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Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length…

Machine Learning · Statistics 2021-06-24 Boris Hanin , Ryan Jeong , David Rolnick

Neural network pruning has been an essential technique to reduce the computation and memory requirements for using deep neural networks for resource-constrained devices. Most existing research focuses primarily on balancing the sparsity and…

Cryptography and Security · Computer Science 2022-08-05 Xiaoyong Yuan , Lan Zhang

We study what provable privacy attacks can be shown on trained, 2-layer ReLU neural networks. We explore two types of attacks; data reconstruction attacks, and membership inference attacks. We prove that theoretical results on the implicit…

Machine Learning · Computer Science 2025-02-11 Guy Smorodinsky , Gal Vardi , Itay Safran

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…

Machine Learning · Computer Science 2021-04-30 Anirbit Mukherjee

Pre-trained Large Language Models (LLMs) are an integral part of modern AI that have led to breakthrough performances in complex AI tasks. Major AI companies with expensive infrastructures are able to develop and train these large models…

Cryptography and Security · Computer Science 2023-05-02 Rouzbeh Behnia , Mohamamdreza Ebrahimi , Jason Pacheco , Balaji Padmanabhan

Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching…

Machine Learning · Computer Science 2021-08-17 Xue Yang , Yan Feng , Weijun Fang , Jun Shao , Xiaohu Tang , Shu-Tao Xia , Rongxing Lu

Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race…

Machine Learning · Computer Science 2018-11-06 Aditi Raghunathan , Jacob Steinhardt , Percy Liang

With the rise of large language models, service providers offer language models as a service, enabling users to fine-tune customized models via uploaded private datasets. However, this raises concerns about sensitive data leakage. Prior…

Cryptography and Security · Computer Science 2026-01-22 Yi Liu , Weixiang Han , Chengjun Cai , Xingliang Yuan , Cong Wang

We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given…

Machine Learning · Computer Science 2018-10-12 Gauri Jagatap , Chinmay Hegde

We present a new approach for input optimization of ReLU networks that explicitly takes into account the effect of changes in activation patterns. We analyze local optimization steps in both the input space and the space of activation…

Machine Learning · Computer Science 2024-06-04 Hongzhan Yu , Sicun Gao

Replacing non-polynomial functions (e.g., non-linear activation functions such as ReLU) in a neural network with their polynomial approximations is a standard practice in privacy-preserving machine learning. The resulting neural network,…

Machine Learning · Computer Science 2024-06-10 Chi Zhang , Jingjing Fan , Man Ho Au , Siu Ming Yiu

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the…

Machine Learning · Computer Science 2020-10-26 Christian Tjandraatmadja , Ross Anderson , Joey Huchette , Will Ma , Krunal Patel , Juan Pablo Vielma

Pruning of deep neural networks has been an effective technique for reducing model size while preserving most of the performance of dense networks, crucial for deploying models on memory and power-constrained devices. While recent sparse…

Computer Vision and Pattern Recognition · Computer Science 2025-12-02 Andy Li , Aiden Durrant , Milan Markovic , Tianjin Huang , Souvik Kundu , Tianlong Chen , Lu Yin , Georgios Leontidis

It has been demonstrated that very simple attacks can fool highly-sophisticated neural network architectures. In particular, so-called adversarial examples, constructed from perturbations of input data that are small or imperceptible to…

Cryptography and Security · Computer Science 2019-04-09 N. Benjamin Erichson , Zhewei Yao , Michael W. Mahoney

Neural networks with ReLU activation play a key role in modern machine learning. Understanding the functions represented by ReLU networks is a major topic in current research as this enables a better interpretability of learning processes.…

Computational Complexity · Computer Science 2025-06-23 Vincent Froese , Moritz Grillo , Martin Skutella

We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural…

Machine Learning · Computer Science 2020-11-30 Surbhi Goel , Adam Klivans , Pasin Manurangsi , Daniel Reichman

A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural networks. So far, either theoretical or empirical studies on…

Machine Learning · Computer Science 2024-11-25 Feng-Lei Fan , Wei Huang , Xiangru Zhong , Lecheng Ruan , Tieyong Zeng , Huan Xiong , Fei Wang

Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity,…

Machine Learning · Computer Science 2021-05-25 Daniel Alabi

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…

Machine Learning · Computer Science 2026-03-26 Emi Zeger , Mert Pilanci

We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction…

Machine Learning · Computer Science 2017-11-27 Alireza Aghasi , Afshin Abdi , Nam Nguyen , Justin Romberg