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As a new programming paradigm, deep learning has expanded its application to many real-world problems. At the same time, deep learning based software are found to be vulnerable to adversarial attacks. Though various defense mechanisms have…

Cryptography and Security · Computer Science 2021-03-16 Zhe Zhao , Guangke Chen , Jingyi Wang , Yiwei Yang , Fu Song , Jun Sun

The choice of activation function fundamentally shapes the representational capacity and parameter efficiency of deep neural networks, yet most widely used activations lack rigorous theoretical guarantees on these properties. We provide a…

Machine Learning · Computer Science 2026-05-14 Ibrahim Albool , Malak Gamal El-Din , Salma Elmalaki , Yasser Shoukry

The study on improving the robustness of deep neural networks against adversarial examples grows rapidly in recent years. Among them, adversarial training is the most promising one, which flattens the input loss landscape (loss change with…

Machine Learning · Computer Science 2020-10-14 Dongxian Wu , Shu-tao Xia , Yisen Wang

We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw.…

We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks…

Machine Learning · Computer Science 2022-02-01 Chandresh Pravin , Ivan Martino , Giuseppe Nicosia , Varun Ojha

Dynamic adaptation in single-neuron response plays a fundamental role in neural coding in biological neural networks. Yet, most neural activation functions used in artificial networks are fixed and mostly considered as an inconsequential…

Machine Learning · Computer Science 2020-06-23 Victor Geadah , Giancarlo Kerg , Stefan Horoi , Guy Wolf , Guillaume Lajoie

Reinforcement Learning (RL) has achieved remarkable success in sequential decision tasks. However, recent studies have revealed the vulnerability of RL policies to different perturbations, raising concerns about their effectiveness and…

Machine Learning · Computer Science 2025-07-08 Buqing Nie , Yangqing Fu , Jingtian Ji , Yue Gao

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of…

Statistics Theory · Mathematics 2020-09-15 Johannes Schmidt-Hieber

In contemporary large language models (LLMs), the swish-gated linear unit (SwiGLU) activation function is widely adopted to regulate the information flow and introduce non-linearity. For large positive inputs, SwiGLU approximates the…

Computation and Language · Computer Science 2026-05-26 Peijie Jiang , Yuqi Feng , Cunyin Peng , Qian Zhao , Jia Liu , KunLong Chen , Zhiqiang Zhang , Jun Zhou

Deep learning training training algorithms are a huge success in recent years in many fields including speech, text,image video etc. Deeper and deeper layers are proposed with huge success with resnet structures having around 152 layers.…

Machine Learning · Computer Science 2024-02-20 Chinmay Rane , Kanishka Tyagi , Michael Manry

Deep neural networks are susceptible to adversarial attacks due to the accumulation of perturbations in the feature level, and numerous works have boosted model robustness by deactivating the non-robust feature activations that cause model…

Computer Vision and Pattern Recognition · Computer Science 2023-03-27 Woo Jae Kim , Yoonki Cho , Junsik Jung , Sung-Eui Yoon

As deep neural networks (DNNs) are widely applied in the physical world, many researches are focusing on physical-world adversarial examples (PAEs), which introduce perturbations to inputs and cause the model's incorrect outputs. However,…

Computer Vision and Pattern Recognition · Computer Science 2024-12-24 Yichen Wang , Yuxuan Chou , Ziqi Zhou , Hangtao Zhang , Wei Wan , Shengshan Hu , Minghui Li

The performance of deep models, including Vision Transformers, is known to be vulnerable to adversarial attacks. Many existing defenses against these attacks, such as adversarial training, rely on full-model fine-tuning to induce robustness…

Machine Learning · Computer Science 2025-02-10 Masih Eskandar , Tooba Imtiaz , Zifeng Wang , Jennifer Dy

Adversarially robust models are locally smooth around each data sample so that small perturbations cannot drastically change model outputs. In modern systems, such smoothness is usually obtained via Adversarial Training, which explicitly…

Machine Learning · Computer Science 2024-10-01 Adrián Rodríguez-Muñoz , Tongzhou Wang , Antonio Torralba

Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the…

Machine Learning · Computer Science 2020-04-28 Yuanhao Xiong , Cho-Jui Hsieh

Adversarial training was introduced as a way to improve the robustness of deep learning models to adversarial attacks. This training method improves robustness against adversarial attacks, but increases the models vulnerability to privacy…

The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often…

Machine Learning · Computer Science 2026-02-10 Taeyoung Kim , Myungjoo Kang

Although Deep Neural Networks (DNNs) achieve excellent performance on many real-world tasks, they are highly vulnerable to adversarial attacks. A leading defense against such attacks is adversarial training, a technique in which a DNN is…

Computer Vision and Pattern Recognition · Computer Science 2021-11-29 Gilad Cohen , Raja Giryes

Despite the empirical success of DNN, their internal training dynamics remain difficult to characterize. In ReLU-based models, the activation pattern induced by a given input determines the piecewise-linear region in which the network…

In recent years, the gap between Deep Learning (DL) methods and analytical or numerical approaches in scientific computing is tried to be filled by the evolution of Physics-Informed Neural Networks (PINNs). However, still, there are many…

Machine Learning · Computer Science 2024-08-16 Jassem Abbasi , Pål Østebø Andersen