Spectral Unit Tests for Predictive Representation Models: A Fault Atlas and Its Scope Conditions

Predictive representation models are trained and monitored through one scalar loss, which can hide a predictor that loses to the unconditional mean of its targets in some directions. We audit the residual spectrally: whitening its second moment against the target covariance makes any generalized eigenvalue above one a certificate of regret against the mean; a covariance ceiling attributes that regret to the predictor, not to irreducible noise. A LayerNorm-aware rank bound predicts the unit-eigenvalue plateau a normalized affine head forces; five public checkpoints saturate it, and excising it makes the spectrum interpretable. On the official I-JEPA head the scalar and the spectrum disagree: its NMSE is below that of a ridge head refit on the audit data, yet its plateau-excluded regret mass is 2.2 times that of the ridge head, a gap that official-loss refits narrow by only 4-10%. A calibrated gate fires at full power on a five percent rise in scalar error for rank, bias and noise faults, and reaches faults confined to low-variance directions, which no calibrated NMSE gate reaches on this source budget. NMSE-matched injected faults leave distinct spectral signatures consistent with the theory's bounds, and rules fit on one checkpoint transfer blind to two others under conditions we state and measure. The audit also caught the HuggingFace I-JEPA export carrying the online encoder rather than the EMA target.