Lin

Yifei Wang, Qi Zhang, Yisen Wang et al. · mit

Recently, contrastive learning has risen to be a promising approach for large-scale self-supervised learning. However, theoretical understanding of how it works is still unclear. In this paper, we propose a new guarantee on the downstream performance without resorting to the conditional independence assumption that is widely adopted in previous work but hardly holds in practice. Our new theory hinges on the insight that the support of different intra-class samples will become more overlapped under aggressive data augmentations, thus simply aligning the positive samples (augmented views of the same sample) could make contrastive learning cluster intra-class samples together. Based on this augmentation overlap perspective, theoretically, we obtain asymptotically closed bounds for downstream performance under weaker assumptions, and empirically, we propose an unsupervised model selection metric ARC that aligns well with downstream accuracy. Our theory suggests an alternative understanding of contrastive learning: the role of aligning positive samples is more like a surrogate task than an ultimate goal, and the overlapped augmented views (i.e., the chaos) create a ladder for contrastive learning to gradually learn class-separated representations. The code for computing ARC is available at https://github.com/zhangq327/ARC.

Yifei Wang, Qi Zhang, Tianqi Du et al. · mit

In recent years, contrastive learning achieves impressive results on self-supervised visual representation learning, but there still lacks a rigorous understanding of its learning dynamics. In this paper, we show that if we cast a contrastive objective equivalently into the feature space, then its learning dynamics admits an interpretable form. Specifically, we show that its gradient descent corresponds to a specific message passing scheme on the corresponding augmentation graph. Based on this perspective, we theoretically characterize how contrastive learning gradually learns discriminative features with the alignment update and the uniformity update. Meanwhile, this perspective also establishes an intriguing connection between contrastive learning and Message Passing Graph Neural Networks (MP-GNNs). This connection not only provides a unified understanding of many techniques independently developed in each community, but also enables us to borrow techniques from MP-GNNs to design new contrastive learning variants, such as graph attention, graph rewiring, jumpy knowledge techniques, etc. We believe that our message passing perspective not only provides a new theoretical understanding of contrastive learning dynamics, but also bridges the two seemingly independent areas together, which could inspire more interleaving studies to benefit from each other. The code is available at https://github.com/PKU-ML/Message-Passing-Contrastive-Learning.

Xingyu Xie, Pan Zhou, Huan Li et al.

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model training speed across deep networks, we propose the ADAptive Nesterov momentum algorithm, Adan for short. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra overhead of computing gradient at the extrapolation point. Then, Adan adopts NME to estimate the gradient's first- and second-order moments in adaptive gradient algorithms for convergence acceleration. Besides, we prove that Adan finds an $ε$-approximate first-order stationary point within $\mathcal{O}(ε^{-3.5})$ stochastic gradient complexity on the non-convex stochastic problems (e.g., deep learning problems), matching the best-known lower bound. Extensive experimental results show that Adan consistently surpasses the corresponding SoTA optimizers on vision, language, and RL tasks and sets new SoTAs for many popular networks and frameworks, e.g., ResNet, ConvNext, ViT, Swin, MAE, DETR, GPT-2, Transformer-XL, and BERT. More surprisingly, Adan can use half of the training cost (epochs) of SoTA optimizers to achieve higher or comparable performance on ViT, GPT-2, MAE, etc., and also shows great tolerance to a large range of minibatch size, e.g., from 1k to 32k. Code is released at https://github.com/sail-sg/Adan, and has been used in multiple popular deep learning frameworks or projects.

Yibo Yang, Haobo Yuan, Xiangtai Li et al.

Few-shot class-incremental learning (FSCIL) has been a challenging problem as only a few training samples are accessible for each novel class in the new sessions. Finetuning the backbone or adjusting the classifier prototypes trained in the prior sessions would inevitably cause a misalignment between the feature and classifier of old classes, which explains the well-known catastrophic forgetting problem. In this paper, we deal with this misalignment dilemma in FSCIL inspired by the recently discovered phenomenon named neural collapse, which reveals that the last-layer features of the same class will collapse into a vertex, and the vertices of all classes are aligned with the classifier prototypes, which are formed as a simplex equiangular tight frame (ETF). It corresponds to an optimal geometric structure for classification due to the maximized Fisher Discriminant Ratio. We propose a neural collapse inspired framework for FSCIL. A group of classifier prototypes are pre-assigned as a simplex ETF for the whole label space, including the base session and all the incremental sessions. During training, the classifier prototypes are not learnable, and we adopt a novel loss function that drives the features into their corresponding prototypes. Theoretical analysis shows that our method holds the neural collapse optimality and does not break the feature-classifier alignment in an incremental fashion. Experiments on the miniImageNet, CUB-200, and CIFAR-100 datasets demonstrate that our proposed framework outperforms the state-of-the-art performances. Code address: https://github.com/NeuralCollapseApplications/FSCIL

Qingyan Meng, Mingqing Xiao, Shen Yan et al. · deepmind

Spiking Neural Network (SNN) is a promising energy-efficient AI model when implemented on neuromorphic hardware. However, it is a challenge to efficiently train SNNs due to their non-differentiability. Most existing methods either suffer from high latency (i.e., long simulation time steps), or cannot achieve as high performance as Artificial Neural Networks (ANNs). In this paper, we propose the Differentiation on Spike Representation (DSR) method, which could achieve high performance that is competitive to ANNs yet with low latency. First, we encode the spike trains into spike representation using (weighted) firing rate coding. Based on the spike representation, we systematically derive that the spiking dynamics with common neural models can be represented as some sub-differentiable mapping. With this viewpoint, our proposed DSR method trains SNNs through gradients of the mapping and avoids the common non-differentiability problem in SNN training. Then we analyze the error when representing the specific mapping with the forward computation of the SNN. To reduce such error, we propose to train the spike threshold in each layer, and to introduce a new hyperparameter for the neural models. With these components, the DSR method can achieve state-of-the-art SNN performance with low latency on both static and neuromorphic datasets, including CIFAR-10, CIFAR-100, ImageNet, and DVS-CIFAR10.

