arXiv:2601.17187cs.IT
High-Rate Quantized Matrix Multiplication I
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Abstract
This paper investigates the problem of quantized matrix multiplication (MatMul), which has become crucial for the efficient deployment of large language models (LLMs). We consider a Generic MatMul setting, where both matrices must be quantized (weight+activation quantization) without specific apriori (calibration) statistical information about the factors. We review the fundamental information-theoretic tradeoff between quantization rate and distortion (high-rate theory), and contrast those with the performance of popular quantization schemes (absmax INT and floating-point (FP)), for which we also derive accurate heuristic approximations. Part II of this paper studies the weight-only quantization setup where second-order statistics of the activation matrices are available at the encoder.
There are also more papers on similar themes. For example, TurboQuant makes use of QJL (quantized Johnson Lindenstrauss transformations). One of the first papers to characterize the QJL and in fact the rate distortion tradeoff for quantized matrix multiplication in general is…
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