Sampling-aware weight refinement: Skipping output-weight reads during nucleus sampling

Autoregressive decoding usually evaluates every row of the output projection before sampling one token. This study tests whether a compressed scan can identify which original rows need to be read. An INT8 approximation gives logit intervals from row-wise quantization residuals. The GPU recomputes rows that could win a fixed Gumbel race using original BF16 weights and FP32 accumulation. Bounds on probability mass then test whether the winner belongs to the top-p nucleus. When membership cannot be certified, the decoder computes the dense result with the same random perturbations. The transformer is unchanged. Tests on one Apple M5 Pro cover SmolLM2-135M and Qwen2.5-0.5B/1.5B. A confirmation on six public PG-19 books uses 128-, 2048- and 8192-token inputs with 128-token continuations, temperature 0.7 and top-p 0.9. Median paired decode speed ratios against the matched dense reference are 1.064x for Qwen 0.5B and 1.044x for Qwen 1.5B. All 4608 checked choices and 108 paired sequences match. The paper also reports a native BF16 output-head comparison, the earlier SmolLM slowdown and high-temperature regressions. The paper derives sharp membership bounds over an independent interval box and an expected logical-payload identity. The measured benefit is small and depends on the model and sampling settings. Tests use batch size one and small models on a single machine. Floating-point safety for all inputs and priority for the tested combination remain unresolved. The evidence archive contains source, frozen protocols, raw results, earlier failed approaches, analysis and restoration scripts for pinned public assets. No private corpus was used. OpenAI Codex assisted with method development, proofs, implementation, experiments, literature comparison, analysis and writing. The work has not been peer reviewed or independently reproduced. The original material is released under CC BY 4.0; third-party dependencies retain their own licenses.