Qingyan Meng, Mingqing Xiao, Shen Yan et al. · deepmind

Spiking Neural Networks (SNNs) are promising energy-efficient models for neuromorphic computing. For training the non-differentiable SNN models, the backpropagation through time (BPTT) with surrogate gradients (SG) method has achieved high performance. However, this method suffers from considerable memory cost and training time during training. In this paper, we propose the Spatial Learning Through Time (SLTT) method that can achieve high performance while greatly improving training efficiency compared with BPTT. First, we show that the backpropagation of SNNs through the temporal domain contributes just a little to the final calculated gradients. Thus, we propose to ignore the unimportant routes in the computational graph during backpropagation. The proposed method reduces the number of scalar multiplications and achieves a small memory occupation that is independent of the total time steps. Furthermore, we propose a variant of SLTT, called SLTT-K, that allows backpropagation only at K time steps, then the required number of scalar multiplications is further reduced and is independent of the total time steps. Experiments on both static and neuromorphic datasets demonstrate superior training efficiency and performance of our SLTT. In particular, our method achieves state-of-the-art accuracy on ImageNet, while the memory cost and training time are reduced by more than 70% and 50%, respectively, compared with BPTT.

Qi Chen, Yifei Wang, Yisen Wang et al. · mit, pku

Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called Graph Implicit Nonlinear Diffusion (GIND), which implicitly has access to infinite hops of neighbors while adaptively aggregating features with nonlinear diffusion to prevent over-smoothing. Notably, we show that the learned representation can be formalized as the minimizer of an explicit convex optimization objective. With this property, we can theoretically characterize the equilibrium of our GIND from an optimization perspective. More interestingly, we can induce new structural variants by modifying the corresponding optimization objective. To be specific, we can embed prior properties to the equilibrium, as well as introducing skip connections to promote training stability. Extensive experiments show that GIND is good at capturing long-range dependencies, and performs well on both homophilic and heterophilic graphs with nonlinear diffusion. Moreover, we show that the optimization-induced variants of our models can boost the performance and improve training stability and efficiency as well. As a result, our GIND obtains significant improvements on both node-level and graph-level tasks.

Mingqing Xiao, Shuxin Zheng, Chang Liu et al. · microsoft-research, tsinghua

Image rescaling is a commonly used bidirectional operation, which first downscales high-resolution images to fit various display screens or to be storage- and bandwidth-friendly, and afterward upscales the corresponding low-resolution images to recover the original resolution or the details in the zoom-in images. However, the non-injective downscaling mapping discards high-frequency contents, leading to the ill-posed problem for the inverse restoration task. This can be abstracted as a general image degradation-restoration problem with information loss. In this work, we propose a novel invertible framework to handle this general problem, which models the bidirectional degradation and restoration from a new perspective, i.e. invertible bijective transformation. The invertibility enables the framework to model the information loss of pre-degradation in the form of distribution, which could mitigate the ill-posed problem during post-restoration. To be specific, we develop invertible models to generate valid degraded images and meanwhile transform the distribution of lost contents to the fixed distribution of a latent variable during the forward degradation. Then restoration is made tractable by applying the inverse transformation on the generated degraded image together with a randomly-drawn latent variable. We start from image rescaling and instantiate the model as Invertible Rescaling Network (IRN), which can be easily extended to the similar decolorization-colorization task. We further propose to combine the invertible framework with existing degradation methods such as image compression for wider applications. Experimental results demonstrate the significant improvement of our model over existing methods in terms of both quantitative and qualitative evaluations of upscaling and colorizing reconstruction from downscaled and decolorized images, and rate-distortion of image compression.

Xiangtai Li, Shilin Xu, Yibo Yang et al.

Panoptic Part Segmentation (PPS) unifies panoptic and part segmentation into one task. Previous works utilize separate approaches to handle things, stuff, and part predictions without shared computation and task association. We aim to unify these tasks at the architectural level, designing the first end-to-end unified framework, Panoptic-PartFormer. Moreover, we find the previous metric PartPQ biases to PQ. To handle both issues, we first design a meta-architecture that decouples part features and things/stuff features, respectively. We model things, stuff, and parts as object queries and directly learn to optimize all three forms of prediction as a unified mask prediction and classification problem. We term our model as Panoptic-PartFormer. Second, we propose a new metric Part-Whole Quality (PWQ), better to measure this task from pixel-region and part-whole perspectives. It also decouples the errors for part segmentation and panoptic segmentation. Third, inspired by Mask2Former, based on our meta-architecture, we propose Panoptic-PartFormer++ and design a new part-whole cross-attention scheme to boost part segmentation qualities further. We design a new part-whole interaction method using masked cross attention. Finally, extensive ablation studies and analysis demonstrate the effectiveness of both Panoptic-PartFormer and Panoptic-PartFormer++. Compared with previous Panoptic-PartFormer, our Panoptic-PartFormer++ achieves 2% PartPQ and 3% PWQ improvements on the Cityscapes PPS dataset and 5% PartPQ on the Pascal Context PPS dataset. On both datasets, Panoptic-PartFormer++ achieves new state-of-the-art results. Our models can serve as a strong baseline and aid future research in PPS. The source code and trained models will be available at~\url{https://github.com/lxtGH/Panoptic-PartFormer}.

Mingqing Xiao, Qingyan Meng, Zongpeng Zhang et al.

Spiking neural networks (SNNs) with event-based computation are promising brain-inspired models for energy-efficient applications on neuromorphic hardware. However, most supervised SNN training methods, such as conversion from artificial neural networks or direct training with surrogate gradients, require complex computation rather than spike-based operations of spiking neurons during training. In this paper, we study spike-based implicit differentiation on the equilibrium state (SPIDE) that extends the recently proposed training method, implicit differentiation on the equilibrium state (IDE), for supervised learning with purely spike-based computation, which demonstrates the potential for energy-efficient training of SNNs. Specifically, we introduce ternary spiking neuron couples and prove that implicit differentiation can be solved by spikes based on this design, so the whole training procedure, including both forward and backward passes, is made as event-driven spike computation, and weights are updated locally with two-stage average firing rates. Then we propose to modify the reset membrane potential to reduce the approximation error of spikes. With these key components, we can train SNNs with flexible structures in a small number of time steps and with firing sparsity during training, and the theoretical estimation of energy costs demonstrates the potential for high efficiency. Meanwhile, experiments show that even with these constraints, our trained models can still achieve competitive results on MNIST, CIFAR-10, CIFAR-100, and CIFAR10-DVS. Our code is available at https://github.com/pkuxmq/SPIDE-FSNN.

Haotong Yang, Zhouchen Lin, Muhan Zhang

Most knowledge graphs (KGs) are incomplete, which motivates one important research topic on automatically complementing knowledge graphs. However, evaluation of knowledge graph completion (KGC) models often ignores the incompleteness -- facts in the test set are ranked against all unknown triplets which may contain a large number of missing facts not included in the KG yet. Treating all unknown triplets as false is called the closed-world assumption. This closed-world assumption might negatively affect the fairness and consistency of the evaluation metrics. In this paper, we study KGC evaluation under a more realistic setting, namely the open-world assumption, where unknown triplets are considered to include many missing facts not included in the training or test sets. For the currently most used metrics such as mean reciprocal rank (MRR) and Hits@K, we point out that their behavior may be unexpected under the open-world assumption. Specifically, with not many missing facts, their numbers show a logarithmic trend with respect to the true strength of the model, and thus, the metric increase could be insignificant in terms of reflecting the true model improvement. Further, considering the variance, we show that the degradation in the reported numbers may result in incorrect comparisons between different models, where stronger models may have lower metric numbers. We validate the phenomenon both theoretically and experimentally. Finally, we suggest possible causes and solutions for this problem. Our code and data are available at https://github.com/GraphPKU/Open-World-KG .

