Bin Gu

Bin Gu, Chenkang Zhang, Huan Xiong et al.

Learning to improve AUC performance is an important topic in machine learning. However, AUC maximization algorithms may decrease generalization performance due to the noisy data. Self-paced learning is an effective method for handling noisy data. However, existing self-paced learning methods are limited to pointwise learning, while AUC maximization is a pairwise learning problem. To solve this challenging problem, we innovatively propose a balanced self-paced AUC maximization algorithm (BSPAUC). Specifically, we first provide a statistical objective for self-paced AUC. Based on this, we propose our self-paced AUC maximization formulation, where a novel balanced self-paced regularization term is embedded to ensure that the selected positive and negative samples have proper proportions. Specially, the sub-problem with respect to all weight variables may be non-convex in our formulation, while the one is normally convex in existing self-paced problems. To address this, we propose a doubly cyclic block coordinate descent method. More importantly, we prove that the sub-problem with respect to all weight variables converges to a stationary point on the basis of closed-form solutions, and our BSPAUC converges to a stationary point of our fixed optimization objective under a mild assumption. Considering both the deep learning and kernel-based implementations, experimental results on several large-scale datasets demonstrate that our BSPAUC has a better generalization performance than existing state-of-the-art AUC maximization methods.

Hualin Zhang, Huan Xiong, Bin Gu

We consider escaping saddle points of nonconvex problems where only the function evaluations can be accessed. Although a variety of works have been proposed, the majority of them require either second or first-order information, and only a few of them have exploited zeroth-order methods, particularly the technique of negative curvature finding with zeroth-order methods which has been proven to be the most efficient method for escaping saddle points. To fill this gap, in this paper, we propose two zeroth-order negative curvature finding frameworks that can replace Hessian-vector product computations without increasing the iteration complexity. We apply the proposed frameworks to ZO-GD, ZO-SGD, ZO-SCSG, ZO-SPIDER and prove that these ZO algorithms can converge to $(ε,δ)$-approximate second-order stationary points with less query complexity compared with prior zeroth-order works for finding local minima.

Bhaskar Mukhoty, Velibor Bojkovic, William de Vazelhes et al.

Spiking neural networks are becoming increasingly popular for their low energy requirement in real-world tasks with accuracy comparable to the traditional ANNs. SNN training algorithms face the loss of gradient information and non-differentiability due to the Heaviside function in minimizing the model loss over model parameters. To circumvent the problem surrogate method uses a differentiable approximation of the Heaviside in the backward pass, while the forward pass uses the Heaviside as the spiking function. We propose to use the zeroth order technique at the neuron level to resolve this dichotomy and use it within the automatic differentiation tool. As a result, we establish a theoretical connection between the proposed local zeroth-order technique and the existing surrogate methods and vice-versa. The proposed method naturally lends itself to energy-efficient training of SNNs on GPUs. Experimental results with neuromorphic datasets show that such implementation requires less than 1 percent neurons to be active in the backward pass, resulting in a 100x speed-up in the backward computation time. Our method offers better generalization compared to the state-of-the-art energy-efficient technique while maintaining similar efficiency.

Xiaofeng Wu, Velibor Bojkovic, Bin Gu et al.

Spiking Neural Networks (SNNs) offer a promising avenue for energy-efficient computing compared with Artificial Neural Networks (ANNs), closely mirroring biological neural processes. However, this potential comes with inherent challenges in directly training SNNs through spatio-temporal backpropagation -- stemming from the temporal dynamics of spiking neurons and their discrete signal processing -- which necessitates alternative ways of training, most notably through ANN-SNN conversion. In this work, we introduce a lightweight Forward Temporal Bias Correction (FTBC) technique, aimed at enhancing conversion accuracy without the computational overhead. We ground our method on provided theoretical findings that through proper temporal bias calibration the expected error of ANN-SNN conversion can be reduced to be zero after each time step. We further propose a heuristic algorithm for finding the temporal bias only in the forward pass, thus eliminating the computational burden of backpropagation and we evaluate our method on CIFAR-10/100 and ImageNet datasets, achieving a notable increase in accuracy on all datasets. Codes are released at a GitHub repository.

Yasser Ashraf, Ahmed Sharshar, Velibor Bojkovic et al.

Spike cameras, bio-inspired vision sensors, asynchronously fire spikes by accumulating light intensities at each pixel, offering ultra-high energy efficiency and exceptional temporal resolution. Unlike event cameras, which record changes in light intensity to capture motion, spike cameras provide even finer spatiotemporal resolution and a more precise representation of continuous changes. In this paper, we introduce the first video action recognition (VAR) dataset using spike camera, alongside synchronized RGB and thermal modalities, to enable comprehensive benchmarking for Spiking Neural Networks (SNNs). By preserving the inherent sparsity and temporal precision of spiking data, our three datasets offer a unique platform for exploring multimodal video understanding and serve as a valuable resource for directly comparing spiking, thermal, and RGB modalities. This work contributes a novel dataset that will drive research in energy-efficient, ultra-low-power video understanding, specifically for action recognition tasks using spike-based data.

William de Vazelhes, Xiao-Tong Yuan, Bin Gu

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also some extra constraints. While prior algorithms have been developed to address this complex scenario with mixed combinatorial and convex constraints, they typically require the closed form projection onto the mixed constraints which might not exist, and/or only provide local guarantees of convergence which is different from the global guarantees commonly sought in sparse optimization. To fill this gap, in this paper, we study the problem of sparse optimization with extra support-preserving constraints commonly encountered in the literature. We present a new variant of iterative hard-thresholding algorithm equipped with a two-step consecutive projection operator customized for these mixed constraints, serving as a simple alternative to the Euclidean projection onto the mixed constraint. By introducing a novel trade-off between sparsity relaxation and sub-optimality, we provide global guarantees in objective value for the output of our algorithm, in the deterministic, stochastic, and zeroth-order settings, under the conventional restricted strong-convexity/smoothness assumptions. As a fundamental contribution in proof techniques, we develop a novel extension of the classic three-point lemma to the considered two-step non-convex projection operator, which allows us to analyze the convergence in objective value in an elegant way that has not been possible with existing techniques. In the zeroth-order case, such technique also improves upon the state-of-the-art result from de Vazelhes et. al. (2022), even in the case without additional constraints, by allowing us to remove a non-vanishing system error present in their work.

William de Vazelhes, Bhaskar Mukhoty, Xiao-Tong Yuan et al.

Sparse recovery is ubiquitous in machine learning and signal processing. Due to the NP-hard nature of sparse recovery, existing methods are known to suffer either from restrictive (or even unknown) applicability conditions, or high computational cost. Recently, iterative regularization methods have emerged as a promising fast approach because they can achieve sparse recovery in one pass through early stopping, rather than the tedious grid-search used in the traditional methods. However, most of those iterative methods are based on the $\ell_1$ norm which requires restrictive applicability conditions and could fail in many cases. Therefore, achieving sparse recovery with iterative regularization methods under a wider range of conditions has yet to be further explored. To address this issue, we propose a novel iterative regularization algorithm, IRKSN, based on the $k$-support norm regularizer rather than the $\ell_1$ norm. We provide conditions for sparse recovery with IRKSN, and compare them with traditional conditions for recovery with $\ell_1$ norm regularizers. Additionally, we give an early stopping bound on the model error of IRKSN with explicit constants, achieving the standard linear rate for sparse recovery. Finally, we illustrate the applicability of our algorithm on several experiments, including a support recovery experiment with a correlated design matrix.