{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/closed-form-interpretation-of-neural-network","title":"Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients","arxiv_id":"2401.04978","date":"2024-01-10","proceeding":null,"authors":["Sebastian Johann Wetzel"],"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.","url_abs":"https://arxiv.org/abs/2401.04978v2","url_pdf":"https://arxiv.org/pdf/2401.04978v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"closed-form-interpretation-of-neural-network","repo_url":"https://github.com/sjwetzel/publicsymbolicnninterpretation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"form","task_name":"Form"},{"task_slug":"symbolic-regression","task_name":"Symbolic Regression"},{"task_slug":"regression-1","task_name":"regression"},{"task_slug":"scientific-discovery","task_name":"scientific discovery"}],"methods":[{"method_slug":"base","method_name":"BASE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2401.04978","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}