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ARXIV:2605.13768 · LLM OPTIMIZATION · SUBMITTED 14 MAY · 20:10 UTC · FRESHNESS FRESH
ARXIV:2605.13768LLM OPTIMIZATIONSUBMITTED 14 MAY · 20:10 UTCFRESHNESS FRESHOr Ordentlich · Yury Polyanskiy · arXiv
Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization.
Opportunity summary
Pain Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization.
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Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization. In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix…
This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$ of…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally.
LLM Optimization moved forward this cycle; last verified May 2026. Public score 3.0/10.
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Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization.
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10.48550/arXiv.2605.13768Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization.
Abstract
This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$ of the columns of the second factor is available. This setting arises in the ubiquitous task of weight-only post-training quantization of LLMs. Weight-only quantization is related to the problem of weighted mean squared error (WMSE) source coding, whose classical (reverse) waterfilling solution dictates how one should distribute rate between coordinates of the vector. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally. A recent scheme (known as ``WaterSIC'') that only uses scalar INT quantizers is analyzed and its high-rate performance is shown to be (a) basis free (i.e., characterized by the determinant of $Σ_X$ and, thus, unlike existing schemes, is immune to applying random rotations); and (b) within a multiplicative factor of $\frac{2πe}{12}$ (or 0.25 bit/entry) of the information-theoretic distortion limit. GPTQ's performance, in turn, is affected by the choice of basis, but for a random rotation and actual $Σ_X$ from Llama-3-8B we find it to be within 0.1 bit (depending on the layer type) of WaterSIC, suggesting that GPTQ with random rotation is also near optimal, at least in the high-rate regime.
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PROBLEM
Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization. In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$...
METHOD
This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$ of the columns of the second factor is available.
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally.
WHY NOW
LLM Optimization moved forward this cycle; last verified May 2026. Public score 3.0/10.
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Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization. In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$ of the columns of the second factor is available.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $Σ_X$ of the columns of the second factor is available.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
LLM Optimization moved forward this cycle; last verified May 2026. Public score 3.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Improving LLM quantization algorithms by applying information-theoretic principles to rate allocation for weight-only post-training quantization.
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