Yifei Wang, Yisen Wang, Jiansheng Yang et al. · mit

Adversarial Training (AT) is known as an effective approach to enhance the robustness of deep neural networks. Recently researchers notice that robust models with AT have good generative ability and can synthesize realistic images, while the reason behind it is yet under-explored. In this paper, we demystify this phenomenon by developing a unified probabilistic framework, called Contrastive Energy-based Models (CEM). On the one hand, we provide the first probabilistic characterization of AT through a unified understanding of robustness and generative ability. On the other hand, our unified framework can be extended to the unsupervised scenario, which interprets unsupervised contrastive learning as an important sampling of CEM. Based on these, we propose a principled method to develop adversarial learning and sampling methods. Experiments show that the sampling methods derived from our framework improve the sample quality in both supervised and unsupervised learning. Notably, our unsupervised adversarial sampling method achieves an Inception score of 9.61 on CIFAR-10, which is superior to previous energy-based models and comparable to state-of-the-art generative models.

Zhouchen Lin, Minming Chen, Yi Ma

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.html

Sha Yuan, Hanyu Zhao, Shuai Zhao et al. · bytedance, pku

With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.

Yibo Yang, Shixiang Chen, Xiangtai Li et al.

Modern deep neural networks for classification usually jointly learn a backbone for representation and a linear classifier to output the logit of each class. A recent study has shown a phenomenon called neural collapse that the within-class means of features and the classifier vectors converge to the vertices of a simplex equiangular tight frame (ETF) at the terminal phase of training on a balanced dataset. Since the ETF geometric structure maximally separates the pair-wise angles of all classes in the classifier, it is natural to raise the question, why do we spend an effort to learn a classifier when we know its optimal geometric structure? In this paper, we study the potential of learning a neural network for classification with the classifier randomly initialized as an ETF and fixed during training. Our analytical work based on the layer-peeled model indicates that the feature learning with a fixed ETF classifier naturally leads to the neural collapse state even when the dataset is imbalanced among classes. We further show that in this case the cross entropy (CE) loss is not necessary and can be replaced by a simple squared loss that shares the same global optimality but enjoys a better convergence property. Our experimental results show that our method is able to bring significant improvements with faster convergence on multiple imbalanced datasets.

Mingqing Xiao, Qingyan Meng, Zongpeng Zhang et al.

Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Recent progress in training methods has enabled successful deep SNNs on large-scale tasks with low latency. Particularly, backpropagation through time (BPTT) with surrogate gradients (SG) is popularly used to achieve high performance in a very small number of time steps. However, it is at the cost of large memory consumption for training, lack of theoretical clarity for optimization, and inconsistency with the online property of biological learning and rules on neuromorphic hardware. Other works connect spike representations of SNNs with equivalent artificial neural network formulation and train SNNs by gradients from equivalent mappings to ensure descent directions. But they fail to achieve low latency and are also not online. In this work, we propose online training through time (OTTT) for SNNs, which is derived from BPTT to enable forward-in-time learning by tracking presynaptic activities and leveraging instantaneous loss and gradients. Meanwhile, we theoretically analyze and prove that gradients of OTTT can provide a similar descent direction for optimization as gradients based on spike representations under both feedforward and recurrent conditions. OTTT only requires constant training memory costs agnostic to time steps, avoiding the significant memory costs of BPTT for GPU training. Furthermore, the update rule of OTTT is in the form of three-factor Hebbian learning, which could pave a path for online on-chip learning. With OTTT, it is the first time that two mainstream supervised SNN training methods, BPTT with SG and spike representation-based training, are connected, and meanwhile in a biologically plausible form. Experiments on CIFAR-10, CIFAR-100, ImageNet, and CIFAR10-DVS demonstrate the superior performance of our method on large-scale static and neuromorphic datasets in small time steps.

Huan Li, Zhouchen Lin

The Alternating Direction Method of Multipliers (ADMM) is widely used for linearly constrained convex problems. It is proven to have an $o(1/\sqrt{K})$ nonergodic convergence rate and a faster $O(1/K)$ ergodic rate after ergodic averaging, which may destroy the sparsity and low-rankness in sparse and low-rank learning, where $K$ is the number of iterations. In this paper, we modify the accelerated ADMM proposed in [Y. Ouyang, Y. Chen, G. Lan, and E. Pasiliao, An Accelerated Linearized Alternating Direction Method of Multipliers, SIAM J. on Imaging Sciences, 2015, 1588-1623] and give an $O(1/K)$ nonergodic convergence rate analysis, which satisfies $|F(x^K)-F(x^*)|\leq O(1/K)$, $\|Ax^K-b\|\leq O(1/K)$ and $x^K$ has a more favorable sparseness and low-rankness than the ergodic result. As far as we know, this is the first $O(1/K)$ nonergodic convergent ADMM type method for general linearly constrained convex problems. Moreover, we show that the lower complexity bound of ADMM type methods for the separable linearly constrained nonsmooth convex problems is $O(1/K)$, which means that our method is optimal.

Risheng Liu, Zhouchen Lin, Siming Wei et al.

In the past decades, exactly recovering the intrinsic data structure from corrupted observations, which is known as robust principal component analysis (RPCA), has attracted tremendous interests and found many applications in computer vision. Recently, this problem has been formulated as recovering a low-rank component and a sparse component from the observed data matrix. It is proved that under some suitable conditions, this problem can be exactly solved by principal component pursuit (PCP), i.e., minimizing a combination of nuclear norm and $l_1$ norm. Most of the existing methods for solving PCP require singular value decompositions (SVD) of the data matrix, resulting in a high computational complexity, hence preventing the applications of RPCA to very large scale computer vision problems. In this paper, we propose a novel algorithm, called $l_1$ filtering, for \emph{exactly} solving PCP with an $O(r^2(m+n))$ complexity, where $m\times n$ is the size of data matrix and $r$ is the rank of the matrix to recover, which is supposed to be much smaller than $m$ and $n$. Moreover, $l_1$ filtering is \emph{highly parallelizable}. It is the first algorithm that can \emph{exactly} solve a nuclear norm minimization problem in \emph{linear time} (with respect to the data size). Experiments on both synthetic data and real applications testify to the great advantage of $l_1$ filtering in speed over state-of-the-art algorithms.

