Canonicalization Leakage: How Canonical Representatives Confound Supervised Learning under Group Symmetry

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.