用克罗内克分解海森矩阵加速量化，提升精度且计算更高效
BaKron: Efficient Quantization with Kronecker-Factored Hessians
- 基于双侧海森矩阵近似，捕捉输出坐标相关性
- 新算法 BaKron 将复杂度从 O(m²n²) 降至 O(mn(m+n))
- 兼容多种量化器和海森估计器，适合模型压缩研究者
我们加速了一类由克罗内克分解海森矩阵指导的神经网络量化算法。传统 GPTQ 风格自适应舍入仅利用输入激活的一侧信息，而双侧克罗内克分解海森矩阵可额外捕获输出坐标的关联性，但直接在向量化权重域应用 GPTQ 计算开销巨大。受 BoA 和 YAQA 的双侧自适应舍入框架启发，我们提出 BaKron，一种结合反对角并行与递归分治结构的高效求解器。对于 $m\times n$ 权重矩阵，BaKron 仅需 $O(m+n)$ 顺序步骤，总工作量从 $O(m^2n^2)$ 降低至 $O(mn(m+n))$，实现与 GPTQ 相当的立方级缩放，同时利用更丰富的曲率信息。此外，BaKron 在基量化器和海森估计器上具有模块化设计。我们还提供了实用基准，考察多种可适配的海森矩阵，提出高效计算方法，并进行实验评估。
原文摘要 · Abstract (English)
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.
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