Yifei Wang, Liangchen Li, Jiansheng Yang et al.

Adversarial Training (AT) has become arguably the state-of-the-art algorithm for extracting robust features. However, researchers recently notice that AT suffers from severe robust overfitting problems, particularly after learning rate (LR) decay. In this paper, we explain this phenomenon by viewing adversarial training as a dynamic minimax game between the model trainer and the attacker. Specifically, we analyze how LR decay breaks the balance between the minimax game by empowering the trainer with a stronger memorization ability, and show such imbalance induces robust overfitting as a result of memorizing non-robust features. We validate this understanding with extensive experiments, and provide a holistic view of robust overfitting from the dynamics of both the two game players. This understanding further inspires us to alleviate robust overfitting by rebalancing the two players by either regularizing the trainer's capacity or improving the attack strength. Experiments show that the proposed ReBalanced Adversarial Training (ReBAT) can attain good robustness and does not suffer from robust overfitting even after very long training. Code is available at https://github.com/PKU-ML/ReBAT.

Haixin Wang, Jianlong Chang, Xiao Luo et al.

Despite recent competitive performance across a range of vision tasks, vision Transformers still have an issue of heavy computational costs. Recently, vision prompt learning has provided an economic solution to this problem without fine-tuning the whole large-scale models. However, the efficiency of existing models are still far from satisfactory due to insertion of extensive prompts blocks and trick prompt designs. In this paper, we propose an efficient vision model named impLicit vIsion prOmpt tuNing (LION), which is motivated by deep implicit models with stable memory costs for various complex tasks. In particular, we merely insect two equilibrium implicit layers in two ends of the pre-trained main backbone with parameters in the backbone frozen. Moreover, we prune the parameters in these two layers according to lottery hypothesis. The performance obtained by our LION are promising on a wide range of datasets. In particular, our LION reduces up to 11.5% of training parameter numbers while obtaining higher performance compared with the state-of-the-art baseline VPT, especially under challenging scenes. Furthermore, we find that our proposed LION had a good generalization performance, making it an easy way to boost transfer learning in the future.

Yibo Yang, Haobo Yuan, Xiangtai Li et al.

How to enable learnability for new classes while keeping the capability well on old classes has been a crucial challenge for class incremental learning. Beyond the normal case, long-tail class incremental learning and few-shot class incremental learning are also proposed to consider the data imbalance and data scarcity, respectively, which are common in real-world implementations and further exacerbate the well-known problem of catastrophic forgetting. Existing methods are specifically proposed for one of the three tasks. In this paper, we offer a unified solution to the misalignment dilemma in the three tasks. Concretely, we propose neural collapse terminus that is a fixed structure with the maximal equiangular inter-class separation for the whole label space. It serves as a consistent target throughout the incremental training to avoid dividing the feature space incrementally. For CIL and LTCIL, we further propose a prototype evolving scheme to drive the backbone features into our neural collapse terminus smoothly. Our method also works for FSCIL with only minor adaptations. Theoretical analysis indicates that our method holds the neural collapse optimality in an incremental fashion regardless of data imbalance or data scarcity. We also design a generalized case where we do not know the total number of classes and whether the data distribution is normal, long-tail, or few-shot for each coming session, to test the generalizability of our method. Extensive experiments with multiple datasets are conducted to demonstrate the effectiveness of our unified solution to all the three tasks and the generalized case.

Zhouchen Lin, Siming Wei

Recent years have witnessed the popularity of using rank minimization as a regularizer for various signal processing and machine learning problems. As rank minimization problems are often converted to nuclear norm minimization (NNM) problems, they have to be solved iteratively and each iteration requires computing a singular value decomposition (SVD). Therefore, their solution suffers from the high computation cost of multiple SVDs. To relieve this issue, we propose using the block Lanczos method to compute the partial SVDs, where the principal singular subspaces obtained in the previous iteration are used to start the block Lanczos procedure. To avoid the expensive reorthogonalization in the Lanczos procedure, the block Lanczos procedure is performed for only a few steps. Our block Lanczos with warm start (BLWS) technique can be adopted by different algorithms that solve NNM problems. We present numerical results on applying BLWS to Robust PCA and Matrix Completion problems. Experimental results show that our BLWS technique usually accelerates its host algorithm by at least two to three times.

Huan Li, Cong Fang, Zhouchen Lin

In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases and the penalized objective function is minimized inexactly rather than exactly, e.g., with only one step of the proximal gradient descent. For such a variant of the quadratic penalty method, we give counterexamples to show that it may not give a solution to the original constrained problem. By choosing special penalty parameters, we ensure the convergence and further establish the convergence rates of $O\left(\frac{1}{\sqrt{K}}\right)$ for the generally convex problems and $O\left(\frac{1}{K}\right)$ for strongly convex ones, where $K$ is the number of iterations. Furthermore, by adopting Nesterov's extrapolation we show that the convergence rates can be improved to $O\left(\frac{1}{K}\right)$ for the generally convex problems and $O\left(\frac{1}{K^2}\right)$ for strongly convex ones. When applied to the decentralized distributed optimization, the penalty methods studied in this paper become the widely used distributed gradient method and the fast distributed gradient method. However, due to the totally different analysis framework, we can improve their $O\left(\frac{\log K}{\sqrt{K}}\right)$ and $O\left(\frac{\log K}{K}\right)$ convergence rates to $O\left(\frac{1}{\sqrt{K}}\right)$ and $O\left(\frac{1}{K}\right)$ with fewer assumptions on the network topology for general convex problems. Using our analysis framework, we also extend the fast distributed gradient method to a communication efficient version, i.e., finding an $\varepsilon$ solution in $O\left(\frac{1}{\varepsilon}\right)$ communications and $O\left(\frac{1}{\varepsilon^{2+δ}}\right)$ computations for the non-smooth problems, where $δ$ is a small constant.

Zenan Ling, Xingyu Xie, Qiuhao Wang et al.

A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding and computes gradients with implicit differentiation. The training dynamics of over-parameterized DEQs are investigated in this study. By supposing a condition on the initial equilibrium point, we show that the unique equilibrium point always exists during the training process, and the gradient descent is proved to converge to a globally optimal solution at a linear convergence rate for the quadratic loss function. In order to show that the required initial condition is satisfied via mild over-parameterization, we perform a fine-grained analysis on random DEQs. We propose a novel probabilistic framework to overcome the technical difficulty in the non-asymptotic analysis of infinite-depth weight-tied models.

