WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessians

The paper introduces WaterKron, a method that integrates two-sided GPTQ with row- and column-dependent waterfilling scales and entropy coding for post‑training quantization. It derives a high‑rate distortion measure relative to the full Hessian, introducing a Kronecker‑Hessian mismatch factor Φ that quantifies the distortion penalty of using a Kronecker approximation. Minimizing Φ leads to a Gaussian covariance‑fitting problem solved via classical flip‑flop updates, yielding a FlipFlop Hessian that empirically improves KL divergence and perplexity compared to other Hessian choices.

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