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We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both…

Machine Learning · Computer Science 2010-02-25 Huan Xu , Constantine Caramanis , Shie Mannor

Post-training quantization (PTQ) is an effective approach for deploying large language models (LLMs) under memory and latency constraints. Most existing PTQ methods determine quantization parameters by minimizing a layer-wise reconstruction…

Artificial Intelligence · Computer Science 2026-05-11 Yanlong Zhao , Xiaoyuan Cheng , Huihang Liu , Baihua He , Xinyu Zhang , Harrison Bo Hua Zhu , Wenlong Chen , Li Zeng , Zhuo Sun

Adversarial examples pose a security risk as they can alter decisions of a machine learning classifier through slight input perturbations. Certified robustness has been proposed as a mitigation where given an input $\mathbf{x}$, a…

Cryptography and Security · Computer Science 2024-09-10 Jiankai Jin , Olga Ohrimenko , Benjamin I. P. Rubinstein

In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…

Quantum Physics · Physics 2026-02-17 Viacheslav Kuzmin , Wilfrid Somogyi , Ekaterina Pankovets , Alexey Melnikov

Adversarial data examples have drawn significant attention from the machine learning and security communities. A line of work on tackling adversarial examples is certified robustness via randomized smoothing that can provide a theoretical…

Machine Learning · Computer Science 2021-08-24 Haowen Lin , Jian Lou , Li Xiong , Cyrus Shahabi

In this paper, we consider a generic probabilistic discriminative learner from the functional viewpoint and argue that, to make it learn well, it is necessary to constrain its hypothesis space to a set of non-trivial piecewise constant…

Machine Learning · Statistics 2018-06-05 Yi-Qing Wang

Although deep Neural Networks (DNNs) have achieved tremendous success in audio classification tasks, their uncertainty calibration are still under-explored. A well-calibrated model should be accurate when it is certain about its prediction…

Sound · Computer Science 2022-06-28 Tong Ye , Shijing Si , Jianzong Wang , Ning Cheng , Jing Xiao

Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their…

Machine Learning · Computer Science 2025-02-05 Jiaqi Yang , Wei Xie , Xiaohua Xu

Randomized smoothing has become a leading method for achieving certified robustness in deep classifiers against l_{p}-norm adversarial perturbations. Current approaches for achieving certified robustness, such as data augmentation with…

Machine Learning · Computer Science 2024-05-28 Jieren Deng , Hanbin Hong , Aaron Palmer , Xin Zhou , Jinbo Bi , Kaleel Mahmood , Yuan Hong , Derek Aguiar

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for…

Machine Learning · Computer Science 2020-06-22 Jingfeng Wu , Wenqing Hu , Haoyi Xiong , Jun Huan , Vladimir Braverman , Zhanxing Zhu

A range of defense methods have been proposed to improve the robustness of neural networks on adversarial examples, among which provable defense methods have been demonstrated to be effective to train neural networks that are certifiably…

Machine Learning · Computer Science 2021-01-21 Mengting Xu , Tao Zhang , Zhongnian Li , Daoqiang Zhang

Robustness verification of neural networks, referring to formally proving that neural networks satisfy robustness properties, is of crucial importance in safety-critical applications, where model failures can result in loss of human life or…

Machine Learning · Computer Science 2026-04-06 Minh Le , Phuong Cao

The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied…

Machine Learning · Statistics 2019-03-08 Yi Zhou , Yingbin Liang , Huishuai Zhang

Randomized smoothing has emerged as a potent certifiable defense against adversarial attacks by employing smoothing noises from specific distributions to ensure the robustness of a smoothed classifier. However, the utilization of Monte…

Machine Learning · Computer Science 2025-04-01 Devansh Bhardwaj , Kshitiz Kaushik , Sarthak Gupta

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization,…

Machine Learning · Computer Science 2017-07-07 Behnam Neyshabur , Srinadh Bhojanapalli , David McAllester , Nathan Srebro

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…

One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…

Machine Learning · Computer Science 2017-10-20 Gintare Karolina Dziugaite , Daniel M. Roy

Randomized smoothing (RS) is an effective and scalable technique for constructing neural network classifiers that are certifiably robust to adversarial perturbations. Most RS works focus on training a good base model that boosts the…

Machine Learning · Computer Science 2021-09-20 Chen Chen , Kezhi Kong , Peihong Yu , Juan Luque , Tom Goldstein , Furong Huang

Overconfidence has been shown to impair generalization and calibration of a neural network. Previous studies remedy this issue by adding a regularization term to a loss function, preventing a model from making a peaked distribution. Label…

Machine Learning · Computer Science 2022-10-26 Dongkyu Lee , Ka Chun Cheung , Nevin L. Zhang

For supervised learning models, the analysis of generalization ability (generalizability) is vital because the generalizability expresses how well a model will perform on unseen data. Traditional generalization methods, such as the VC…

Machine Learning · Computer Science 2021-03-01 Shuyue Guan , Murray Loew