Yibo Yang, Hong Wang, Haobo Yuan et al.

Automated machine learning has been widely explored to reduce human efforts in designing neural architectures and looking for proper hyperparameters. In the domain of neural initialization, however, similar automated techniques have rarely been studied. Most existing initialization methods are handcrafted and highly dependent on specific architectures. In this paper, we propose a differentiable quantity, named GradCosine, with theoretical insights to evaluate the initial state of a neural network. Specifically, GradCosine is the cosine similarity of sample-wise gradients with respect to the initialized parameters. By analyzing the sample-wise optimization landscape, we show that both the training and test performance of a network can be improved by maximizing GradCosine under gradient norm constraint. Based on this observation, we further propose the neural initialization optimization (NIO) algorithm. Generalized from the sample-wise analysis into the real batch setting, NIO is able to automatically look for a better initialization with negligible cost compared with the training time. With NIO, we improve the classification performance of a variety of neural architectures on CIFAR-10, CIFAR-100, and ImageNet. Moreover, we find that our method can even help to train large vision Transformer architecture without warmup.

Huan Li, Zhouchen Lin

Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the nonconvex problem $\min_{U\in\mathcal{R}^{n\times r}} g(U)=f(UU^T)$ under the assumptions that $f(X)$ is restricted $μ$-strongly convex and $L$-smooth on the set $\{X:X\succeq 0,rank(X)\leq r\}$. We propose an accelerated gradient method with alternating constraint that operates directly on the $U$ factors and show that the method has local linear convergence rate with the optimal dependence on the condition number of $\sqrt{L/μ}$. Globally, our method converges to the critical point with zero gradient from any initializer. Our method also applies to the problem with the asymmetric factorization of $X=\widetilde U\widetilde V^T$ and the same convergence result can be obtained. Extensive experimental results verify the advantage of our method.

Yuxuan Du, Yibo Yang, Tongliang Liu et al.

Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have limitations: the former is plagued by the predictive uncertainty and the latter lacks the generalization ability. Here we propose a data-centric learning paradigm combining the strength of these two approaches to facilitate diverse quantum system learning (QSL) tasks. Particularly, our paradigm utilizes classical shadows along with other easily obtainable information of quantum systems to create the training dataset, which is then learnt by neural networks to unveil the underlying mapping rule of the explored QSL problem. Capitalizing on the generalization power of neural networks, this paradigm can be trained offline and excel at predicting previously unseen systems at the inference stage, even with few state copies. Besides, it inherits the characteristic of classical shadows, enabling memory-efficient storage and faithful prediction. These features underscore the immense potential of the proposed data-centric approach in discovering novel and large-scale quantum systems. For concreteness, we present the instantiation of our paradigm in quantum state tomography and direct fidelity estimation tasks and conduct numerical analysis up to 60 qubits. Our work showcases the profound prospects of data-centric artificial intelligence to advance QSL in a faithful and generalizable manner.

Zhengyang Shen, Tao Hong, Qi She et al.

Steerable models can provide very general and flexible equivariance by formulating equivariance requirements in the language of representation theory and feature fields, which has been recognized to be effective for many vision tasks. However, deriving steerable models for 3D rotations is much more difficult than that in the 2D case, due to more complicated mathematics of 3D rotations. In this work, we employ partial differential operators (PDOs) to model 3D filters, and derive general steerable 3D CNNs, which are called PDO-s3DCNNs. We prove that the equivariant filters are subject to linear constraints, which can be solved efficiently under various conditions. As far as we know, PDO-s3DCNNs are the most general steerable CNNs for 3D rotations, in the sense that they cover all common subgroups of $SO(3)$ and their representations, while existing methods can only be applied to specific groups and representations. Extensive experiments show that our models can preserve equivariance well in the discrete domain, and outperform previous works on SHREC'17 retrieval and ISBI 2012 segmentation tasks with a low network complexity.

Yang Hu, Xiyuan Wang, Zhouchen Lin et al.

Link prediction is one important application of graph neural networks (GNNs). Most existing GNNs for link prediction are based on one-dimensional Weisfeiler-Lehman (1-WL) test. 1-WL-GNNs first compute node representations by iteratively passing neighboring node features to the center, and then obtain link representations by aggregating the pairwise node representations. As pointed out by previous works, this two-step procedure results in low discriminating power, as 1-WL-GNNs by nature learn node-level representations instead of link-level. In this paper, we study a completely different approach which can directly obtain node pair (link) representations based on \textit{two-dimensional Weisfeiler-Lehman (2-WL) tests}. 2-WL tests directly use links (2-tuples) as message passing units instead of nodes, and thus can directly obtain link representations. We theoretically analyze the expressive power of 2-WL tests to discriminate non-isomorphic links, and prove their superior link discriminating power than 1-WL. Based on different 2-WL variants, we propose a series of novel 2-WL-GNN models for link prediction. Experiments on a wide range of real-world datasets demonstrate their competitive performance to state-of-the-art baselines and superiority over plain 1-WL-GNNs.

Hao Wang, Licheng Pan, Zhichao Chen et al.

Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on experimental feedback data collected from human annotators under controlled and costly conditions. In this work, we introduce observational reward modeling -- learning reward models with observational user feedback (e.g., clicks, copies, and upvotes) -- as a scalable and cost-effective alternative. We identify two fundamental challenges in this setting: (1) observational feedback is noisy due to annotation errors, which deviates it from true user preference; (2) observational feedback is biased by user preference, where users preferentially provide feedback on responses they feel strongly about, which creats a distribution shift between training and inference data. To address these challenges, we propose CausalRM, a causal-theoretic reward modeling framework that aims to learn unbiased reward models from observational feedback. To tackle challenge (1), CausalRM introduces a noise-aware surrogate loss term that is provably equivalent to the primal loss under noise-free conditions by explicitly modeling the annotation error generation process. To tackle challenge (2), CausalRM uses propensity scores -- the probability of a user providing feedback for a given response -- to reweight training samples, yielding a loss function that eliminates user preference bias. Extensive experiments across diverse LLM backbones and benchmark datasets validate that CausalRM effectively learns accurate reward signals from noisy and biased observational feedback and delivers substantial performance improvements on downstream RLHF tasks -- including a 49.2% gain on WildGuardMix and a 32.7% improvement on HarmBench. Code is available on our project website.

Jianghui Wang, Yang Chen, Xingyu Xie et al.

