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Even in recent neural network architectures such as Transformers and Extended LSTM (xLSTM), and traditional ones like Convolutional Neural Networks, Activation Functions are an integral part of nearly all neural networks. They enable more…

Machine Learning · Computer Science 2024-10-01 Matias Roodschild , Jorge Gotay-Sardiñas , Victor A. Jimenez , Adrian Will

Large Language Models (LLMs) inevitably memorize sensitive information during training, posing significant privacy risks. Machine unlearning has emerged as a promising solution to selectively remove such information without full retraining.…

Machine Learning · Computer Science 2026-04-02 Yuze Wang , Yujia Tong , Xuan Liu , Junhao Dong

The full-size MLPs and the projection layers in attention introduce tremendous model sizes of large language models (LLMs), consuming extensive computational resources in pre-training. We empirically observe that the activations of…

Machine Learning · Computer Science 2025-10-03 Ziyue Liu , Ruijie Zhang , Zhengyang Wang , Mingsong Yan , Zi Yang , Paul Hovland , Bogdan Nicolae , Franck Cappello , Sui Tang , Zheng Zhang

Deep artificial neural networks achieve surprising generalization abilities that remain poorly understood. In this paper, we present a new approach to analyzing generalization for deep feed-forward ReLU networks that takes advantage of the…

Machine Learning · Computer Science 2023-07-06 Ramchandran Muthukumar , Jeremias Sulam

Large Language Models (LLMs) often generate inconsistent responses when prompted with semantically equivalent paraphrased inputs. Recently, activation steering, a technique that modulates LLMs' behaviours by adjusting their latent…

Computation and Language · Computer Science 2025-01-23 Jingyuan Yang , Rongjun Li , Weixuan Wang , Ziyu Zhou , Zhiyong Feng , Wei Peng

As the context window expands, self-attention increasingly dominates the transformer's inference time. Therefore, accelerating attention computation while minimizing performance degradation is essential for the efficient deployment of Large…

Computation and Language · Computer Science 2025-03-14 Eli Sason , Darya Frolova , Boris Nazarov , Felix Goldberd

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

Despite the unresolved 'dying ReLU problem', the classical ReLU activation function (AF) has been extensively applied in Deep Neural Networks (DNN), in particular Convolutional Neural Networks (CNN), for image classification. The common…

Machine Learning · Computer Science 2021-04-30 Stamatis Mastromichalakis

We observe an empirical phenomenon in Large Language Models (LLMs) -- very few activations exhibit significantly larger values than others (e.g., 100,000 times larger). We call them massive activations. First, we demonstrate the widespread…

Computation and Language · Computer Science 2024-08-15 Mingjie Sun , Xinlei Chen , J. Zico Kolter , Zhuang Liu

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

Machine Learning · Statistics 2021-10-14 Nicola Picchiotti , Marco Gori

While mobile devices provide ever more compute power, improvements in DRAM bandwidth are much slower. This is unfortunate for large language model (LLM) token generation, which is heavily memory-bound. Previous work has proposed to leverage…

Machine Learning · Computer Science 2025-04-04 Marco Federici , Davide Belli , Mart van Baalen , Amir Jalalirad , Andrii Skliar , Bence Major , Markus Nagel , Paul Whatmough

Large language models (LLMs) have demonstrated remarkable performance and tremendous potential across a wide range of tasks. However, deploying these models has been challenging due to the astronomical amount of model parameters, which…

Machine Learning · Computer Science 2023-12-08 Haihao Shen , Hanwen Chang , Bo Dong , Yu Luo , Hengyu Meng

Recently, neural networks have been widely applied in the power system area. They can be used for better predicting input information and modeling system performance with increased accuracy. In some applications such as battery degradation…

Machine Learning · Computer Science 2025-05-27 Cunzhi Zhao , Fan Jiang , Xingpeng Li

The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most…

Machine Learning · Computer Science 2020-04-14 Garrett Bingham , William Macke , Risto Miikkulainen

This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set $\mathscr{A}$ is defined to encompass the majority of commonly used activation functions, such as…

Machine Learning · Computer Science 2024-02-28 Shijun Zhang , Jianfeng Lu , Hongkai Zhao

Modern large language models (LLMs) have established state-of-the-art performance through architectural improvements, but still require significant computational cost for inference. In an effort to reduce the inference cost, post-training…

Computation and Language · Computer Science 2024-05-24 Jaewoo Yang , Hayun Kim , Younghoon Kim

To enhance the nonlinearity of neural networks and increase their mapping abilities between the inputs and response variables, activation functions play a crucial role to model more complex relationships and patterns in the data. In this…

Computer Vision and Pattern Recognition · Computer Science 2021-12-20 Haigen Hu , Aizhu Liu , Qiu Guan , Xiaoxin Li , Shengyong Chen , Qianwei Zhou

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

Large Language Models (LLMs) herald a transformative era in artificial intelligence (AI). However, the expansive scale of data and parameters of LLMs requires high-demand computational and memory resources, restricting their accessibility…

Machine Learning · Computer Science 2024-11-26 Shengwen Ding , Chenhui Hu

An appropriate choice of the activation function (like ReLU, sigmoid or swish) plays an important role in the performance of (deep) multilayer perceptrons (MLP) for classification and regression learning. Prototype-based classification…

Machine Learning · Computer Science 2019-01-21 Thomas Villmann , John Ravichandran , Andrea Villmann , David Nebel , Marika Kaden