Second-order optimization techniques have the potential to achieve faster convergence rates compared to first-order methods through the incorporation of second-order derivatives or statistics. However, their utilization in deep learning is limited due to their computational inefficiency. Various approaches have been proposed to address this issue, primarily centered on minimizing the size of the matrix to be inverted. Nevertheless, the necessity of performing the inverse operation iteratively persists. In this work, we present a fast natural gradient descent (FNGD) method that only requires inversion during the first epoch. Specifically, it is revealed that natural gradient descent (NGD) is essentially a weighted sum of per-sample gradients. Our novel approach further proposes to share these weighted coefficients across epochs without affecting empirical performance. Consequently, FNGD exhibits similarities to the average sum in first-order methods, leading to the computational complexity of FNGD being comparable to that of first-order methods. Extensive experiments on image classification and machine translation tasks demonstrate the efficiency of the proposed FNGD. For training ResNet-18 on CIFAR-100, FNGD can achieve a speedup of 2.07$\times$ compared with KFAC. For training Transformer on Multi30K, FNGD outperforms AdamW by 24 BLEU score while requiring almost the same training time.

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.

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.

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.

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.

Multi-frame methods improve monocular depth estimation over single-frame approaches by aggregating spatial-temporal information via feature matching. However, the spatial-temporal feature leads to accuracy degradation in dynamic scenes. To enhance the performance, recent methods tend to propose complex architectures for feature matching and dynamic scenes. In this paper, we show that a simple learning framework, together with designed feature augmentation, leads to superior performance. (1) A novel dynamic objects detecting method with geometry explainability is proposed. The detected dynamic objects are excluded during training, which guarantees the static environment assumption and relieves the accuracy degradation problem of the multi-frame depth estimation. (2) Multi-scale feature fusion is proposed for feature matching in the multi-frame depth network, which improves feature matching, especially between frames with large camera motion. (3) The robust knowledge distillation with a robust teacher network and reliability guarantee is proposed, which improves the multi-frame depth estimation without computation complexity increase during the test. The experiments show that our proposed methods achieve great performance improvement on the multi-frame depth estimation.

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.

Existing Out-of-Distribution (OoD) detection methods address to detect OoD samples from In-Distribution data (InD) mainly by exploring differences in features, logits and gradients in Deep Neural Networks (DNNs). We in this work propose a new perspective upon loss landscape and mode ensemble to investigate OoD detection. In the optimization of DNNs, there exist many local optima in the parameter space, or namely modes. Interestingly, we observe that these independent modes, which all reach low-loss regions with InD data (training and test data), yet yield significantly different loss landscapes with OoD data. Such an observation provides a novel view to investigate the OoD detection from the loss landscape and further suggests significantly fluctuating OoD detection performance across these modes. For instance, FPR values of the RankFeat method can range from 46.58% to 84.70% among 5 modes, showing uncertain detection performance evaluations across independent modes. Motivated by such diversities on OoD loss landscape across modes, we revisit the deep ensemble method for OoD detection through mode ensemble, leading to improved performance and benefiting the OoD detector with reduced variances. Extensive experiments covering varied OoD detectors and network structures illustrate high variances across modes and also validate the superiority of mode ensemble in boosting OoD detection. We hope this work could attract attention in the view of independent modes in the OoD loss landscape and more reliable evaluations on OoD detectors.

The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of Locally-Adaptive-Bandwidths (LAB) as trainable parameters to enhance the Radial Basis Function (RBF) kernel, giving rise to the LAB RBF kernel. The parameters in LAB RBF kernels are data-dependent, and its number can increase with the dataset, allowing for better adaptation to diverse data patterns and enhancing the flexibility of the learned function. This newfound flexibility also brings challenges, particularly with regards to asymmetry and the need for an efficient learning algorithm. To address these challenges, this paper for the first time establishes an asymmetric kernel ridge regression framework and introduces an iterative kernel learning algorithm. This novel approach not only reduces the demand for extensive support data but also significantly improves generalization by training bandwidths on the available training data. Experimental results on real datasets underscore the remarkable performance of the proposed algorithm, showcasing its superior capability in handling large-scale datasets compared to Nystr\"om approximation-based algorithms. Moreover, it demonstrates a significant improvement in regression accuracy over existing kernel-based learning methods and even surpasses residual neural networks.

Multitask learning (MTL) leverages task-relatedness to enhance performance. With the emergence of multimodal data, tasks can now be referenced by multiple indices. In this paper, we employ high-order tensors, with each mode corresponding to a task index, to naturally represent tasks referenced by multiple indices and preserve their structural relations. Based on this representation, we propose a general framework of low-rank MTL methods with tensorized support vector machines (SVMs) and least square support vector machines (LSSVMs), where the CP factorization is deployed over the coefficient tensor. Our approach allows to model the task relation through a linear combination of shared factors weighted by task-specific factors and is generalized to both classification and regression problems. Through the alternating optimization scheme and the Lagrangian function, each subproblem is transformed into a convex problem, formulated as a quadratic programming or linear system in the dual form. In contrast to previous MTL frameworks, our decision function in the dual induces a weighted kernel function with a task-coupling term characterized by the similarities of the task-specific factors, better revealing the explicit relations across tasks in MTL. Experimental results validate the effectiveness and superiority of our proposed methods compared to existing state-of-the-art approaches in MTL. The code of implementation will be available at https://github.com/liujiani0216/TSVM-MTL.