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Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $\eta$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/\eta$, after which it…

Machine Learning · Computer Science 2024-06-07 Philip M. Long , Peter L. Bartlett

Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a…

Machine Learning · Computer Science 2021-06-30 Jungmin Kwon , Jeongseop Kim , Hyunseo Park , In Kwon Choi

Sharpness-Aware Minimization (SAM) is a recent optimization framework aiming to improve the deep neural network generalization, through obtaining flatter (i.e. less sharp) solutions. As SAM has been numerically successful, recent papers…

Machine Learning · Statistics 2023-05-22 Kayhan Behdin , Rahul Mazumder

Brain-inspired spiking neural networks (SNNs) are recognized as a promising avenue for achieving efficient, low-energy neuromorphic computing. Direct training of SNNs typically relies on surrogate gradient (SG) learning to estimate…

Neural and Evolutionary Computing · Computer Science 2025-11-18 Jiaqiang Jiang , Wenfeng Xu , Jing Fan , Rui Yan

Large language models exhibit strong reasoning capabilities, yet often rely on shortcuts such as surface pattern matching and answer memorization rather than genuine logical inference. We propose Shortcut-Aware Reasoning Training (SART), a…

Computation and Language · Computer Science 2026-03-24 Hongyu Cao , Kunpeng Liu , Dongjie Wang , Yanjie Fu

Spiking Neural Networks (SNNs) have gained significant traction in both computational neuroscience and artificial intelligence for their potential in energy-efficient computing. In contrast, artificial neural networks (ANNs) excel at…

Neural and Evolutionary Computing · Computer Science 2025-09-30 Nhan T. Luu , Duong T. Luu , Pham Ngoc Nam , Truong Cong Thang

Sharpness-Aware Minimization (SAM) is an optimizer that takes a descent step based on the gradient at a perturbation $y_t = x_t + \rho \frac{\nabla f(x_t)}{\lVert \nabla f(x_t) \rVert}$ of the current point $x_t$. Existing studies prove…

Machine Learning · Computer Science 2023-10-30 Dongkuk Si , Chulhee Yun

Sharpness-Aware Minimization (SAM) is widely used to seek flatter minima -- often linked to better generalization. In its standard implementation, SAM updates the current iterate using the loss gradient evaluated at a point perturbed by…

Machine Learning · Computer Science 2026-02-06 Chanwoong Park , Uijeong Jang , Ernest K. Ryu , Insoon Yang

Low-latency deep spiking neural networks (SNNs) have become a promising alternative to conventional artificial neural networks (ANNs) because of their potential for increased energy efficiency on event-driven neuromorphic hardware. Neural…

Computer Vision and Pattern Recognition · Computer Science 2021-10-25 Souvik Kundu , Massoud Pedram , Peter A. Beerel

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Machine Learning · Computer Science 2017-11-23 Haiping Huang , Taro Toyoizumi

Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are…

Optimization and Control · Mathematics 2023-03-22 Hanbaek Lyu

Spiking neural networks (SNNs) have shown their competence in handling spatial-temporal event-based data with low energy consumption. Similar to conventional artificial neural networks (ANNs), SNNs are also vulnerable to gradient-based…

Computer Vision and Pattern Recognition · Computer Science 2025-03-07 Li Lun , Kunyu Feng , Qinglong Ni , Ling Liang , Yuan Wang , Ying Li , Dunshan Yu , Xiaoxin Cui

The recently proposed optimization algorithm for deep neural networks Sharpness Aware Minimization (SAM) suggests perturbing parameters before gradient calculation by a gradient ascent step to guide the optimization into parameter space…

Machine Learning · Computer Science 2025-10-03 Marlon Becker , Frederick Altrock , Benjamin Risse

The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware…

Machine Learning · Computer Science 2023-10-12 Zixiang Chen , Junkai Zhang , Yiwen Kou , Xiangning Chen , Cho-Jui Hsieh , Quanquan Gu

Spiking Neural Networks (SNNs) have attracted great attention for their energy-efficient operations and biologically inspired structures, offering potential advantages over Artificial Neural Networks (ANNs) in terms of energy efficiency and…

Neural and Evolutionary Computing · Computer Science 2024-06-03 Yujia Liu , Tong Bu , Jianhao Ding , Zecheng Hao , Tiejun Huang , Zhaofei Yu

Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD):…

Machine Learning · Statistics 2018-01-09 Haw-Shiuan Chang , Erik Learned-Miller , Andrew McCallum

Spiking neural networks (SNNs), recognized as an energy-efficient alternative to traditional artificial neural networks (ANNs), have advanced rapidly through the scaling of models and datasets. However, such scaling incurs considerable…

Neural and Evolutionary Computing · Computer Science 2025-10-07 Chenxiang Ma , Xinyi Chen , Yujie Wu , Kay Chen Tan , Jibin Wu

SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and…

Machine Learning · Computer Science 2025-02-04 Javier Bernal , Jose Torres-Jimenez

We consider Sharpness-Aware Minimization (SAM), a gradient-based optimization method for deep networks that has exhibited performance improvements on image and language prediction problems. We show that when SAM is applied with a convex…

Machine Learning · Computer Science 2023-04-12 Peter L. Bartlett , Philip M. Long , Olivier Bousquet

Spiking neural networks (SNNs) offer a promising energy-efficient alternative to artificial neural networks (ANNs), in virtue of their high biological plausibility, rich spatial-temporal dynamics, and event-driven computation. The direct…

Neural and Evolutionary Computing · Computer Science 2024-07-12 Chenlin Zhou , Han Zhang , Liutao Yu , Yumin Ye , Zhaokun Zhou , Liwei Huang , Zhengyu Ma , Xiaopeng Fan , Huihui Zhou , Yonghong Tian