{"paper":{"title":"Learning High-Dimensional Parity Functions with Product Networks using Gradient Descent","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"France), France (2) T\\'el\\'ecom Paris, Ghaya Rekaya (2) ((1) Orange Research, Guillaume Larue (1), Hadi Ghauch (2), Institut Polytechnique de Paris, Louis-Adrien Dufr\\`ene (1), Meylan, Palaiseau, Quentin Lampin (1)","submitted_at":"2026-05-27T15:26:16Z","abstract_excerpt":"Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting, standard neural network architectures typically require exponential sample complexity, making gradient-based optimization intractable for large number of inputs $N$. We demonstrate that compact product-based neural architectures combined with stochastic data sparsity (Bernoulli inputs with $p_e \\leq 1/N$) and appropriate hyperparameter choice enable efficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28612","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.28612/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}