Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these methods effectively model the relationships between latent factors and the low-rank tensor using Dirac delta distributions. However, tensor low-rank decomposition is inherently non-unique, leading to a multimodal distribution over possible solutions. Critically, such prior knowledge is rarely available in practical scenarios, particularly regarding the optimal rank structure and contraction rules. To address this issue, we propose a score-based model that eliminates the need for predefined structural or distributional assumptions, enabling the learning of compatibility between tensors and latent factors. Specifically, a neural network is designed to learn the energy function, which is optimized via score matching to capture the gradient of the joint log-probability of tensor entries and latent factors. Our method allows for modeling structures and distributions beyond the Dirac delta assumption. Moreover, integrating the block coordinate descent (BCD) algorithm with the proposed smooth regularization enables the model to perform both tensor completion and denoising. Experimental results demonstrate significant performance improvements across various tensor types, including sparse and continuous-time tensors, as well as visual data.

Conformal prediction (CP) is a general framework to quantify the predictive uncertainty of machine learning models that uses a set prediction to include the true label with a valid probability. To align the uncertainty measured by CP, conformal training methods minimize the size of the prediction sets. A typical way is to use a surrogate indicator function, usually Sigmoid or Gaussian error function. However, these surrogate functions do not have a uniform error bound to the indicator function, leading to uncontrollable learning bounds. In this paper, we propose a simple cost-sensitive conformal training algorithm that does not rely on the indicator approximation mechanism. Specifically, we theoretically show that minimizing the expected size of prediction sets is upper bounded by the expected rank of true labels. To this end, we develop an importance weighting strategy that assigns the weight using the rank of true label on each data. Our analysis provably demonstrates the tightness between the proposed weighted objective and the expected size of conformal prediction sets. Extensive experiments verify the validity of our theoretical insights, and superior empirical performance over other conformal training in terms of predictive efficiency with 21.38% reduction for average prediction set size.

Sparse neural systems are gaining traction for efficient continual learning due to their modularity and low interference. Architectures like Sparse Distributed Memory Multi-Layer Perceptrons (SDMLP) construct task-specific subnetworks via Top-K activation and have shown resilience against catastrophic forgetting. However, their rigid modularity poses two fundamental challenges: (1) the isolation of sparse subnetworks severely limits cross-task knowledge reuse; and (2) increased sparsity reduces interference but often degrades performance due to constrained feature sharing.We propose Selective Subnetwork Distillation (SSD), a structurally guided continual learning framework that treats distillation not as a regularizer, but as a topology-aligned information conduit. By identifying neurons with high activation frequency, SSD selectively distills knowledge within previous Top-K subnetworks and output logits—without requiring replay or task labels—preserving both sparsity and functional specialization.Unlike conventional distillation, SSD operates under hard modular constraints and enables structural realignment without altering the sparse architecture.While our method is validated on SDMLP, its structure-aligned mechanism has the potential to generalize to other sparse networks as a plug-in module for promoting representation sharing.Comprehensive experiments on Split CIFAR-10, CIFAR-100, and MNIST demonstrate that SSD improves accuracy, retention, and manifold coverage, offering a structurally grounded solution to sparse continual learning.

In recent years, with the advancements in brain science, spiking neural networks (SNNs) have garnered significant attention. SNNs can generate spikes that mimic the function of neurons transmission in humans brain, thereby significantly reducing computational costs by the event-driven nature during training. While deep SNNs have shown impressive performance on classification tasks, they still face challenges in more complex tasks such as object detection. In this paper, we propose SpikingYOLOX, extending the structure of the original YOLOX by introducing signed spiking neurons and fast Fourier convolution (FFC). The designed ternary signed spiking neurons could generate three kinds of spikes to obtain more robust features in the deep layer of the backbone. Meanwhile, we integrate FFC with SNN modules to enhance object detection performance, because its global receptive field is beneficial to the object detection task. Extensive experiments demonstrate that the proposed SpikingYOLOX achieves state-of-the-art performance among other SNN-based object detection methods.

Considering the importance of capturing both global conversational topics and local speaker dependencies for multimodal emotion recognition in conversations, current approaches first utilize sequence models like Transformer to extract global context information, then apply Graph Neural Networks to model local speaker dependencies for local context information extraction, coupled with Graph Contrastive Learning (GCL) to enhance node representation learning. However, this sequential design introduces potential biases: the extracted global context information inevitably influences subsequent processing, compromising the independence and diversity of the original local features; current graph augmentation methods in GCL cannot consider both global and local context information in conversations to evaluate the node importance, hindering the learning of key information. Inspired by the human brain excels at handling complex tasks by efficiently integrating local and global information processing mechanisms, we propose an aligned global-local context fusion framework for sequence-based design to address these problems. This design includes a dual-attention Transformer and a dual-evaluation method for graph augmentation in GCL. The dual-attention Transformer combines global attention for overall context extraction with sliding-window attention for local context capture, both enhanced by spiking neuron dynamics. The dual-evaluation method in GCL comprises global importance evaluation to identify nodes crucial for overall conversation context, and local importance evaluation to detect nodes significant for local semantics, generating augmented graph views that preserve both global and local information. This approach ensures balanced information processing throughout the pipeline, enhancing biological plausibility and achieving superior emotion recognition.

