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[Submitted on 20 Aug 2026] Title:Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation View a PDF of the paper titled Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation, by Venkata Subbaiah Yerrapati and 2 other authors View PDF HTML (experimental) 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 this https URL Subjects: Machine Learning (cs.LG); Commutative Algebra (math.AC) MSC classes: 13P25, 68T07 Cite as: arXiv:2609.30279 [cs.LG] (or arXiv:2609.30279v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.30279 arXiv-issued DOI via DataCite Submission history From: Venkata Subbaiah Yerrapati [view email] [v1] Thu, 20 Aug 2026 03:51:23 UTC (3,740 KB) Full-text links: Access Paper: View a PDF of the paper titled Neural Ideals and Neural Codes: An Algebraic Framework for Neural Network Classification and Feature Interpretation, by Venkata Subbaiah Yerrapati and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs math math.AC References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)