Pre-training has achieved remarkable success when transferred to downstream tasks. In machine learning, we care about not only the good performance of a model but also its behavior under reasonable shifts of condition. The same philosophy holds when pre-training a foundation model. However, the foundation model may not uniformly behave well for a series of related downstream tasks. This happens, for example, when conducting mask recovery regression where the recovery ability or the training instances diverge like pattern features are extracted dominantly on pre-training, but semantic features are also required on a downstream task. This paper considers pre-training a model that guarantees a uniformly good performance over the downstream tasks. We call this goal as $\textit{downstream-task robustness}$. Our method first separates the upstream task into several representative ones and applies a simple minimax loss for pre-training. We then design an efficient algorithm to solve the minimax loss and prove its convergence in the convex setting. In the experiments, we show both on large-scale natural language processing and computer vision datasets our method increases the metrics on worse-case downstream tasks. Additionally, some theoretical explanations for why our loss is beneficial are provided. Specifically, we show fewer samples are inherently required for the most challenging downstream task in some cases.

Pengyun Yue, Hanzhen Zhao, Cong Fang et al.

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose a new technique named Common randOm REconstruction(CORE), which can be used to compress the information transmitted between machines in order to reduce communication complexity without other strict conditions. Especially, our technique CORE projects the vector-valued information to a low-dimensional one through common random vectors and reconstructs the information with the same random noises after communication. We apply CORE to two distributed tasks, respectively convex optimization on linear models and generic non-convex optimization, and design new distributed algorithms, which achieve provably lower communication complexities. For example, we show for linear models CORE-based algorithm can encode the gradient vector to $\mathcal{O}(1)$-bits (against $\mathcal{O}(d)$), with the convergence rate not worse, preceding the existing results.

Hao Wang, Licheng Pan, Qingsong Wen et al.

Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and the label sequences, presenting two central research challenges: (1) designing neural architectures that model autocorrelation in history sequences, and (2) devising learning objectives that model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper provides a comprehensive review of deep time-series forecasting from the perspective of autocorrelation modeling. In contrast to existing surveys, this work makes two distinctive contributions. First, it proposes a novel taxonomy that encompasses recent literature on both model architectures and learning objectives -- whereas prior surveys neglect or inadequately discuss the latter aspect. Second, it offers a thorough analysis of the motivations, insights, and progression of the surveyed literature from a unified, autocorrelation-centric perspective, providing a holistic overview of the evolution of deep time-series forecasting. The full list of papers and resources is available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Shihong Ding, Hanze Dong, Cong Fang et al.

We consider the non-convex non-concave objective function in two-player zero-sum continuous games. The existence of pure Nash equilibrium requires stringent conditions, posing a major challenge for this problem. To circumvent this difficulty, we examine the problem of identifying a mixed Nash equilibrium, where strategies are randomized and characterized by probability distributions over continuous domains. To this end, we propose PArticle-based Primal-dual ALgorithm (PAPAL) tailored for a weakly entropy-regularized min-max optimization over probability distributions. This algorithm employs the stochastic movements of particles to represent the updates of random strategies for the $ε$-mixed Nash equilibrium. We offer a comprehensive convergence analysis of the proposed algorithm, demonstrating its effectiveness. In contrast to prior research that attempted to update particle importance without movements, PAPAL is the first implementable particle-based algorithm accompanied by non-asymptotic quantitative convergence results, running time, and sample complexity guarantees. Our framework contributes novel insights into the particle-based algorithms for continuous min-max optimization in the general non-convex non-concave setting.

Fan Zhang, Haoxuan Li, Shengju Qian et al.

Multimodal Large Language Models (MLLMs) have revolutionized numerous research fields, including computer vision and affective computing. As a pivotal challenge in this interdisciplinary domain, facial expression recognition (FER) has evolved from separate, domain-specific models to more unified approaches. One promising avenue to unify FER tasks is converting conventional FER datasets into visual question-answering (VQA) formats, enabling the direct application of powerful generalist MLLMs for inference. However, despite the success of cutting-edge MLLMs in various tasks, their performance on FER tasks remains largely unexplored. To address this gap, we provide FERBench, a systematic benchmark that incorporates 20 state-of-the-art MLLMs across four widely used FER datasets. Our results reveal that, while MLLMs exhibit good classification performance, they still face significant limitations in reasoning and interpretability. To this end, we introduce post-training strategies aimed at enhancing the facial expression reasoning capabilities of MLLMs. Specifically, we curate two high-quality and large-scale datasets: UniFER-CoT-230K for cold-start initialization and UniFER-RLVR-360K for reinforcement learning with verifiable rewards (RLVR), respectively. Building upon them, we develop a unified and interpretable FER foundation model termed UniFER-7B, which outperforms many open-sourced and closed-source generalist MLLMs (e.g., Gemini-2.5-Pro and Qwen2.5-VL-72B).

Mingjie Li, Hao Kong, Zhouchen Lin

Recently, many works have demonstrated that Symmetric Non-negative Matrix Factorization~(SymNMF) enjoys a great superiority for various clustering tasks. Although the state-of-the-art algorithms for SymNMF perform well on synthetic data, they cannot consistently obtain satisfactory results with desirable properties and may fail on real-world tasks like clustering. Considering the flexibility and strong representation ability of the neural network, in this paper, we propose a neural network called SymNMF-Net for the Symmetric NMF problem to overcome the shortcomings of traditional optimization algorithms. Each block of SymNMF-Net is a differentiable architecture with an inversion layer, a linear layer and ReLU, which are inspired by a traditional update scheme for SymNMF. We show that the inference of each block corresponds to a single iteration of the optimization. Furthermore, we analyze the constraints of the inversion layer to ensure the output stability of the network to a certain extent. Empirical results on real-world datasets demonstrate the superiority of our SymNMF-Net and confirm the sufficiency of our theoretical analysis.

Hao Wang, Haocheng Yang, Licheng Pan et al.

Reward modeling represents a long-standing challenge in reinforcement learning from human feedback (RLHF) for aligning language models. Current reward modeling is heavily contingent upon experimental feedback data with high collection costs. In this work, we study \textit{implicit reward modeling} -- learning reward models from implicit human feedback (e.g., clicks and copies) -- as a cost-effective alternative. We identify two fundamental challenges in implicit reward modeling: (1) Implicit preference data lacks definitive negative samples, which makes standard positive-negative classification methods inapplicable; (2) Implicit preference data suffers from user preference bias, where different responses have different propensities to elicit user feedback actions, which exacerbates the difficulty of distinguishing definitive negative samples. To address these challenges, we propose ImplicitRM, which aims to learn unbiased reward models from implicit preference data. ImplicitRM stratifies training samples into four latent groups via a stratification model. Building on this, it derives a learning objective through likelihood maximization, which we prove is theoretically unbiased, effectively resolving both challenges. Experiments demonstrate that ImplicitRM learns accurate reward models across implicit preference datasets. Code is available on our project website.