Pixel-level vision tasks, such as semantic segmentation, require extensive and high-quality annotated data, which is costly to obtain. Semi-supervised semantic segmentation (SSSS) has emerged as a solution to alleviate the labeling burden by leveraging both labeled and unlabeled data through self-training techniques. Meanwhile, the advent of foundational segmentation models pre-trained on massive data, has shown the potential to generalize across domains effectively. This work explores whether a foundational segmentation model can address label scarcity in the pixel-level vision task as an annotator for unlabeled images. Specifically, we investigate the efficacy of using SEEM, a Segment Anything Model (SAM) variant fine-tuned for textual input, to generate predictive masks for unlabeled data. To address the shortcomings of using SEEM-generated masks as supervision, we propose ConformalSAM, a novel SSSS framework which first calibrates the foundation model using the target domain's labeled data and then filters out unreliable pixel labels of unlabeled data so that only high-confidence labels are used as supervision. By leveraging conformal prediction (CP) to adapt foundation models to target data through uncertainty calibration, ConformalSAM exploits the strong capability of the foundational segmentation model reliably which benefits the early-stage learning, while a subsequent self-reliance training strategy mitigates overfitting to SEEM-generated masks in the later training stage. Our experiment demonstrates that, on three standard benchmarks of SSSS, ConformalSAM achieves superior performance compared to recent SSSS methods and helps boost the performance of those methods as a plug-in.

Artificial neural networks (ANNs) have demonstrated outstanding performance in numerous tasks, but deployment in resource-constrained environments remains a challenge due to their high computational and memory requirements. Spiking neural networks (SNNs) operate through discrete spike events and offer superior energy efficiency, providing a bio-inspired alternative. However, current ANN-to-SNN conversion often results in significant accuracy loss and increased inference time due to conversion errors such as clipping, quantization, and uneven activation. This paper proposes a novel ANN-to-SNN conversion framework based on error compensation learning. We introduce a learnable threshold clipping function, dual-threshold neurons, and an optimized membrane potential initialization strategy to mitigate the conversion error. Together, these techniques address the clipping error through adaptive thresholds, dynamically reduce the quantization error through dual-threshold neurons, and minimize the non-uniformity error by effectively managing the membrane potential. Experimental results on CIFAR-10, CIFAR-100, ImageNet datasets show that our method achieves high-precision and ultra-low latency among existing conversion methods. Using only two time steps, our method significantly reduces the inference time while maintains competitive accuracy of 94.75% on CIFAR-10 dataset under ResNet-18 structure. This research promotes the practical application of SNNs on low-power hardware, making efficient real-time processing possible.

Meta-learning is a practical learning paradigm to transfer skills across tasks from a few examples. Nevertheless, the existence of task distribution shifts tends to weaken meta-learners' generalization capability, particularly when the training task distribution is naively hand-crafted or based on simple priors that fail to cover critical scenarios sufficiently. Here, we consider explicitly generative modeling task distributions placed over task identifiers and propose robustifying fast adaptation from adversarial training. Our approach, which can be interpreted as a model of a Stackelberg game, not only uncovers the task structure during problem-solving from an explicit generative model but also theoretically increases the adaptation robustness in worst cases. This work has practical implications, particularly in dealing with task distribution shifts in meta-learning, and contributes to theoretical insights in the field. Our method demonstrates its robustness in the presence of task subpopulation shifts and improved performance over SOTA baselines in extensive experiments. The code is available at the project site https://sites.google.com/view/ar-metalearn.

Brain-inspired Spiking Neural Networks (SNNs) have garnered significant attention due to their bio-plausibility and low power consumption advantages compared to Artificial Neural Networks (ANNs). However, the application of SNN in computer vision remains limited, primarily due to their inferior performance. In this work, we aim to bridge the performance gap between ANNs and SNNs in object detection by our Advanced SpikingYOLOX. The proposed approach extends the SpikingYOLOX with two key innovations: PSA-SNN and 2D-Spiking Transformer, both designed to enhance object detection performance. PSA-SNN extends spike-based self-attention by incorporating high-speed partial self-attention with an SNN-based 2D-Spiking Transformer in the deepest layer of the backbone, significantly improving feature extraction. The 2D-Spiking Transformer redefines the role of spiking neurons in Transformer sequences (Key, Query, Value), demonstrating that applying an additional spiking layer solely to the Value sequence yields the best performance while maintaining computational efficiency in spike-driven Transformers. We conduct extensive experiments on static images and the Advanced SpikingYOLOX achieves state-of-the-art performance among other SNN-based object detection methods. This work paves the way for more advanced SNN applications in object detection and broader computer vision tasks.

Continual model merging integrates independently fine-tuned models sequentially without access to the original training data, offering a scalable and efficient solution for continual learning. However, existing methods face two critical challenges: parameter interference among tasks, which leads to catastrophic forgetting, and limited adaptability to evolving test distributions. To address these issues, we introduce the task of Test-Time Continual Model Merging (TTCMM), which leverages a small set of unlabeled test samples during inference to alleviate parameter conflicts and handle distribution shifts. We propose MINGLE, a novel framework for TTCMM. MINGLE employs a mixture-of-experts architecture with parameter-efficient, low-rank experts, which enhances adaptability to evolving test distributions while dynamically merging models to mitigate conflicts. To further reduce forgetting, we propose Null-Space Constrained Gating, which restricts gating updates to subspaces orthogonal to prior task representations, thereby suppressing activations on old tasks and preserving past knowledge. We further introduce an Adaptive Relaxation Strategy that adjusts constraint strength dynamically based on interference signals observed during test-time adaptation, striking a balance between stability and adaptability. Extensive experiments on standard continual merging benchmarks demonstrate that MINGLE achieves robust generalization, significantly reduces forgetting, and consistently surpasses previous state-of-the-art methods by 7–9% on average across diverse task orders. Our code is available at: https://github.com/zihuanqiu/MINGLE

