Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation
Abstract
Understanding the features captured by the hidden layers of neural networks is a fundamental challenge in machine learning, despite their widespread success across various classification problems. In this work, we propose an algebraic framework for examining neural networks that model classification problems. Certain results, such as the correspondence between the neural network and neural ideals, algorithms for computing the neural ideals, and a stabilization theorem that enables approximation of the neural ideals, are first established. As an application to the framework, we present algorithms to identify and interpret the features captured by each hidden-layer neuron. Along with these theoretical developments, the practical performance has been demonstrated on the MNIST digit dataset, and the results highlight the pivotal role of neural ideals as a mathematical and computational tool for analyzing the features captured by neural networks. Further, we develop an interactive software that builds on the presented framework to visualize the features captured by each neuron. This tool is available at https://github.com/yvs1967/neural-network-representation-explorer
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BibTeX
@misc{yerrapati2026neural,
title = {{Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation}},
author = {Venkata Subbaiah Yerrapati and Rahul Dixit and Ajay Kumar Shukla},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30279},
eprint = {2609.30279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30279},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation
AU - Venkata Subbaiah Yerrapati
AU - Rahul Dixit
AU - Ajay Kumar Shukla
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.30279
UR - https://arxiv.org/abs/2609.30279
AB - Understanding the features captured by the hidden layers of neural networks is a fundamental challenge in machine learning, despite their widespread success across various classification problems. In this work, we propose an algebraic framework for examining neural networks that model classification problems. Certain results, such as the correspondence between the neural network and neural ideals, algorithms for computing the neural ideals, and a stabilization theorem that enables approximation of the neural ideals, are first established. As an application to the framework, we present algorithms to identify and interpret the features captured by each hidden-layer neuron. Along with these theoretical developments, the practical performance has been demonstrated on the MNIST digit dataset, and the results highlight the pivotal role of neural ideals as a mathematical and computational tool for analyzing the features captured by neural networks. Further, we develop an interactive software that builds on the presented framework to visualize the features captured by each neuron. This tool is available at https://github.com/yvs1967/neural-network-representation-explorer
ER -