Dihong Jiang, Ruoqi Cao, Zhiyuan Dang et al.

While traditional tree-based ensemble methods have long dominated tabular tasks, deep neural networks and emerging foundation models have challenged this primacy, yet no consensus exists on a universally superior paradigm. Existing benchmarks typically contain fewer than 100 datasets, raising concerns about evaluation sufficiency and potential selection biases. To address these limitations, we introduce OmniTabBench, the largest tabular benchmark to date, comprising 3030 datasets spanning diverse tasks that are comprehensively collected from diverse sources and categorized by industry using large language models. We conduct an unprecedented large-scale empirical evaluation of state-of-the-art models from all model families on OmniTabBench, confirming the absence of a dominant winner. Furthermore, through a decoupled metafeature analysis, which examines individual properties such as dataset size, feature types, feature and target skewness/kurtosis, we elucidate conditions favoring specific model categories, providing clearer, more actionable guidance than prior compound-metric studies.

Haotong Yang, Yi Hu, Shijia Kang et al.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs. Our benchmark and code are released at https://github.com/GraphPKU/number_cookbook.

Shihao Shao, Cong Fang, Zhouchen Lin et al.

We study a new learning protocol, termed partial-feedback online learning, where each instance admits a set of acceptable labels, but the learner observes only one acceptable label per round. We highlight that, while classical version space is widely used for online learnability, it does not directly extend to this setting. We address this obstacle by introducing a collection version space, which maintains sets of hypotheses rather than individual hypotheses. Using this tool, we obtain a tight characterization of learnability in the set-realizable regime. In particular, we define the Partial-Feedback Littlestone dimension (PFLdim) and the Partial-Feedback Measure Shattering dimension (PMSdim), and show that they tightly characterize the minimax regret for deterministic and randomized learners, respectively. We further identify a nested inclusion condition under which deterministic and randomized learnability coincide, resolving an open question of Raman et al. (2024b). Finally, given a hypothesis space H, we show that beyond set realizability, the minimax regret can be linear even when |H|=2, highlighting a barrier beyond set realizability.

Mingqing Xiao, Qingyan Meng, Zongpeng Zhang et al.

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is still challenging. Most recent methods leverage spatial and temporal backpropagation (BP), not adhering to neuromorphic properties. Despite the efforts of some online training methods, tackling spatial credit assignments by alternatives with comparable performance as spatial BP remains a significant problem. In this work, we propose a novel method, online pseudo-zeroth-order (OPZO) training. Our method only requires a single forward propagation with noise injection and direct top-down signals for spatial credit assignment, avoiding spatial BP's problem of symmetric weights and separate phases for layer-by-layer forward-backward propagation. OPZO solves the large variance problem of zeroth-order methods by the pseudo-zeroth-order formulation and momentum feedback connections, while having more guarantees than random feedback. Combining online training, OPZO can pave paths to on-chip SNN training. Experiments on neuromorphic and static datasets with fully connected and convolutional networks demonstrate the effectiveness of OPZO with similar performance compared with spatial BP, as well as estimated low training costs.

Xinpeng Lv, Yunxin Mao, Renzhe Xu et al.

Strategic classification(SC) studies the interaction between decision models and agents who strategically manipulate their features for favorable outcomes. Existing SC frameworks typically rely on the idealized assumption that agents are strictly rational. However, evidence from behavioral economics and psychology consistently shows that real-world decision-making is often shaped by cognitive biases, deviating from pure rationality. To formalize this limitation, we identify and define a new problem setting, termed the behaviorally realistic strategic classification problem, where agents' strategic manipulations deviate from full rationality due to psychological biases. Motivated by the identified limitation, we propose the Prospect-Guided Strategic Framework (Pro-SF) to address the problem, a principled framework grounded in prospect theory to model and learn under behaviorally realistic strategic responses. Specifically, to capture behaviorally realistic strategic manipulations, our framework reformulates the Stackelberg-style interaction between agents and the decision-maker by incorporating three key mechanisms inspired by prospect theory, including the asymmetry between benefits and costs, different subjective reference points, and non-rational probability distortion. Experiments on synthetic and real-world datasets establish Pro-SF as a behaviorally grounded approach to strategic classification, bridging machine learning and behavioral economics for more reliable deployment in the real world.

Xinpeng Lv, Yunxin Mao, Renzhe Xu et al.

Tabular foundation models based on pretrained prior-data fitted networks~(PFNs) have shown strong generalization on diverse tabular tasks, but they are typically designed for \emph{non-strategic} settings where data distributions are independent of deployed classifiers. In many real-world decision scenarios, however, individuals may strategically modify their features after deployment to obtain favorable outcomes, inducing a post-deployment distribution shift. This paper studies whether PFN-style tabular foundation models can generalize to such \emph{strategic} tabular data. We show that strategic manipulation creates a mismatch between the non-strategic prior learned during pretraining and the post-manipulation strategic prior, which leads to systematic prediction bias. To address this issue, we propose \textbf{Strategic Prior-data Fitted Network}~\textit{(SPN)}, an inference-time strategy-aware framework that adapts tabular foundation models to strategic environments without retraining. SPN constructs strategic in-context examples to approximate post-manipulation inputs and aligns PFN predictions with the induced strategic distribution. Experiments on real-world and synthetic tabular datasets show that SPN consistently improves robustness and predictive performance under strategic manipulation compared with both tabular foundation models and classical tabular methods.

Huan Li, Yiming Dong, Zhouchen Lin

This paper studies the AdamW-style Shampoo optimizer, an effective implementation of classical Shampoo that notably won the external tuning track of the AlgoPerf neural network training algorithm competition. Our analysis unifies one-sided and two-sided preconditioning and establishes the convergence rate $\frac{1}{K}\sum_{k=1}^K E\left[\|\nabla f(X_k)\|_*\right]\leq O(\frac{\sqrt{m+n}C}{K^{1/4}})$ measured by nuclear norm, where $K$ represents the iteration number, $(m,n)$ denotes the size of matrix parameters, and $C$ matches the constant in the optimal convergence rate of SGD. Theoretically, we have $\|\nabla f(X)\|_F\leq \|\nabla f(X)\|_*\leq \sqrt{m+n}\|\nabla f(X)\|_F$, supporting that our convergence rate can be considered to be analogous to the optimal $\frac{1}{K}\sum_{k=1}^KE\left[\|\nabla f(X_k)\|_F\right]\leq O(\frac{C}{K^{1/4}})$ convergence rate of SGD in the ideal case of $\|\nabla f(X)\|_*= Θ(\sqrt{m+n})\|\nabla f(X)\|_F$.

