Second-order screen predicts quantization mismatch on five language models
Original title: How Far Does Second-Order Linear Response Predict Quantization Mismatch? Pre-Registered Measurements on Five Language Models
On unseen Mistral-7B-v0.3, all six predictions fell in band and vLLM throughput was predicted within 0.4%.
The paper tests whether a Fisher-information screen, using one-half delta transpose F delta, predicts KL divergence caused by post-training quantization. GPU batches cover channel-wise int8, per-tensor fp8 and group-wise int4 on Qwen3-8B, Qwen3-4B, OLMo-2-7B, Qwen3-32B and Qwen3-30B-A3B. Relative predictions hold across perturbation scales, int4 group sizes and rounding modes, while absolute predictions are heavy-tailed. The authors also build a one-pass fp32 Fisher screener with trimmed tensor-block predictions and per-layer format allocation.
- A trimmed average puts 10 of 12 Qwen3-4B and OLMo-2 cells within 15% of measured KL.
- On the MoE model, int8 KL scales as alpha to the 0.63 at small perturbations.
- bf16 per-sequence gradients can cause fourfold prediction errors, removed by fp32 in the lower backward pass.
- Batch-invariant kernels run at 0.55 times throughput; reduction-order changes add 0.17-0.22 nats per sequence.
- Products
- vLLM
From the original article
1 min read at arxiv.orgServing systems choose a weight format for each model and deployment. A low-cost screen predicts the resulting KL divergence from the unquantized model's Fisher information using $\tfrac12Δ^\top FΔ$, the expansion underlying Hessian-aware and second-order post-training quantizers.
By Dezhen Lu · arxiv.org
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