Multi-modal learning aims to enhance performance by unifying models from various modalities but often faces the "modality imbalance" problem in real data, leading to a bias towards dominant modalities and neglecting others, thereby limiting its overall effectiveness. To address this challenge, the core idea is to balance the optimization of each modality to achieve a joint optimum. Existing approaches often employ a modal-level control mechanism for adjusting the update of each modal parameter. However, such a global-wise updating mechanism ignores the different importance of each parameter. Inspired by subnetwork optimization, we explore a uniform sampling-based optimization strategy and find it more effective than global-wise updating. According to the findings, we further propose a novel importance sampling-based, element-wise joint optimization method, called Adaptively Mask Subnetworks Considering Modal Significance (AMSS). Specifically, we incorporate mutual information rates to determine the modal significance and employ non-uniform adaptive sampling to select foreground subnetworks from each modality for parameter updates, thereby rebalancing multi-modal learning. Additionally, we demonstrate the reliability of the AMSS strategy through convergence analysis. Building upon theoretical insights, we further enhance the multi-modal mask subnetwork strategy using unbiased estimation, referred to as AMSS+. Extensive experiments reveal the superiority of our approach over comparison methods.

Non-exemplar class incremental learning (NECIL) aims to continuously assimilate new knowledge without forgetting previously acquired ones when historical data are un-available. One of the generative NECIL methods is to in-vert the images of old classes for joint training. However, these synthetic images suffer significant domain shifts compared with real data, hampering the recognition of old classes. In this paper, we present a novel method termed Dual-Consistency Model Inversion (DCMI) to generate better synthetic samples of old classes through two pivotal consistency alignments: (1) the semantic consistency between the synthetic images and the corresponding prototypes, and (2) domain consistency between synthetic and real images of new classes. Besides, we introduce Prototypical Routing (PR) to provide task-prior information and generate unbi-ased and accurate predictions. Our comprehensive experiments across diverse datasets consistently showcase the superiority of our method over previous state-of-the-art approaches.

In safety-critical applications such as medical imaging and autonomous driving, where decisions have profound implications for patient health and road safety, it is imperative to maintain both high adversarial robustness to protect against potential adversarial attacks and reliable uncertainty quantification in decision-making. With extensive research focused on enhancing adversarial robustness through various forms of adversarial training (AT), a notable knowledge gap remains concerning the uncertainty inherent in adversarially trained models. To address this gap, this study investigates the uncertainty of deep learning models by examining the performance of conformal prediction (CP) in the context of standard adversarial attacks within the adversarial defense community. It is first unveiled that existing CP methods do not produce informative prediction sets under the commonly used $l_{\infty}$-norm bounded attack if the model is not adversarially trained, which underpins the importance of adversarial training for CP. Our paper next demonstrates that the prediction set size (PSS) of CP using adversarially trained models with AT variants is often worse than using standard AT, inspiring us to research into CP-efficient AT for improved PSS. We propose to optimize a Beta-weighting loss with an entropy minimization regularizer during AT to improve CP-efficiency, where the Beta-weighting loss is shown to be an upper bound of PSS at the population level by our theoretical analysis. Moreover, our empirical study on four image classification datasets across three popular AT baselines validates the effectiveness of the proposed Uncertainty-Reducing AT (AT-UR).

Multimodal learning falls into the trap of the optimization dilemma due to the modality imbalance phenomenon, leading to unsatisfactory performance in real applications. A core reason for modality imbalance is that the models of each modality converge at different rates. Many attempts naturally focus on adjusting learning procedures adaptively. Essentially, the reason why models converge at different rates is because the difficulty of fitting category labels is inconsistent for each modality during learning. From the perspective of fitting labels, we find that appropriate positive intervention label fitting can correct this difference in learning ability. By exploiting the ability of contrastive learning to intervene in the learning of category label fitting, we propose a novel multimodal learning approach that dynamically integrates unsupervised contrastive learning and supervised multimodal learning to address the modality imbalance problem. We find that a simple yet heuristic integration strategy can significantly alleviate the modality imbalance phenomenon. Moreover, we design a learning-based integration strategy to integrate two losses dynamically, further improving the performance. Experiments on widely used datasets demonstrate the superiority of our method compared with state-of-the-art (SOTA) multimodal learning approaches. The code is available at https://github.com/njustkmg/NeurIPS24-LFM.

Open-set Semi-supervised Learning (OSSL) holds a realistic setting that unlabeled data may come from classes unseen in the labeled set, i.e., out-of-distribution (OOD) data, which could cause performance degradation in conventional SSL models. To handle this issue, except for the traditional in-distribution (ID) classifier, some existing OSSL approaches employ an extra OOD detection module to avoid the potential negative impact of the OOD data. Nevertheless, these approaches typically employ the entire set of open-set data during their training process, which may contain data unfriendly to the OSSL task that can negatively influence the model performance. This inspires us to develop a robust open-set data selection strategy for OSSL. Through a theoretical understanding from the perspective of learning theory, we propose Wise Open-set Semi-supervised Learning (WiseOpen), a generic OSSL framework that selectively leverages the open-set data for training the model. By applying a gradient-variance-based selection mechanism, WiseOpen exploits a friendly subset instead of the whole open-set dataset to enhance the model's capability of ID classification. Moreover, to reduce the computational expense, we also propose two practical variants of WiseOpen by adopting low-frequency update and loss-based selection respectively. Extensive experiments demonstrate the effectiveness of WiseOpen in comparison with the state-of-the-art.