Jianlong Wu, Wei Liu, Ye Liu et al.

The recent advancement in video temporal grounding (VTG) has significantly enhanced fine-grained video understanding, primarily driven by multimodal large language models (MLLMs). With superior multimodal comprehension and reasoning abilities, VTG approaches based on MLLMs (VTG-MLLMs) are gradually surpassing traditional fine-tuned methods. They not only achieve competitive performance but also excel in generalization across zero-shot, multi-task, and multi-domain settings. Despite extensive surveys on general video-language understanding, comprehensive reviews specifically addressing VTG-MLLMs remain scarce. To fill this gap, this survey systematically examines current research on VTG-MLLMs through a three-dimensional taxonomy: 1) the functional roles of MLLMs, highlighting their architectural significance; 2) training paradigms, analyzing strategies for temporal reasoning and task adaptation; and 3) video feature processing techniques, which determine spatiotemporal representation effectiveness. We further discuss benchmark datasets, evaluation protocols, and summarize empirical findings. Finally, we identify existing limitations and propose promising research directions. For additional resources and details, readers are encouraged to visit our repository at https://github.com/ki-lw/Awesome-MLLMs-for-Video-Temporal-Grounding.

Haotong Yang, Fanxu Meng, Zhouchen Lin et al.

The pre-trained large language models (LLMs) have shown their extraordinary capacity to solve reasoning tasks, even on tasks that require a complex process involving multiple sub-steps. However, given the vast possible generation space of all the tasks, how the pretrained model learns the reasoning ability remains an open question. We firstly propose that an intrinsic structural constraint on the generated sequence of language-based reasoning -- we called it template-content structure (T-C structure) -- is the key to explain why LLMs can solve a large number of complex reasoning problems with limited training data by showing this structure can reduce the possible space from exponential level to linear level. Furthermore, by generalizing this structure to the hierarchical case, we demonstrate that models can achieve task composition, further reducing the space needed to learn from linear to logarithmic, thereby effectively learning on complex reasoning involving multiple steps. We provide both examples and formal theory of our T-C structure. We also experimentally validate the existence of the T-C structure in some current LLMs and its effectiveness for reasoning.

Hao Wang, Licheng Pan, Zhichao Chen et al. · pku

Training time-series forecast models presents unique challenges in designing effective learning objectives. Existing methods predominantly utilize the temporal mean squared error, which faces two critical challenges: (1) label autocorrelation, which leads to bias from the label sequence likelihood; (2) excessive amount of tasks, which increases with the forecast horizon and complicates optimization. To address these challenges, we propose Time-o1, a transformation-augmented learning objective tailored for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Extensive experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Yisen Wang, Yichuan Mo, Dongxian Wu et al.

Skip connection is an essential ingredient for modern deep models to be deeper and more powerful. Despite their huge success in normal scenarios (state-of-the-art classification performance on natural examples), we investigate and identify an interesting property of skip connections under adversarial scenarios, namely, the use of skip connections allows easier generation of highly transferable adversarial examples. Specifically, in ResNet-like models (with skip connections), we find that using more gradients from the skip connections rather than the residual modules according to a decay factor during backpropagation allows one to craft adversarial examples with high transferability. The above method is termed as Skip Gradient Method (SGM). Although starting from ResNet-like models in vision domains, we further extend SGM to more advanced architectures, including Vision Transformers (ViTs) and models with length-varying paths and other domains, i.e. natural language processing. We conduct comprehensive transfer attacks against various models including ResNets, Transformers, Inceptions, Neural Architecture Search, and Large Language Models (LLMs). We show that employing SGM can greatly improve the transferability of crafted attacks in almost all cases. Furthermore, considering the big complexity for practical use, we further demonstrate that SGM can even improve the transferability on ensembles of models or targeted attacks and the stealthiness against current defenses. At last, we provide theoretical explanations and empirical insights on how SGM works. Our findings not only motivate new adversarial research into the architectural characteristics of models but also open up further challenges for secure model architecture design. Our code is available at https://github.com/mo666666/SGM.

Shihao Shao, Yikang Li, Zhouchen Lin et al.

Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors that preserve symmetry presents a significant challenge. The ICT decomposition and a basis of this equivariant space are difficult to obtain for high-rank tensors. After decades of research, Bonvicini (2024) has recently achieved an explicit ICT decomposition for $n=5$ with factorial time/space complexity. In this work we, for the first time, obtain decomposition matrices for ICTs up to rank $n=9$ with reduced and affordable complexity, by constructing what we call path matrices. The path matrices are obtained via performing chain-like contractions with Clebsch-Gordan matrices following the parentage scheme. We prove and leverage that the concatenation of path matrices is an orthonormal change-of-basis matrix between the Cartesian tensor product space and the spherical direct sum spaces. Furthermore, we identify a complete orthogonal basis for the equivariant space, rather than a spanning set (Pearce-Crump, 2023b), through this path matrices technique. Our method avoids the RREF algorithm and maintains a fully analytical derivation of each ICT decomposition matrix, thereby significantly improving the algorithm's speed to obtain arbitrary rank orthogonal ICT decomposition matrices and orthogonal equivariant bases. We further extend our result to the arbitrary tensor product and direct sum spaces, enabling free design between different spaces while keeping symmetry. The Python code is available at https://github.com/ShihaoShao-GH/ICT-decomposition-and-equivariant-bases, where the $n=6,\dots,9$ ICT decomposition matrices are obtained in 1s, 3s, 11s, and 4m32s on 28-core Intel(R) Xeon(R) Gold 6330 CPU @ 2.00GHz, respectively.

Haotong Yang, Zitong Wang, Shijia Kang et al.

While Large Language Models (LLMs) have demonstrated strong math reasoning abilities through Reinforcement Learning with *Verifiable Rewards* (RLVR), many advanced mathematical problems are proof-based, with no guaranteed way to determine the authenticity of a proof by simple answer matching. To enable automatic verification, a Reward Model (RM) capable of reliably evaluating full proof processes is required. In this work, we design a *scalable* data-construction pipeline that, with minimal human effort, leverages LLMs to generate a large quantity of high-quality "**question-proof-check**" triplet data. By systematically varying problem sources, generation methods, and model configurations, we create diverse problem-proof pairs spanning multiple difficulty levels, linguistic styles, and error types, subsequently filtered through hierarchical human review for label alignment. Utilizing these data, we train a proof-checking RM, incorporating additional process reward and token weight balance to stabilize the RL process. Our experiments validate the model's scalability and strong performance from multiple perspectives, including reward accuracy, generalization ability and test-time guidance, providing important practical recipes and tools for strengthening LLM mathematical capabilities.