发表机构
S. V. National Institute of Technology（S. V. 国立理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个代数框架，通过神经理想分析神经网络分类问题，并开发算法与交互软件以识别和解释各隐藏层神经元捕获的特征，在MNIST数据集上验证了其有效性。
AI 中文摘要
理解神经网络隐藏层所捕获的特征是机器学习中的一个基本挑战，尽管神经网络在各种分类问题中取得了广泛成功。在这项工作中，我们提出了一个用于研究建模分类问题的神经网络的代数框架。首先建立了若干结果，例如神经网络与神经理想之间的对应关系、计算神经理想的算法，以及一个能够近似神经理想的稳定化定理。作为该框架的一个应用，我们提出了用于识别和解释每个隐藏层神经元所捕获特征的算法。伴随这些理论发展，我们在MNIST手写数字数据集上展示了实际性能，结果凸显了神经理想作为分析和理解神经网络所捕获特征的数学与计算工具的关键作用。此外，我们开发了一个交互式软件，该软件基于所提出的框架来可视化每个神经元所捕获的特征。该工具可在以下网址获取：此https URL
英文摘要
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
