Files
turboquant_plus/docs/papers
TheTomandClaude Opus 4.7 0ca1439b3c [paper] When better reconstruction breaks models — MSE is not a valid proxy for KV cache quantization
Adds the empirical study covering the broader 35-hypothesis investigation
spawned by the EDEN/Mitzenmacher/Portnoy critique (#87, #89). Companion
to eden-optimal-s-revisit.md.

Headline result: a K-cache centroid table that improves per-vector
reconstruction MSE by 1–13% across five model families (Qwen3-0.6B,
Llama-3.2-1B, Mistral-7B, Phi-3-mini, Gemma-2-2b) causes 70–90% mean
KL@D regressions and 50–60% catastrophic-rate failures at the model
output. This is a sign inversion, not a small mismatch: methods that
are strictly better under MSE are systematically worse under KL@D in
deployment.

The paper is structured in three acts:
- Act 1: K cache is sub-Gaussian post-WHT (H8); V is Gaussian
- Act 2: per-prompt fitting fails (PDS), ensemble (ens_4way) reaches an
  irreducible ~8% catastrophic floor at scale (N=100)
- Act 3: the universal-K cross-model counterexample (F3) demonstrates
  the MSE→KL inversion at the cleanest possible level

Includes a 2-D toy attention illustration of the softmax bucket-flip
mechanism, an explicit decision boundary for when MSE proxies quality
(linear consumers) vs when it doesn't (attention softmax), an
ablation summary distinguishing first-order from second-order factors,
operational guidance for practitioners, and a "why this wasn't caught
earlier" diagnosis of the methodology blind spots.

Companion paper handles the algorithmic claim head-on. This paper is
the broader evaluation-methodology critique.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-05 12:00:49 -05:00
..