{"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/newton-puiseux-analysis-for-interpretability","title":"Newton-Puiseux Analysis for Interpretability and Calibration of Complex-Valued Neural Networks","arxiv_id":"2504.19176","date":"2025-04-27","proceeding":null,"authors":["Piotr Migus"],"abstract":"Complex-valued neural networks (CVNNs) excel where phase matters, yet their multi-sheeted decision surfaces defy standard explainability and calibration tools. We propose a \\emph{Newton-Puiseux} framework that fits a local polynomial surrogate to a high-uncertainty input and analytically decomposes this surrogate into fractional-power series. The resulting Puiseux expansions, dominant Puiseux coefficients, and phase-aligned curvature descriptors deliver closed-form estimates of robustness and over-confidence that gradient - or perturbation-based methods (saliency, LIME, SHAP) cannot provide. On a controlled $\\mathbb{C}^2$ helix the surrogate attains RMSE $< 0.09$ while recovering the number of decision sheets; quartic coefficients predict adversarial flip radii within $10^{-3}$. On the real-world MIT-BIH arrhythmia corpus, Puiseux-guided, phase-aware temperature scaling lowers expected calibration error from 0.087 to 0.034, contributing to the advancement of CVNNs. Full code, pre-trained weights, and scripts are at https://github.com/piotrmgs/puiseux-cvnn.","url_abs":"https://arxiv.org/abs/2504.19176v1","url_pdf":"https://arxiv.org/pdf/2504.19176v1.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":"newton-puiseux-analysis-for-interpretability","repo_url":"https://github.com/piotrmgs/puiseux-cvnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"flip","method_name":"FLIP"},{"method_slug":"lime","method_name":"LIME"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}