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OAC: Output-adaptive Calibration for Accurate Post-training Quantization
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Proposes Output-adaptive Calibration (OAC), which builds PTQ Hessians from gradients of the output cross-entropy loss (Fisher approximation) instead of layer-wise l2 error, improving 2-bit and binary LLM quantization over SpQR and BiLLM.
Problem
Post-training quantization of LLMs usually minimizes a layer-wise l2 output error, ignoring the effect on the model's final output, which causes accuracy drops at extreme low precision (2-bit and binary).
Approach
Replace the layer-wise l2 Hessian with an output-adaptive Hessian derived from the cross-entropy loss, approximated via the Fisher information identity as the sum of per-sample gradient outer products G^T G, with cross-layer and cross-row independence assumptions and row-Hessian aggregation to reduce memory; plug it into SpQR (2-bit) and BiLLM (binary) calibration.
Key results
- On 2-bit LLaMA2-7B, OAC reaches WikiText2 perplexity 9.48 vs 11.09 for SpQR at 2.09 average bits.
- On binarized LLaMA2-13B (1.08 bits), OAC reduces WikiText2 perplexity from 18.54 (BiLLM) to 13.15 and raises average reasoning score from 37.01 to 42.42.
- Across seeds on 2-bit OPT-13B, OAC outperforms SpQR on WikiText2 (13.39±0.09 vs 13.47±0.07), a small margin.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa2-7B 2-bit PTQ · LLaMa2-7B, 2-bit | C4 perplexity: 13.22 -> 11.9 | Helped |
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa2-7B 2-bit PTQ · LLaMa2-7B, 2-bit | WikiText2 perplexity: 11.09 -> 9.48 | Helped |
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa2-7B 2-bit PTQ · LLaMa2-7B, 2-bit | LMEH average score: 42.90 -> 45.56 | Helped |
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa2-13B 2-bit PTQ · LLaMa2-13B, 2-bit | WikiText2 perplexity: 7.58 -> 7.39 | Helped |
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa-13B binary PTQ · LLaMa-13B, binary | C4 perplexity: 14.93 -> 15.17 | Hurt |
| Replace output-agnostic calibration with output-adaptive calibration | LLaMa-13B binary PTQ · LLaMa-13B, binary | Average reasoning score: 42.65 -> 44.31 | Helped |
| Use FP16 rather than FP32 gradient computations (ablation) | OAC on LLaMa-7B · LLaMa-7B, 2-bit | WikiText2 perplexity: 9.57 -> 9.40$_{\pm 0.07}$ | Helped |
| Use FP16 rather than FP32 gradient computations (ablation) | OAC on LLaMa-13B · LLaMa-13B, 2-bit | WikiText2 perplexity: 7.45 -> 7.50$_{\pm 0.04}$ | Hurt |
| Skip division by N when reducing the Hessian (ablation) | OAC on LLaMa-13B · LLaMa-13B, 2-bit | WikiText2 perplexity: 7.58 -> 7.45 | Helped |
Surprising findings
- On LLaMA-13B binary, BiLLM slightly beats OAC on C4 perplexity (14.93 vs 15.17).
- SpQR collapses under binarization (e.g., LLaMA-7B WikiText2 perplexity 1.7e5), showing it is not designed for binary PTQ.
Limitations
- OAC needs gradient computation over calibration data, requiring more time and memory than response-agnostic baselines (e.g., 8h50m and 146 GB for LLaMA-13B vs 1h37m and 5.6 GB for SpQR).
- Relies on independence assumptions (cross-layer, cross-row) and aggregating row Hessians as an upper bound, which are approximations.
- Experiments limited to single seed for most results due to computational cost.
Experimental setup
Datasets: C4 RedPajama WikiText2
Benchmarks: WikiText2 C4 PTB WinoGrande PiQA HellaSwag ARC-easy ARC-challenge GSM8K
Metrics: perplexity zero-shot accuracy exact match
Baselines: RTN OPTQ QuIP SpQR OmniQuant SqueezeLLM BiLLM
Builds on: SpQR BiLLM OPTQ
Closest papers by meaning
- Exploring Post-training Quantization in LLMs from Comprehensive Study to Low Rank Compensation (AAAI 2024 · similarity 0.90)
- ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals (ICML 2025 · similarity 0.89)
- CBQ: Cross-Block Quantization for Large Language Models (ICLR 2025 · similarity 0.89)
- Norm Tweaking: High-Performance Low-Bit Quantization of Large Language Models (AAAI 2024 · similarity 0.88)
- Coverage-Based Calibration for Post-Training Quantization via Weighted Maximum Coverage over Outlier Channels (NeurIPS 2026 · similarity 0.88)
- QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Language Models (ICLR 2024 · similarity 0.88)
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