arXiv subjects

Johann Birnick

Publications and source records attributed to Johann Birnick.

3 recordsLinked to original sources

arXiv2026

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

How should a Kronecker-factored Hessian approximation be chosen for post-training quantization? We address this question through WaterKron, which combines two-sided GPTQ with row- and column-dependent waterfilling scales and entropy coding. We derive its high-rate distortion with respect to the full Hessian using an explicit Kronecker-Hessian mismatch factor $Φ$. This factor quantifies the asymptotic distortion penalty due to the Kronecker Hessian approximation and provides a criterion for selecting the factors optimally. Minimizing $Φ$ leads to a Gaussian covariance-fitting problem with classical ``flip-flop'' updates. We thus give a rate-distortion justification for using the resulting FlipFlop Hessian in quantization. We evaluate it empirically, finding that the FlipFlop Hessian consistently improves KL divergence and perplexity over input-only, marginal, and Frobenius-based Hessian choices.

cs.LG↗

arXiv2026

BaKron: Efficient Quantization with Kronecker-Factored Hessians

We accelerate a family of algorithms for neural network quantization whose geometry is informed by any Kronecker-factored approximation of the Hessian. GPTQ-style adaptive rounding typically uses one-sided information derived from input activations. Two-sided Kronecker-factored Hessian approximations can additionally capture correlations across output coordinates, but applying GPTQ directly in the vectorized weight domain is computationally expensive. Building on the two-sided adaptive-rounding formulation used by BoA and YAQA, we introduce BaKron, an efficient solver that combines anti-diagonal parallelism with a recursive divide-and-conquer construction. For an $m\times n$ weight matrix, BaKron uses $O(m+n)$ sequential steps while reducing the total work from $O(m^2n^2)$ to $O(mn(m+n))$. Thus, it matches the cubic scaling of GPTQ while exploiting richer curvature information. Moreover, BaKron is modular with respect to both the base quantizer and the Hessian estimator. We also provide practical benchmarks, consider a range of Hessians that BaKron can be called with, find an efficient technique to compute these Hessians, and evaluate the algorithm experimentally.

cs.LG↗

arXiv2026

The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm

We explain how data-driven quantization of a linear unit in a neural network corresponds to solving the closest vector problem for a certain lattice generated by input data. We prove that the GPTQ algorithm is equivalent to Babai's well-known nearest-plane algorithm. We furthermore provide geometric intuition for both algorithms. Lastly, we note the consequences of these results, in particular hinting at the possibility of using lattice basis reduction for improved quantization.

cs.LG↗