Excess Spectral Suppression: Why Deep Forecasters Sacrifice Predictable Tail Modes

Deep forecasters are widely reported to over-smooth their targets. Yet any MSE-optimal predictor must discard unpredictable variance, so comparing output spectra with data spectra cannot separate legitimate shrinkage from genuine bias, and no existing definition of that bias is anchored to a Bayes reference. We supply one: excess suppression (ES), the per-mode skill gap to the Bayes reference, measured in the SVD mode space of the target matrix. We measure it on a synthetic family with an analytic Bayes predictor and on eight real benchmarks under a conservative attainable-skill proxy, across rank and time budgets, four intervention families (one applied at inference time), and three zero-shot foundation forecasters. The sacrifice is all-or-nothing: under a tight rank budget, models realize none of the attainable tail skill (median unrealized-to-attainable ratio $1.000$ over all $29$ skill-bearing channels), and tail-ES falls monotonically as the bottleneck widens. The effective rank of the prediction operator is the only axis that tracks the sacrifice across every intervention (Spearman $-0.89$); feature-spectrum entropy dissociates from it. Per-mode loss reweighting closes $31$–$64\%$ of the tail gap while improving overall MSE on all four datasets with attainable tail skill, and the foundation forecasters show tail-ES within $\pm 0.05$ of zero on all eight benchmarks. Tail sacrifice is thus an artifact of narrow budgets and the MSE objective, not of the data: it is measurable, diagnosable at inference time, and correctable in the loss. Code and run outputs are available at https://anonymous.4open.science/r/excess-spectral-suppression-6980.