Currently, deep learning methods represented by convolutional neural networks (CNNs) or Transformers are of great interest in hyperspectral image (HSI) classification. And recent works show that hybrid models using CNN and Transformer modules are expected to achieve better performance than when they are used alone. However, these hybrid models applied to HSI classification consider the combination of 2D CNN and Transformer, which makes the models have high computational complexity. And the information of multiple spectral dimensions different from ordinary RGB images has not been fully excavated. Based on this, we propose DBCTNet, a double branch Convolution-Transformer network. Specifically, a MSpeFE module is used for multiscale spectral feature extraction at the early stage of the proposed network. Then a ConvTE block is designed to improve the original Transformer encoder, where a Conv spectral projection unit and a convolutional multihead self-attention (CMHSA) unit are proposed to extract spatial and global spectral features. A double branch module is further built based on 3D CNN and ConvTE. This module can fully integrate spatial and local-global spectral features, while also having low computational complexity. Experiment results on four public datasets, Pavia University, Houston, WHU-Hi-LongKou and HuangHeKou, show that DBCTNet achieves satisfactory performance with a small number of parameters and relatively excellent efficiency compared to nine other networks. The implement of DBCTNet will be available publicly at https://github.com/xurui-joei/DBCTNet.

Recent years have seen the ever-increasing importance of pre-trained models and their downstream training in deep learning research and applications. At the same time, the defense for adversarial examples has been mainly inves-tigated in the context of training from random initialization on simple classification tasks. To better exploit the potential of pre-trained models in adversarial robustness, this paper focuses on the fine-tuning of an adversarially pre-trained model in various classification tasks. Existing research has shown that since the robust pre-trained model has already learned a robust feature extractor, the crucial question is how to maintain the robustness in the pre-trained model when learning the downstream task. We study the model-based and data-based approaches for this goal and find that the two common approaches cannot achieve the objective of improving both generalization and adversarial robustness. Thus, we propose a novel statistics-based approach, Two-WIng NormliSation (TWINS)fine-tuning framework, which consists of two neural networks where one of them keeps the population means and variances of pre-training data in the batch normalization layers. Besides the robust information transfer, TWINS increases the effective learning rate without hurting the training stability since the relationship between a weight norm and its gradient norm in standard batch normalization layer is broken, resulting in a faster es-cape from the sub-optimal initialization and alleviating the robust overfitting. Finally, TWINS is shown to be effective on a wide range of image classification datasets in terms of both generalization and robustness.

Offline reinforcement learning suffers from the out-of-distribution issue and extrapolation error. Most policy constraint methods regularize the density of the trained policy towards the behavior policy, which is too restrictive in most cases. We propose Supported Trust Region optimization (STR) which performs trust region policy optimization with the policy constrained within the support of the behavior policy, enjoying the less restrictive support constraint. We show that, when assuming no approximation and sampling error, STR guarantees strict policy improvement until convergence to the optimal support-constrained policy in the dataset. Further with both errors incorporated, STR still guarantees safe policy improvement for each step. Empirical results validate the theory of STR and demonstrate its state-of-the-art performance on MuJoCo locomotion domains and much more challenging AntMaze domains.

Offline reinforcement learning suffers from the extrapolation error and value overestimation caused by out-of-distribution (OOD) actions. To mitigate this issue, value regularization approaches aim to penalize the learned value functions to assign lower values to OOD actions. However, existing value regularization methods lack a proper distinction between the regularization effects on in-distribution (ID) and OOD actions, and fail to guarantee optimal convergence results of the policy. To this end, we propose Supported Value Regularization (SVR), which penalizes the Q-values for all OOD actions while maintaining standard Bellman updates for ID ones. Specifically, we utilize the bias of importance sampling to compute the summation of Q-values over the entire OOD region, which serves as the penalty for policy evaluation. This design automatically separates the regularization for ID and OOD actions without manually distinguishing between them. In tabular MDP, we show that the policy evaluation operator of SVR is a contraction, whose fixed point outputs unbiased Q-values for ID actions and underestimated Q-values for OOD actions. Furthermore, the policy iteration with SVR guarantees strict policy improvement until convergence to the optimal support-constrained policy in the dataset. Empirically, we validate the theoretical properties of SVR in a tabular maze environment and demonstrate its state-of-the-art performance on a range of continuous control tasks in the D4RL benchmark.

Active learning (AL) methods have been proven to be an effective way to reduce the labeling effort by intelligently selecting valuable instances for annotation. Despite their great success with in-distribution (ID) scenarios, AL methods suffer from performance degradation in many real-world applications because out-of-distribution (OOD) instances are always inevitably contained in unlabeled data, which may lead to inefficient sampling. Therefore, several attempts have been explored open-set AL by strategically selecting pure ID instances while filtering OOD instances. However, concentrating solely on selecting pseudo-ID instances may cause the training constraint of the ID classifier and OOD detector. To address this issue, we propose a simple yet effective sampling scheme, Progressive Active Learning (PAL), which employs a progressive sampling mechanism to leverage the active selection of valuable OOD instances. The proposed PAL measures unlabeled instances by synergistically evaluating instances' informativeness and representativeness, and thus it can balance the pseudo-ID and pseudo-OOD instances in each round to enhance both the capacity of the ID classifier and the OOD detector. %Meanwhile, PAL measures unlabeled instances by synergistically evaluating instances' informativeness and representativeness, which can more effectively estimate the values of instances. Extensive experiments on various open-set AL scenarios demonstrate the effectiveness of the proposed PAL, compared with the state-of-the-art methods. The code is available at \url{https://github.com/njustkmg/PAL}.

