Related papers: Wormhole Dynamics in Deep Neural Networks

Deep Neural Networks (DNNs) share important similarities with structural glasses. Both have many degrees of freedom, and their dynamics are governed by a high-dimensional, non-convex landscape representing either the loss or energy,…

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

Recurrent Neural Networks (RNNs) are rich models for the processing of sequential data. Recent work on advancing the state of the art has been focused on the optimization or modelling of RNNs, mostly motivated by adressing the problems of…

Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it…

Analysis of over-parameterized neural networks has drawn significant attention in recentyears. It was shown that such systems behave like convex systems under various restrictedsettings, such as for two-level neural networks, and when…

This paper aims to analyze the generalization power of deep neural networks (DNNs) from the perspective of interactions. Unlike previous analysis of a DNN's generalization power in a highdimensional feature space, we find that the…

Neural networks are often over-parameterized and hence benefit from aggressive regularization. Conventional regularization methods, such as Dropout or weight decay, do not leverage the structures of the network's inputs and hidden states.…

A longstanding problem for Deep Neural Networks (DNNs) is understanding their puzzling ability to generalize well. We approach this problem through the unconventional angle of \textit{cognitive abstraction mechanisms}, drawing inspiration…

Training Deep Neural Networks relies on the model converging on a high-dimensional, non-convex loss landscape toward a good minimum. Yet, much of the phenomenology of training remains ill understood. We focus on three seemingly disparate…

It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning.…

Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about…

Deep neural networks (DNNs) are becoming an integral part of most software systems. Previous work has shown that DNNs have bugs. Unfortunately, existing debugging techniques do not support localizing DNN bugs because of the lack of…

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…

Neural collapse (NC) and its multi-layer variant, deep neural collapse (DNC), describe a structured geometry that occurs in the features and weights of trained deep networks. Recent theoretical work by Sukenik et al. using a deep…

The ability to learn polynomials and generalize out-of-distribution is essential for simulation metamodels in many disciplines of engineering, where the time step updates are described by polynomials. While feed forward neural networks can…

Deep neural networks (DNNs) often suffer from the overconfidence issue, where incorrect predictions are made with high confidence scores, hindering the applications in critical systems. In this paper, we propose a novel approach called…

Neural Collapse is a phenomenon where the last-layer representations of a well-trained neural network converge to a highly structured geometry. In this paper, we focus on its first (and most basic) property, known as NC1: the within-class…

Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also…

Gradient-based meta-learning (GBML) with deep neural nets (DNNs) has become a popular approach for few-shot learning. However, due to the non-convexity of DNNs and the bi-level optimization in GBML, the theoretical properties of GBML with…

Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural…