Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape

A self-hosted assistant is too expensive because its model uses most of the GPU memory.

What you would change

Try the paper's supported lower-precision weights on a copy of your serving setup.

Try the paper's supported lower-precision weights on a copy of your serving setup.

Compare against

The same model at its original precision, on the same GPU.

1. Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.
2. Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.
3. Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.
4. Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test.

What to measure

Peak memory, task pass rate, latency, and total serving cost at the same context and load.

When to keep it

Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation.

recommendation

test

research area

quantization

technical change

Closed-form scale selection for GPTQ quantization

published

2026-09-29

The reader running GPTQ on a single 24 GB GPU can adopt this without extra hardware, but because the method fails at 2 bits and depends on Hadamard preprocessing, it should be validated on their specific models and target bit-width before production use.

1. claim 01Paperraft inference
   Read the brief interpretation

   This replaces the max-based or grid-searched scale selection in GPTQ-family post-training quantization with a closed-form Gaussian-optimal scale derived from a proved limit of the quantization error landscape, combined with Hadamard incoherence preprocessing. The cost is modest: a Hadamard transform per layer and the Gaussian-optimal scale computation, which removes the per-layer scale search but adds preprocessing complexity to the quantization pipeline. It can fail on raw weights without incoherence processing, where the Gaussian-optimal scale underperforms, and it remains clearly worse than searched rules at 2 bits, so it does not solve the extreme low-bit regime.

   This is a Paperraft inference. It is not pinned to a verified PDF passage.

   Inspect the source
2. claim 02Paperraft inference

   The Gaussian-optimal scale, applied after Hadamard incoherence processing, matches the best grid-searched scale rule at 3 bits and above without any search; scale-rule choice changes perplexity substantially at 2–3 bits and negligibly from 6 bits on. No multiplicative perplexity factor is reported.

   This is a Paperraft inference. It is not pinned to a verified PDF passage.

   Inspect the source