Natural untrimmed videos provide rich visual content for self-supervised learning. Yet most previous efforts to learn spatio-temporal representations rely on manually trimmed videos, such as Kinetics dataset (Carreira and Zisserman 2017), resulting in limited diversity in visual patterns and limited performance gains. In this work, we aim to improve video representations by leveraging the rich information in natural untrimmed videos. For this purpose, we propose learning a hierarchy of temporal consistencies in videos, i.e., visual consistency and topical consistency, corresponding respectively to clip pairs that tend to be visually similar when separated by a short time span, and clip pairs that share similar topics when separated by a long time span. Specifically, we present a Hierarchical Consistency (HiCo++) learning framework, in which the visually consistent pairs are encouraged to share the same feature representations by contrastive learning, while topically consistent pairs are coupled through a topical classifier that distinguishes whether they are topic-related, i.e., from the same untrimmed video. Additionally, we impose a gradual sampling algorithm for the proposed hierarchical consistency learning, and demonstrate its theoretical superiority. Empirically, we show that HiCo++ can not only generate stronger representations on untrimmed videos, but also improve the representation quality when applied to trimmed videos. This contrasts with standard contrastive learning, which fails to learn powerful representations from untrimmed videos. Source code will be made available here.

Channel pruning has been broadly recognized as an effective technique to reduce the computation and memory cost of deep convolutional neural networks. However, conventional pruning methods have limitations in that: they are restricted to pruning process only, and they require a fully pre-trained large model. Such limitations may lead to sub-optimal model quality as well as excessive memory and training cost. In this paper, we propose a novel Channel Exploration methodology, dubbed as CHEX, to rectify these problems. As opposed to pruning-only strategy, we propose to repeatedly prune and regrow the channels throughout the training process, which reduces the risk of pruning important channels prematurely. More exactly: From intra-Layer's aspect, we tackle the channel pruning problem via a well-known column subset selection (CSS) formulation. From inter-Layer's aspect, our regrowing stages open a path for dynamically re-allocating the number of channels across all the layers under a global channel sparsity constraint. In addition, all the exploration process is done in a single training from scratch without the need of a pre-trained large model. Experimental results demonstrate that CHEX can effectively reduce the FLOPs of diverse CNN architectures on a variety of computer vision tasks, including image classification, object detection, instance segmentation, and 3D vision. For example, our compressed ResNet-50 model on ImageNet dataset achieves 76% top-l accuracy with only 25% FLOPs of the original ResNet-50 model, outperforming previous state-of-the-art channel pruning methods. The checkpoints and code are available at here.

Natural videos provide rich visual contents for selfsupervised learning. Yet most existing approaches for learning spatio-temporal representations rely on manually trimmed videos, leading to limited diversity in visual patterns and limited performance gain. In this work, we aim to learn representations by leveraging more abundant information in untrimmed videos. To this end, we propose to learn a hierarchy of consistencies in videos, i.e., visual consistency and topical consistency, corresponding respectively to clip pairs that tend to be visually similar when separated by a short time span and share similar topics when separated by a long time span. Specifically, a hierarchical consistency learning framework HiCo is presented, where the visually consistent pairs are encouraged to have the same representation through contrastive learning, while the topically consistent pairs are coupled through a topical classifier that distinguishes whether they are topicrelated. Further, we impose a gradual sampling algorithm for proposed hierarchical consistency learning, and demonstrate its theoretical superiority. Empirically, we show that not only HiCo can generate stronger representations on untrimmed videos, it also improves the representation quality when applied to trimmed videos. This is in contrast to standard contrastive learning that fails to learn appropriate representations from untrimmed videos.

As a dominant paradigm, fine-tuning a pre-trained model on the target data is widely used in many deep learning applications, especially for small data sets. However, recent studies have empirically shown that training from scratch has the final performance that is no worse than this pre-training strategy once the number of training samples is increased in some vision tasks. In this work, we revisit this phenomenon from the perspective of generalization analysis by using excess risk bound which is popular in learning theory. The result reveals that the excess risk bound may have a weak dependency on the pre-trained model. The observation inspires us to leverage pre-training data for fine-tuning, since this data is also available for fine-tuning. The generalization result of using pre-training data shows that the excess risk bound on a target task can be improved when the appropriate pre-training data is included in fine-tuning. With the theoretical motivation, we propose a novel selection strategy to select a subset from pre-training data to help improve the generalization on the target task. Extensive experimental results for image classification tasks on 8 benchmark data sets verify the effectiveness of the proposed data selection based fine-tuning pipeline. Our code is available at https://github.com/ziquanliu/NeurIPS2022UOTfine_tuning.

