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Understanding implicit bias of gradient descent for generalization capability of ReLU networks has been an important research topic in machine learning research. Unfortunately, even for a single ReLU neuron trained with the square loss, it…

Machine Learning · Computer Science 2022-06-14 Sangmin Lee , Byeongsu Sim , Jong Chul Ye

The nonlinearity of activation functions used in deep learning models are crucial for the success of predictive models. There are several commonly used simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU…

Machine Learning · Computer Science 2020-10-16 Nalinda Kulathunga , Nishath Rajiv Ranasinghe , Daniel Vrinceanu , Zackary Kinsman , Lei Huang , Yunjiao Wang

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

Machine Learning · Computer Science 2025-06-25 Daan Huybrechs

The hidden state threat model of differential privacy (DP) assumes that the adversary has access only to the final trained machine learning (ML) model, without seeing intermediate states during training. However, the current privacy…

Machine Learning · Computer Science 2025-05-27 Rob Romijnders , Antti Koskela

Large language models (LLMs) do not preserve privacy at inference-time. The LLM's outputs can inadvertently reveal information about the model's context, which presents a privacy challenge when the LLM is augmented via tools or databases…

Computation and Language · Computer Science 2026-02-03 Rushil Thareja , Preslav Nakov , Praneeth Vepakomma , Nils Lukas

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

Artificial Intelligence · Computer Science 2017-05-22 Guy Katz , Clark Barrett , David Dill , Kyle Julian , Mykel Kochenderfer

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to…

Machine Learning · Computer Science 2023-03-28 Hong Jun Jeon , Yifan Zhu , Benjamin Van Roy

Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the…

Machine Learning · Statistics 2019-05-01 Gang Wang , Georgios B. Giannakis , Jie Chen

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 introduce the "inverse square root linear unit" (ISRLU) to speed up learning in deep neural networks. ISRLU has better performance than ELU but has many of the same benefits. ISRLU and ELU have similar curves and characteristics. Both…

Machine Learning · Computer Science 2017-11-13 Brad Carlile , Guy Delamarter , Paul Kinney , Akiko Marti , Brian Whitney

We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to…

Optimization and Control · Mathematics 2022-01-10 Bjarne Grimstad , Henrik Andersson

For most state-of-the-art architectures, Rectified Linear Unit (ReLU) becomes a standard component accompanied with each layer. Although ReLU can ease the network training to an extent, the character of blocking negative values may suppress…

Computer Vision and Pattern Recognition · Computer Science 2017-11-20 Xuanyi Dong , Guoliang Kang , Kun Zhan , Yi Yang

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive…

Machine Learning · Computer Science 2025-01-10 Nandan Kumar Jha , Brandon Reagen

We present SEALion: an extensible framework for privacy-preserving machine learning with homomorphic encryption. It allows one to learn deep neural networks that can be seamlessly utilized for prediction on encrypted data. The framework…

Machine Learning · Computer Science 2019-04-30 Tim van Elsloo , Giorgio Patrini , Hamish Ivey-Law

Rectified Linear Units (ReLU) seem to have displaced traditional 'smooth' nonlinearities as activation-function-du-jour in many - but not all - deep neural network (DNN) applications. However, nobody seems to know why. In this article, we…

Machine Learning · Computer Science 2015-09-18 Andrew J. R. Simpson

Rectifier neuron units (ReLUs) have been widely used in deep convolutional networks. An ReLU converts negative values to zeros, and does not change positive values, which leads to a high sparsity of neurons. In this work, we first examine…

Computer Vision and Pattern Recognition · Computer Science 2017-05-16 Shaohuai Shi , Xiaowen Chu

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

Billions of dollars and countless GPU hours are currently spent on training Deep Neural Networks (DNNs) for a variety of tasks. Thus, it is essential to determine the difficulty of extracting all the parameters of such neural networks when…

The growing adoption of machine learning in sensitive areas such as healthcare and defense introduces significant privacy and security challenges. These domains demand robust data protection, as models depend on large volumes of sensitive…

Cryptography and Security · Computer Science 2025-08-18 Nges Brian Njungle , Michel A. Kinsy

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Machine Learning · Computer Science 2025-11-11 Longqing Ye
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