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Normalization layers (e.g., Batch Normalization, Layer Normalization) were introduced to help with optimization difficulties in very deep nets, but they clearly also help generalization, even in not-so-deep nets. Motivated by the long-held…

Machine Learning · Computer Science 2023-01-18 Kaifeng Lyu , Zhiyuan Li , Sanjeev Arora

In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the…

Machine Learning · Computer Science 2019-09-13 Chris Finlay , Jeff Calder , Bilal Abbasi , Adam Oberman

The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be {\it $\epsilon$-adversarially…

Machine Learning · Computer Science 2020-11-17 Yuxin Wen , Shuai Li , Kui Jia

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…

Machine Learning · Computer Science 2018-11-20 Farzan Farnia , Jesse M. Zhang , David Tse

Lifted neural networks (i.e. neural architectures explicitly optimizing over respective network potentials to determine the neural activities) can be combined with a type of adversarial training to gain robustness for internal as well as…

Machine Learning · Computer Science 2025-03-12 Christopher Zach

It has been argued in the past that high-dimensional neural networks do not exhibit local minima capable of trapping an optimisation algorithm. However, the relationship between loss surface modality and the neural architecture parameters,…

Machine Learning · Computer Science 2020-01-31 Anna Sergeevna Bosman , Andries Engelbrecht , Mardé Helbig

Algorithmic stability is an established tool for analyzing generalization. While adversarial training enhances model robustness, it often suffers from robust overfitting and an enlarged generalization gap. Although recent work has…

Machine Learning · Computer Science 2025-09-24 Hesam Hosseini , Ying Cao , Ali H. Sayed

Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of…

Machine Learning · Statistics 2019-10-29 Ryo Karakida , Shotaro Akaho , Shun-ichi Amari

We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the propagation of parameter updates between symmetry-related…

While deep neural networks have achieved remarkable success in various computer vision tasks, they often fail to generalize to new domains and subtle variations of input images. Several defenses have been proposed to improve the robustness…

Computer Vision and Pattern Recognition · Computer Science 2021-09-08 Omid Poursaeed , Tianxing Jiang , Harry Yang , Serge Belongie , SerNam Lim

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

Adversarial training is extensively utilized to improve the adversarial robustness of deep neural networks. Yet, mitigating the degradation of standard generalization performance in adversarial-trained models remains an open problem. This…

Machine Learning · Computer Science 2024-03-27 Xiangyu Yin , Wenjie Ruan

Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{exploration} by encouraging the selection of more stochastic policies. In this work, we analyze this claim…

Machine Learning · Computer Science 2019-06-11 Zafarali Ahmed , Nicolas Le Roux , Mohammad Norouzi , Dale Schuurmans

Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…

Machine Learning · Computer Science 2022-04-25 Nicholas M. Boffi , Stephen Tu , Jean-Jacques E. Slotine

Generative Adversarial Networks (GANs) have shown remarkable performance in image generation. However, GAN training suffers from the problem of instability. One of the main approaches to address this problem is to modify the loss function,…

Machine Learning · Computer Science 2024-03-19 Iu Yahiro , Takashi Ishida , Naoto Yokoya

In adversarial machine learning, there was a common belief that robustness and accuracy hurt each other. The belief was challenged by recent studies where we can maintain the robustness and improve the accuracy. However, the other…

Machine Learning · Computer Science 2021-06-01 Jingfeng Zhang , Jianing Zhu , Gang Niu , Bo Han , Masashi Sugiyama , Mohan Kankanhalli

Classical model-based imaging methods for ultrasound elasticity inverse problem require prior constraints about the underlying elasticity patterns, while finding the appropriate hand-crafted prior for each tissue type is a challenge. In…

Image and Video Processing · Electrical Eng. & Systems 2021-06-16 Narges Mohammadi , Marvin M. Doyley , Mujdat Cetin

Convolutional neural networks are currently the state-of-the-art algorithms for many remote sensing applications such as semantic segmentation or object detection. However, these algorithms are extremely sensitive to over-fitting, domain…

Computer Vision and Pattern Recognition · Computer Science 2021-05-31 Adrien Chan-Hon-Tong , Gaston Lenczner , Aurelien Plyer

Despite their empirical success, neural networks remain vulnerable to small, adversarial perturbations. A longstanding hypothesis suggests that flat minima, regions of low curvature in the loss landscape, offer increased robustness. While…

Machine Learning · Computer Science 2025-10-17 Nils Philipp Walter , Linara Adilova , Jilles Vreeken , Michael Kamp

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

Machine Learning · Computer Science 2024-08-23 Jie Wang , Rui Gao , Yao Xie