While semi-supervised learning (SSL) has received tremendous attentions in many machine learning tasks due to its successful use of unlabeled data, existing SSL algorithms use either all unlabeled examples or the unlabeled examples with a fixed high-confidence prediction during the training progress. However, it is possible that too many correct/wrong pseudo labeled examples are eliminated/selected. In this work we develop a simple yet powerful framework, whose key idea is to select a subset of training examples from the unlabeled data when performing existing SSL methods so that only the unlabeled examples with pseudo labels related to the labeled data will be used to train models. The selection is performed at each updating iteration by only keeping the examples whose losses are smaller than a given threshold that is dynamically adjusted through the iteration. Our proposed approach, Dash, enjoys its adaptivity in terms of unlabeled data selection and its theoretical guarantee. Specifically, we theoretically establish the convergence rate of Dash from the view of non-convex optimization. Finally, we empirically demonstrate the effectiveness of the proposed method in comparison with state-of-the-art over benchmarks.

Deep AUC (area under the ROC curve) Maximization (DAM) has attracted much attention recently due to its great potential for imbalanced data classification. However, the research on Federated Deep AUC Maximization (FDAM) is still limited. Compared with standard federated learning (FL) approaches that focus on decomposable minimization objectives, FDAM is more complicated due to its minimization objective is non-decomposable over individual examples. In this paper, we propose improved FDAM algorithms for heterogeneous data by solving the popular non-convex strongly-concave min-max formulation of DAM in a distributed fashion, which can also be applied to a class of non-convex strongly-concave min-max problems. A striking result of this paper is that the communication complexity of the proposed algorithm is a constant independent of the number of machines and also independent of the accuracy level, which improves an existing result by orders of magnitude. The experiments have demonstrated the effectiveness of our FDAM algorithm on benchmark datasets, and on medical chest X-ray images from different organizations. Our experiment shows that the performance of FDAM using data from multiple hospitals can improve the AUC score on testing data from a single hospital for detecting life-threatening diseases based on chest radiographs.

In this paper, we propose a practical online method for solving a class of distributional robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural networks. In the literature, most methods for solving DRO are based on stochastic primal-dual methods. However, primal-dual methods for DRO suffer from several drawbacks: (1) manipulating a high-dimensional dual variable corresponding to the size of data is time expensive; (2) they are not friendly to online learning where data is coming sequentially. To address these issues, we consider a class of DRO with an KL divergence regularization on the dual variables, transform the min-max problem into a compositional minimization problem, and propose practical duality-free online stochastic methods without requiring a large mini-batch size. We establish the state-of-the-art complexities of the proposed methods with and without a Polyak-Łojasiewicz (PL) condition of the objective. Empirical studies on large-scale deep learning tasks (i) demonstrate that our method can speed up the training by more than 2 times than baseline methods and save days of training time on a large-scale dataset with ∼ 265K images, and (ii) verify the supreme performance of DRO over Empirical Risk Minimization (ERM) on imbalanced datasets. Of independent interest, the proposed method can be also used for solving a family of stochastic compositional problems with state-of-the-art complexities.

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cases. We develop stochastic algorithms and establish their first-order convergence for finding a (nearly) stationary solution of the target non-convex function under different conditions of the component functions. To the best of our knowledge, this is the first work that comprehensively studies stochastic optimization of non-convex inf-projection minimization problems with provable convergence guarantee. Our algorithms enable efficient stochastic optimization of a family of non-decomposable DC functions and a family of bi-convex functions. To demonstrate the power of the proposed algorithms we consider an important application in variance-based regularization. Experiments verify the effectiveness of our inf-projection based formulation and the proposed stochastic algorithm in comparison with previous stochastic algorithms based on the min-max formulation for achieving the same effect.

Epoch gradient descent method (a.k.a. Epoch-GD) proposed by (Hazan and Kale, 2011) was deemeda breakthrough for stochastic strongly convex minimization, which achieves theoptimal convergence rate of O(1/T) with T iterative updates for the objective gap. However, its extension to solving stochastic min-max problems with strong convexity and strong concavity still remains open, and it is still unclear whethera fast rate ofO(1/T)for theduality gapis achievable for stochastic min-max optimization under strong convexity and strong concavity. Although some re-cent studies have proposed stochastic algorithms with fast convergence rates formin-max problems, they require additional assumptions about the problem, e.g.,smoothness, bi-linear structure, etc. In this paper, we bridge this gap by providinga sharp analysis of epoch-wise stochastic gradient descent ascent method (referredto as Epoch-GDA) for solving strongly convex strongly concave (SCSC) min-maxproblems, without imposing any additional assumption about smoothness or the function’s structure. To the best of our knowledge, our result is the first one that shows Epoch-GDA can achieve the optimal rate ofO(1/T)for the duality gapof general SCSC min-max problems. We emphasize that such generalization of Epoch-GD for strongly convex minimization problems to Epoch-GDA for SCSC min-max problems is non-trivial and requires novel technical analysis. Moreover, we notice that the key lemma can also be used for proving the convergence of Epoch-GDA for weakly-convex strongly-concave min-max problems, leading to a nearly optimal complexity without resorting to smoothness or other structural conditions.

