规范化泄漏:群对称下的规范代表如何混淆监督学习
Canonicalization Leakage: How Canonical Representatives Confound Supervised Learning under Group Symmetry
研究概述
研究模型利用规范代表中的表示伪迹而非学习不变结构的问题,并提出 CL-DIAG 诊断方法。
原文摘要(英文)
Models trained on canonical representatives of equivalence classes under group symmetry can exploit representation artifacts rather than learning invariant structure. We propose CL-DIAG, a six-step diagnostic protocol that detects, localizes, and quantifies this "canonicalization leakage." Applied to circuit complexity prediction over 616,126 NPN equivalence classes of 5-input Boolean functions (|G| = 7,680), CL-DIAG reveals that a baseline MLP achieves Spearman r_s = 0.788 on canonical data but only r_s = 0.254 when NPN-averaged, with 0% prediction consistency. Signal decomposition shows canonical performance decomposes into classical invariant signal (r_s = 0.635), neural invariant signal (+0.142), and canonicalization leakage (+0.011). NPN augmentation at 7x recovers r_s = 0.777, exceeding the classical invariant ceiling by 14 percentage points. A matched-volume control confirms the gain is from symmetry-consistent augmentation, not generic regularization.