Decentralized Kernel Ridge Regression Based on Data-dependent Random Feature

Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random features on different nodes are identical. However, in many applications, data on different nodes varies significantly on the number or distribution, which calls for adaptive and data-dependent methods that generate different RFs. To tackle the essential difficulty, we propose a new decentralized KRR algorithm that pursues consensus on decision functions, which allows great flexibility and well adapts data on nodes. The convergence is rigorously given and the effectiveness is numerically verified: by capturing the characteristics of the data on each node, while maintaining the same communication costs as other methods, we achieved an average regression accuracy improvement of 25.5\% across six real-world data sets.

Resolve Domain Conflicts for Generalizable Remote Physiological Measurement

Remote photoplethysmography (rPPG) technology has become increasingly popular due to its non-invasive monitoring of various physiological indicators, making it widely applicable in multimedia interaction, healthcare, and emotion analysis. Existing rPPG methods utilize multiple datasets for training to enhance the generalizability of models. However, they often overlook the underlying conflict issues across different datasets, such as (1) label conflict resulting from different phase delays between physiological signal labels and face videos at the instance level, and (2) attribute conflict stemming from distribution shifts caused by head movements, illumination changes, skin types, etc. To address this, we introduce the DOmain-HArmonious framework (DOHA). Specifically, we first propose a harmonious phase strategy to eliminate uncertain phase delays and preserve the temporal variation of physiological signals. Next, we design a harmonious hyperplane optimization that reduces irrelevant attribute shifts and encourages the model's optimization towards a global solution that fits more valid scenarios. Our experiments demonstrate that DOHA significantly improves the performance of existing methods under multiple protocols. Our code is available at https://github.com/SWY666/rPPG-DOHA.

Revisiting Random Weight Perturbation for Efficiently Improving Generalization

Improving the generalization ability of modern deep neural networks (DNNs) is a fundamental challenge in machine learning. Two branches of methods have been proposed to seek flat minima and improve generalization: one led by sharpness-aware minimization (SAM) minimizes the worst-case neighborhood loss through adversarial weight perturbation (AWP), and the other minimizes the expected Bayes objective with random weight perturbation (RWP). While RWP offers advantages in computation and is closely linked to AWP on a mathematical basis, its empirical performance has consistently lagged behind that of AWP. In this paper, we revisit the use of RWP for improving generalization and propose improvements from two perspectives: i) the trade-off between generalization and convergence and ii) the random perturbation generation. Through extensive experimental evaluations, we demonstrate that our enhanced RWP methods achieve greater efficiency in enhancing generalization, particularly in large-scale problems, while also offering comparable or even superior performance to SAM. The code is released at https://github.com/nblt/mARWP.

OrthCaps: An Orthogonal CapsNet with Sparse Attention Routing and Pruning

Redundancy is a persistent challenge in Capsule Networks (CapsNet),leading to high computational costs and parameter counts. Although previous works have introduced pruning after the initial capsule layer, dynamic routing's fully connected nature and non-orthogonal weight matrices reintroduce redundancy in deeper layers. Besides, dynamic routing requires iterating to converge, further increasing computational demands. In this paper, we propose an Orthogonal Capsule Network (OrthCaps) to reduce redundancy, improve routing performance and decrease parameter counts. Firstly, an efficient pruned capsule layer is introduced to discard redundant capsules. Secondly, dynamic routing is replaced with orthogonal sparse attention routing, eliminating the need for iterations and fully connected structures. Lastly, weight matrices during routing are orthogonalized to sustain low capsule similarity, which is the first approach to introduce orthogonality into CapsNet as far as we know. Our experiments on baseline datasets affirm the efficiency and robustness of OrthCaps in classification tasks, in which ablation studies validate the criticality of each component. Remarkably, OrthCaps-Shallow outperforms other Capsule Network benchmarks on four datasets, utilizing only 110k parameters, which is a mere 1.25% of a standard Capsule Network's total. To the best of our knowledge, it achieves the smallest parameter count among existing Capsule Networks. Similarly, OrthCaps-Deep demonstrates competitive performance across four datasets, utilizing only 1.2% of the parameters required by its counterparts.

Friendly Sharpness-Aware Minimization

Sharpness-Aware Minimization (SAM) has been instrumental in improving deep neural network training by minimizing both training loss and loss sharpness. Despite the practical success, the mechanisms behind SAM's generalization enhancements remain elusive, limiting its progress in deep learning optimization. In this work, we investigate SAM's core components for generalization improvement and introduce "Friendly-SAM" (F-SAM) to further enhance SAM's generalization. Our investigation reveals the key role of batch-specific stochastic gradient noise within the adversarial perturbation, i.e., the current minibatch gradient, which significantly influences SAM's generalization performance. By decomposing the adversarial perturbation in SAM into full gradient and stochastic gradient noise components, we discover that relying solely on the full gradient component degrades generalization while excluding it leads to improved performance. The possible reason lies in the full gradient component's increase in sharpness loss for the entire dataset, creating inconsistencies with the subsequent sharpness minimization step solely on the current minibatch data. Inspired by these insights, F-SAM aims to mitigate the negative effects of the full gradient component. It removes the full gradient estimated by an exponentially moving average (EMA) of historical stochastic gradients, and then leverages stochastic gradient noise for improved generalization. Moreover, we provide theoretical validation for the EMA approximation and prove the convergence of F-SAM on non-convex problems. Extensive experiments demonstrate the superior generalization performance and robustness of F-SAM over vanilla SAM. Code is available at https://github.com/nblt/F-SAM.