An important class of non-convex objectives that has wide applications in machine learning consists of a sum of $n$ smooth functions and a non-smooth convex function. Tremendous studies have been devoted to conquering these problems by leveraging one of the two types of variance reduction techniques, i.e., SVRG-type that computes a full gradient occasionally and SAGA-type that maintains $n$ stochastic gradients at every iteration. In practice, SVRG-type is preferred to SAGA-type due to its potentially less memory costs. An interesting question that has been largely ignored is how to improve the complexity of variance reduction methods for problems with a large condition number that measures the degree to which the objective is close to a convex function. In this paper, we present a simple but non-trivial boosting of a state-of-the-art SVRG-type method for convex problems (namely Katyusha) to enjoy an improved complexity for solving non-convex problems with a large condition number (that is close to a convex function). To the best of our knowledge, its complexity has the best dependence on $n$ and the degree of non-convexity, and also matches that of a recent SAGA-type accelerated stochastic algorithm for a constrained non-convex smooth optimization problem.

Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC functions have been extensively studied, stochastic optimization that is more suitable for learning with big data remains under-explored. In this paper, we propose new stochastic optimization algorithms and study their first-order convergence theories for solving a broad family of DC functions. We improve the existing algorithms and theories of stochastic optimization for DC functions from both practical and theoretical perspectives. Moreover, we extend the proposed stochastic algorithms for DC functions to solve problems with a general non-convex non-differentiable regularizer, which does not necessarily have a DC decomposition but enjoys an efficient proximal mapping. To the best of our knowledge, this is the first work that gives the first non-asymptotic convergence for solving non-convex optimization whose objective has a general non-convex non-differentiable regularizer.

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation.

Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics. However, to the best of our knowledge no non-asymptotic convergence analysis of SPG exists for non-convex optimization with a non-smooth and non-convex regularizer. All existing non-asymptotic analysis of SPG for solving non-smooth non-convex problems require the non-smooth regularizer to be a convex function, and hence are not applicable to a non-smooth non-convex regularized problem. This work initiates the analysis to bridge this gap and opens the door to non-asymptotic convergence analysis of non-smooth non-convex regularized problems. We analyze several variants of mini-batch SPG methods for minimizing a non-convex objective that consists of a smooth non-convex loss and a non-smooth non-convex regularizer. Our contributions are two-fold: (i) we show that they enjoy the same complexities as their counterparts for solving convex regularized non-convex problems in terms of finding an approximate stationary point; (ii) we develop more practical variants using dynamic mini-batch size instead of a fixed mini-batch size without requiring the target accuracy level of solution. The significance of our results is that they improve upon the-state-of-art results for solving non-smooth non-convex regularized problems. We also empirically demonstrate the effectiveness of the considered SPG methods in comparison with other peer stochastic methods.

Although the convergence rates of existing variants of ADAGRAD have a better dependence on the number of iterations under the strong convexity condition, their iteration complexities have a explicitly linear dependence on the dimensionality of the problem. To alleviate this bad dependence, we propose a simple yet novel variant of ADAGRAD for stochastic (weakly) strongly convex optimization. Different from existing variants, the proposed variant (referred to as SADAGRAD) uses an adaptive restarting scheme in which (i) ADAGRAD serves as a sub-routine and is restarted periodically; (ii) the number of iterations for restarting ADAGRAD depends on the history of learning that incorporates knowledge of the geometry of the data. In addition to the adaptive proximal functions and adaptive number of iterations for restarting, we also develop a variant that is adaptive to the (implicit) strong convexity from the data, which together makes the proposed algorithm strongly adaptive. In terms of iteration complexity, in the worst case SADAGRAD has an O(1/\epsilon) for finding an \epsilon-optimal solution similar to other variants. However, it could enjoy faster convergence and much better dependence on the problem’s dimensionality when stochastic gradients are sparse. Extensive experiments on large-scale data sets demonstrate the efficiency of the proposed algorithms in comparison with several variants of ADAGRAD and stochastic gradient method.

(This is a theory paper) In this paper, we consider first-order methods for solving stochastic non-convex optimization problems. The key building block of the proposed algorithms is first-order procedures to extract negative curvature from the Hessian matrix through a principled sequence starting from noise, which are referred to {\it NEgative-curvature-Originated-from-Noise or NEON} and are of independent interest. Based on this building block, we design purely first-order stochastic algorithms for escaping from non-degenerate saddle points with a much better time complexity (almost linear time in the problem's dimensionality). In particular, we develop a general framework of {\it first-order stochastic algorithms} with a second-order convergence guarantee based on our new technique and existing algorithms that may only converge to a first-order stationary point. For finding a nearly {\it second-order stationary point} $\x$ such that $\|\nabla F(\x)\|\leq \epsilon$ and $\nabla^2 F(\x)\geq -\sqrt{\epsilon}I$ (in high probability), the best time complexity of the presented algorithms is $\widetilde O(d/\epsilon^{3.5})$, where $F(\cdot)$ denotes the objective function and $d$ is the dimensionality of the problem. To the best of our knowledge, this is the first theoretical result of first-order stochastic algorithms with an almost linear time in terms of problem's dimensionality for finding second-order stationary points, which is even competitive with existing stochastic algorithms hinging on the second-order information.

In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling high-dimensionality challenge in machine learning. Recently, various non-oblivious randomized reduction methods have been developed and deployed for solving many numerical problems such as matrix product approximation, low-rank matrix approximation, etc. However, they are less explored for the machine learning tasks, e.g., classification. More seriously, the theoretical analysis of excess risk bounds for risk minimization, an important measure of generalization performance, has not been established for non-oblivious randomized reduction methods. It therefore remains an open problem what is the benefit of using them over previous oblivious random projection based approaches. To tackle these challenges, we propose an algorithmic framework for employing non-oblivious randomized reduction method for general empirical risk minimizing in machine learning tasks, where the original high-dimensional features are projected onto a random subspace that is derived from the data with a small matrix approximation error. We then derive the first excess risk bound for the proposed non-oblivious randomized reduction approach without requiring strong assumptions on the training data. The established excess risk bound exhibits that the proposed approach provides much better generalization performance and it also sheds more insights about different randomized reduction approaches. Finally, we conduct extensive experiments on both synthetic and real-world benchmark datasets, whose dimension scales to O(10^7), to demonstrate the efficacy of our proposed approach.

