Improve the layerwise probabilistic quantization-error bounds

Improve the layerwise probabilistic bounds for quantization error in mixed-precision post-training quantization, with the aim of obtaining tighter or otherwise stronger theoretical guarantees than those established by the current layerwise analysis.

Background

The paper derives probabilistic bounds that separate quantization error propagated from preceding layers from the local perturbation introduced at each layer. These bounds support the proposed local sensitivity score and greedy bit-width allocation method, but the discussion identifies their improvement as an unresolved theoretical issue.

The open problem is explicitly framed as a theoretical direction for future work and concerns the quality of the layerwise probabilistic guarantees themselves, rather than the empirical performance of the allocation algorithm.