Inverse-Free Fast Natural Gradient Descent Method for Deep Learning

Second-order methods can converge much faster than first-order methods by incorporating second-order derivates or statistics, but they are far less prevalent in deep learning due to their computational inefficiency. To handle this, many of the existing solutions focus on reducing the size of the matrix to be inverted. However, it is still needed to perform the inverse operator in each iteration. In this paper, we present a fast natural gradient descent (FNGD) method, which only requires computing the inverse during the first epoch. Firstly, we reformulate the gradient preconditioning formula in the natural gradient descent (NGD) as a weighted sum of per-sample gradients using the Sherman-Morrison-Woodbury formula. Building upon this, to avoid the iterative inverse operation involved in computing coefficients, the weighted coefficients are shared across epochs without affecting the empirical performance. FNGD approximates the NGD as a fixed-coefficient weighted sum, akin to the average sum in first-order methods. Consequently, the computational complexity of FNGD can approach that of first-order methods. To demonstrate the efficiency of the proposed FNGD, we perform empirical evaluations on image classification and machine translation tasks. For training ResNet-18 on the CIFAR-100 dataset, FNGD can achieve a speedup of 2.05$\times$ compared with KFAC. For training Transformer on Multi30K, FNGD outperforms AdamW by 24 BLEU score while requiring almost the same training time.

Machine Unlearning by Suppressing Sample Contribution

Machine Unlearning (MU) is to forget data from a well-trained model, which is practically important due to the "right to be forgotten". In this paper, we start from the fundamental distinction between training data and unseen data on their contribution to the model: the training data contributes to the final model while the unseen data does not. We theoretically discover that the input sensitivity can approximately measure the contribution and practically design an algorithm, called MU-Mis (machine unlearning via minimizing input sensitivity), to suppress the contribution of the forgetting data. Experimental results demonstrate that MU-Mis outperforms state-of-the-art MU methods significantly. Additionally, MU-Mis aligns more closely with the application of MU as it does not require the use of remaining data.

Kernel PCA for Out-of-Distribution Detection

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs). Existing works have shown the insufficiency of Principal Component Analysis (PCA) straightforwardly applied on the features of DNNs in detecting OoD data from In-Distribution (InD) data. The failure of PCA suggests that the network features residing in OoD and InD are not well separated by simply proceeding in a linear subspace, which instead can be resolved through proper nonlinear mappings. In this work, we leverage the framework of Kernel PCA (KPCA) for OoD detection, seeking subspaces where OoD and InD features are allocated with significantly different patterns. We devise two feature mappings that induce non-linear kernels in KPCA to advocate the separability between InD and OoD data in the subspace spanned by the principal components. Given any test sample, the reconstruction error in such subspace is then used to efficiently obtain the detection result with $\mathcal{O}(1)$ time complexity in inference. Extensive empirical results on multiple OoD data sets and network structures verify the superiority of our KPCA-based detector in efficiency and efficacy with state-of-the-art OoD detection performances.

Learn What You Need in Personalized Federated Learning

Personalized federated learning aims to address data heterogeneity across local clients in federated learning. However, current methods blindly incorporate either full model parameters or predefined partial parameters in personalized federated learning. They fail to customize the collaboration manner according to each local client's data characteristics, causing unpleasant aggregation results. To address this essential issue, we propose $\textit{Learn2pFed}$, a novel algorithm-unrolling-based personalized federated learning framework, enabling each client to adaptively select which part of its local model parameters should participate in collaborative training. The key novelty of the proposed $\textit{Learn2pFed}$ is to optimize each local model parameter's degree of participant in collaboration as learnable parameters via algorithm unrolling methods. This approach brings two benefits: 1) mathmatically determining the participation degree of local model parameters in the federated collaboration, and 2) obtaining more stable and improved solutions. Extensive experiments on various tasks, including regression, forecasting, and image classification, demonstrate that $\textit{Learn2pFed}$ significantly outperforms previous personalized federated learning methods.

Online Continual Learning via Logit Adjusted Softmax

Online continual learning is a challenging problem where models must learn from a non-stationary data stream while avoiding catastrophic forgetting. Inter-class imbalance during training has been identified as a major cause of forgetting, leading to model prediction bias towards recently learned classes. In this paper, we theoretically analyze that inter-class imbalance is entirely attributed to imbalanced class-priors, and the function learned from intra-class intrinsic distributions is the Bayes-optimal classifier. To that end, we present that a simple adjustment of model logits during training can effectively resist prior class bias and pursue the corresponding Bayes-optimum. Our proposed method, Logit Adjusted Softmax, can mitigate the impact of inter-class imbalance not only in class-incremental but also in realistic general setups, with little additional computational cost. We evaluate our approach on various benchmarks and demonstrate significant performance improvements compared to prior arts. For example, our approach improves the best baseline by 4.6% on CIFAR10.