In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function $F(\mathbf{w})$ in the $\epsilon$-sublevel set grows as fast as $\|\mathbf{w} - \mathbf{w}_*\|_2^{1/\theta}$, where $\mathbf{w}_*$ represents the closest optimal solution to $\mathbf{w}$ and $\theta\in(0,1]$ quantifies the local growth rate, the iteration complexity of first-order stochastic optimization for achieving an $\epsilon$-optimal solution can be $\widetilde O(1/\epsilon^{2(1-\theta)})$, which is optimal at most up to a logarithmic factor. This result is fundamentally better in contrast with the previous works that either assume a global growth condition in the entire domain or achieve a local faster convergence under the local faster growth condition. To achieve the faster global convergence, we develop two different accelerated stochastic subgradient methods by iteratively solving the original problem approximately in a local region around a historical solution with the size of the local region gradually decreasing as the solution approaches the optimal set. Besides the theoretical improvements, this work also include new contributions towards making the proposed algorithms practical: (i) we present practical variants of accelerated stochastic subgradient methods that can run without the knowledge of multiplicative growth constant and even the growth rate $\theta$; (ii) we consider a broad family of problems in machine learning to demonstrate that the proposed algorithms enjoy faster convergence than traditional stochastic subgradient method. For example, when applied to the $\ell_1$ regularized empirical polyhedral loss minimization (e.g., hinge loss, absolute loss), the proposed stochastic methods have a logarithmic iteration complexity.

Alternating direction method of multipliers (ADMM) has received tremendous interest for solving numerous problems in machine learning, statistics and signal processing. However, it is known that the performance of ADMM and many of its variants is very sensitive to the penalty parameter of a quadratic penalty applied to the equality constraints. Although several approaches have been proposed for dynamically changing this parameter during the course of optimization, they do not yield theoretical improvement in the convergence rate and are not directly applicable to stochastic ADMM. In this paper, we develop a new ADMM and its linearized variant with a new adaptive scheme to update the penalty parameter. Our methods can be applied under both deterministic and stochastic optimization settings for structured non-smooth objective function. The novelty of the proposed scheme lies at that it is adaptive to a local sharpness property of the objective function, which marks the key difference from previous adaptive scheme that adjusts the penalty parameter per-iteration based on certain conditions on iterates. On theoretical side, given the local sharpness characterized by an exponent $\theta\in(0, 1]$, we show that the proposed ADMM enjoys an improved iteration complexity of $\widetilde O(1/\epsilon^{1-\theta})$\footnote{$\widetilde O()$ suppresses a logarithmic factor.} in the deterministic setting and an iteration complexity of $\widetilde O(1/\epsilon^{2(1-\theta)})$ in the stochastic setting without smoothness and strong convexity assumptions. The complexity in either setting improves that of the standard ADMM which only uses a fixed penalty parameter. On the practical side, we demonstrate that the proposed algorithms converge comparably to, if not much faster than, ADMM with a fine-tuned fixed penalty parameter.

Error bound, an inherent property of an optimization problem, has recently revived in the development of algorithms with improved global convergence without strong convexity. The most studied error bound is the quadratic error bound, which generalizes strong convexity and is satisfied by a large family of machine learning problems. Quadratic error bound have been leveraged to achieve linear convergence in many first-order methods including the stochastic variance reduced gradient (SVRG) method, which is one of the most important stochastic optimization methods in machine learning. However, the studies along this direction face the critical issue that the algorithms must depend on an unknown growth parameter (a generalization of strong convexity modulus) in the error bound. This parameter is difficult to estimate exactly and the algorithms choosing this parameter heuristically do not have theoretical convergence guarantee. To address this issue, we propose novel SVRG methods that automatically search for this unknown parameter on the fly of optimization while still obtain almost the same convergence rate as when this parameter is known. We also analyze the convergence property of SVRG methods under H\"{o}lderian error bound, which generalizes the quadratic error bound.

In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration complexity for solving such non-smooth optimization problems is $O(1/\epsilon)$ without any assumption on the strong convexity. In this work, we will show that the proposed HOPS achieved a lower iteration complexity of $\tilde O(1/\epsilon^{1-\theta})$ with $\theta\in(0,1]$ capturing the local sharpness of the objective function around the optimal solutions. To the best of our knowledge, this is the lowest iteration complexity achieved so far for the considered non-smooth optimization problems without strong convexity assumption. The HOPS algorithm employs Nesterov's smoothing technique and Nesterov's accelerated gradient method and runs in stages, which gradually decreases the smoothing parameter in a stage-wise manner until it yields a sufficiently good approximation of the original function. We show that HOPS enjoys a linear convergence for many well-known non-smooth problems (e.g., empirical risk minimization with a piece-wise linear loss function and $\ell_1$ norm regularizer, finding a point in a polyhedron, cone programming, etc). Experimental results verify the effectiveness of HOPS in comparison with Nesterov's smoothing algorithm and the primal-dual style of first-order methods.