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For almost 70 years, researchers have typically selected the width of neural networks' layers either manually or through automated hyperparameter tuning methods such as grid search and, more recently, neural architecture search. This paper…

Machine Learning · Computer Science 2026-02-17 Federico Errica , Henrik Christiansen , Viktor Zaverkin , Mathias Niepert , Francesco Alesiani

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Machine Learning · Computer Science 2023-10-24 Lifu Wang , Tianyu Wang , Shengwei Yi , Bo Shen , Bo Hu , Xing Cao

Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification…

Machine Learning · Computer Science 2016-07-21 Julius , Gopinath Mahale , Sumana T. , C. S. Adityakrishna

Modern deep neural networks exhibit strong generalization even in highly overparameterized regimes. Significant progress has been made to understand this phenomenon in the context of supervised learning, but for unsupervised tasks such as…

Machine Learning · Statistics 2025-06-02 Jonghyun Ham , Maximilian Fleissner , Debarghya Ghoshdastidar

We provide quantitative bounds measuring the $L^2$ difference in function space between the trajectory of a finite-width network trained on finitely many samples from the idealized kernel dynamics of infinite width and infinite data. An…

Machine Learning · Statistics 2022-10-18 Benjamin Bowman , Guido Montufar

Wide neural networks with linear output layer have been shown to be near-linear, and to have near-constant neural tangent kernel (NTK), in a region containing the optimization path of gradient descent. These findings seem counter-intuitive…

Machine Learning · Computer Science 2022-03-11 Chaoyue Liu , Libin Zhu , Mikhail Belkin

This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained…

Machine Learning · Computer Science 2022-12-01 Lénaïc Chizat , Maria Colombo , Xavier Fernández-Real , Alessio Figalli

We develop a variational framework to understand the properties of functions learned by fitting deep neural networks with rectified linear unit activations to data. We propose a new function space, which is reminiscent of classical bounded…

Machine Learning · Statistics 2022-04-18 Rahul Parhi , Robert D. Nowak

To understand the training dynamics of neural networks (NNs), prior studies have considered the infinite-width mean-field (MF) limit of two-layer NN, establishing theoretical guarantees of its convergence under gradient flow training as…

Machine Learning · Computer Science 2022-10-31 Zhengdao Chen , Eric Vanden-Eijnden , Joan Bruna

Deep linear networks have been extensively studied, as they provide simplified models of deep learning. However, little is known in the case of finite-width architectures with multiple outputs and convolutional layers. In this manuscript,…

Machine Learning · Statistics 2025-06-26 Federico Bassetti , Marco Gherardi , Alessandro Ingrosso , Mauro Pastore , Pietro Rotondo

Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…

Machine Learning · Computer Science 2022-11-10 Massimo Fornasier , Timo Klock , Marco Mondelli , Michael Rauchensteiner

Binary neural networks (BNNs), where both weights and activations are binarized into 1 bit, have been widely studied in recent years due to its great benefit of highly accelerated computation and substantially reduced memory footprint that…

Computer Vision and Pattern Recognition · Computer Science 2021-01-01 Zhuo Su , Linpu Fang , Deke Guo , Dewen Hu , Matti Pietikäinen , Li Liu

Recent studies have shown that many important aspects of neural network learning take place within the very earliest iterations or epochs of training. For example, sparse, trainable sub-networks emerge (Frankle et al., 2019), gradient…

Machine Learning · Computer Science 2020-02-25 Jonathan Frankle , David J. Schwab , Ari S. Morcos

Low bit-width weights and activations are an effective way of combating the increasing need for both memory and compute power of Deep Neural Networks. In this work, we present a probabilistic training method for Neural Network with both…

Machine Learning · Computer Science 2018-09-11 Jorn W. T. Peters , Max Welling

Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we…

Machine Learning · Statistics 2022-11-29 Jiayu Yao , Yaniv Yacoby , Beau Coker , Weiwei Pan , Finale Doshi-Velez

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the…

Artificial Intelligence · Computer Science 2016-05-12 Mauro Scanagatta , Giorgio Corani , Cassio P. de Campos , Marco Zaffalon

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…

Machine Learning · Statistics 2023-06-02 Francesco Cagnetta , Alessandro Favero , Matthieu Wyart

For the efficient execution of deep convolutional neural networks (CNN) on edge devices, various approaches have been presented which reduce the bit width of the network parameters down to 1 bit. Binarization of the first layer was always…

Machine Learning · Computer Science 2018-12-11 Robert Dürichen , Thomas Rocznik , Oliver Renz , Christian Peters

In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth. However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore…

Machine Learning · Computer Science 2025-10-17 Max Milkert , David Hyde , Forrest Laine

Biological and artificial neural networks develop internal representations that enable them to perform complex tasks. In artificial networks, the effectiveness of these models relies on their ability to build task specific representation, a…