揭示量化算法与格点最近向量问题的几何等价性
The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm
- 将神经网络量化建模为输入数据生成的格点最近向量问题
- 证明GPTQ算法等价于经典的Babai最近平面算法
- 为改进量化提供基于格基约化的理论新思路
我们解释了神经网络中线性单元的数据驱动量化如何对应于由输入数据生成的特定格点的最近向量问题。我们证明GPTQ算法等价于著名的Babai最近平面算法，并为两个算法提供了几何直观。最后，我们指出这些结果的含义，特别是暗示了利用格基约化改进量化方法的可能性。
原文摘要 · Abstract (English)
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.
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