Learning to Compress: Local Rank and Information Compression in Deep Neural Networks

Fuente: arXiv
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Main Authors: Patel, Niket, Shwartz-Ziv, Ravid
Format: Preprint
Published: 2024
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author Patel, Niket
Shwartz-Ziv, Ravid
author_facet Patel, Niket
Shwartz-Ziv, Ravid
contents Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.
format Preprint
id arxiv_https___arxiv_org_abs_2410_07687
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Learning to Compress: Local Rank and Information Compression in Deep Neural Networks
Patel, Niket
Shwartz-Ziv, Ravid
Machine Learning
Information Theory
Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.
title Learning to Compress: Local Rank and Information Compression in Deep Neural Networks
topic Machine Learning
Information Theory
url https://arxiv.org/abs/2410.07687