KronQ: Hessian-Based LLM Quantization
UniversityofSouthernCalifornia · hf · 2026-07-13
KronQ is a novel framework for LLM post-training quantization (PTQ) that incorporates gradient covariance into the quantization process, rather than relying solely on input activation statistics.
Key Improvements
- Under the Kronecker-factored Hessian approximation, quantization loss is jointly influenced by activation covariance and gradient covariance.
- Introduces bidirectional incoherence processing: alongside standard input-side random rotations, it leverages gradient covariance to extend into the output dimension, reducing weight magnitude variance in both directions.
- Derives a novel sensitivity metric for mixed-precision layer allocation, determining per-layer quantization precision based on the trace of the gradient and activation Hessians.
Results
In 2-bit weight-only quantization on LLaMA-3-70B, while GPTQ and GPTAQ diverge or suffer severe degradation (WikiText-2 perplexity > 2000), KronQ achieves a 7.93 perplexity.
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