Posterior Frequencies and the Cost of Not Fitting: A Correction to a Memorization Lower Bound
Feldman's memorization lower bound assigns a frequency coefficient based on how often a point appears in the training sample. We give an exact three-point counterexample to its conditional and averaged forms, using independent fair labels and a permutation-equivariant learner. A sequence of sampling priors makes the ratio of the proposed penalty to actual excess risk grow exponentially, ruling out a universal positive constant-factor repair. The priors vary with sample size, the offending profiles become rare, and both quantities vanish. Retaining the original model, we obtain an exact replacement using full-sample posterior probabilities. Under exchangeability, these depend on multiplici...
| Authors | Zhenisbek Assylbekov, Rustem Takhanov |
|---|---|
| Primary category | stat.ML |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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