Cosine-Scheduled Parameter EMA Does Not Stabilize Raw Calibration in Small Noisy Classifiers

Parameter averaging is often used as a cheap way to smooth stochastic optimization trajectories, and a natural hypothesis is that the averaging horizon should grow as a cosine learning-rate schedule decays. We evaluate this hypothesis for small supervised classifiers under symmetric training-label noise. The proposed readout is a deterministic cosine-scheduled exponential moving average of parameters, compared under matched seeds with the final iterate, fixed-coefficient EMAs, and uniform tail Polyak averages. The executed study covers Gaussian blobs, two moons, handwritten digits, and breast-cancer classification, with 20 deterministic seeds per dataset and noise level, clean validation and test labels, and raw plus temperature-scaled probability metrics. The main result is negative: in the preregistered two-hidden-layer MLP condition, cosine-scheduled EMA achieved 0 of 4 dataset-level primary successes against the strongest non-scheduled averaging baseline on raw top-label ECE. Raw ECE was worse for cosine-scheduled EMA on all four datasets, even though test NLL and accuracy often improved. The algebraic filter properties of the schedule were verified, and the readout reduced late validation-NLL variance relative to a fixed EMA with coefficient 0.999, but sharpness and path-movement diagnostics did not support a broad smoothing explanation. These findings reject the headline calibration-stability claim for the tested small-classifier regime while preserving a narrower conclusion: schedule-coupled averaging is a valid convex readout with useful loss-stability behavior, but raw calibration gains are metric-dependent and cannot be inferred from smoothing alone.