Deep Neural Networks via Complex Network Theory: a Perspective

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: La Malfa, Emanuele, La Malfa, Gabriele, Nicosia, Giuseppe, Latora, Vito
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911844758716416
author La Malfa, Emanuele
La Malfa, Gabriele
Nicosia, Giuseppe
Latora, Vito
author_facet La Malfa, Emanuele
La Malfa, Gabriele
Nicosia, Giuseppe
Latora, Vito
contents Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for interpreting neural networks by analysing their weights and neuron structures. However, classic works adapt CNT metrics that only permit a topological analysis as they do not account for the effect of the input data. In addition, CNT metrics have been applied to a limited range of architectures, mainly including Fully Connected neural networks. In this work, we extend the existing CNT metrics with measures that sample from the DNNs' training distribution, shifting from a purely topological analysis to one that connects with the interpretability of deep learning. For the novel metrics, in addition to the existing ones, we provide a mathematical formalisation for Fully Connected, AutoEncoder, Convolutional and Recurrent neural networks, of which we vary the activation functions and the number of hidden layers. We show that these metrics differentiate DNNs based on the architecture, the number of hidden layers, and the activation function. Our contribution provides a method rooted in physics for interpreting DNNs that offers insights beyond the traditional input-output relationship and the CNT topological analysis.
format Preprint
id arxiv_https___arxiv_org_abs_2404_11172
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Deep Neural Networks via Complex Network Theory: a Perspective
La Malfa, Emanuele
La Malfa, Gabriele
Nicosia, Giuseppe
Latora, Vito
Machine Learning
Artificial Intelligence
Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for interpreting neural networks by analysing their weights and neuron structures. However, classic works adapt CNT metrics that only permit a topological analysis as they do not account for the effect of the input data. In addition, CNT metrics have been applied to a limited range of architectures, mainly including Fully Connected neural networks. In this work, we extend the existing CNT metrics with measures that sample from the DNNs' training distribution, shifting from a purely topological analysis to one that connects with the interpretability of deep learning. For the novel metrics, in addition to the existing ones, we provide a mathematical formalisation for Fully Connected, AutoEncoder, Convolutional and Recurrent neural networks, of which we vary the activation functions and the number of hidden layers. We show that these metrics differentiate DNNs based on the architecture, the number of hidden layers, and the activation function. Our contribution provides a method rooted in physics for interpreting DNNs that offers insights beyond the traditional input-output relationship and the CNT topological analysis.
title Deep Neural Networks via Complex Network Theory: a Perspective
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2404.11172