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arXiv · 2401.04978

Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients

Sebastian Johann Wetzel
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Abstract

I introduce a unified framework for finding a closed-form interpretation of any single neuron in an artificial neural network. Using this framework I demonstrate how to interpret neural network classifiers to reveal closed-form expressions of the concepts encoded in their decision boundaries. In contrast to neural network-based regression, for classification, it is in general impossible to express the neural network in the form of a symbolic equation even if the neural network itself bases its classification on a quantity that can be written as a closed-form equation. The interpretation framework is based on embedding trained neural networks into an equivalence class of functions that encode the same concept. I interpret these neural networks by finding an intersection between the equivalence class and human-readable equations defined by a symbolic search space. The approach is not limited to classifiers or full neural networks and can be applied to arbitrary neurons in hidden layers or latent spaces.

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Sebastian Johann Wetzel. 2024-01-10. Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients. https://arxiv.org/abs/2401.04978

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