mlsanityData to 14 Oct 2026

WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantization

arXiv 2603.04956 ↗First posted 5 Mar 2026cs.LG cs.IT math.ITcited by 7

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Abstract (arXiv)

This paper considers the problem of converting a given dense linear layer to low precision. The tradeoff between compressed length and output discrepancy is analyzed information theoretically (IT). It is shown that a popular GPTQ algorithm may have an arbitrarily large gap to the IT limit. To alleviate this problem, a novel algorithm, termed ``WaterSIC'', is proposed and is shown to be within a rate gap of 0.255 bits to the IT limit, uniformly over all possible covariance matrices of input activations. The key innovation of WaterSIC's is to allocate different quantization rates to different columns (in-features) of the weight matrix, mimicking the classical IT solution known as "waterfilling". Applying WaterSIC to the Llama and Qwen family of LLMs establishes new state-of-the-art performance for all quantization rates from 1 to 4 bits. Our code is available at https://github.com/egorlifar/watersic.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 31 of its 45 references that are in the map. First posted on arXiv 5 Mar 2026.

Builds on

31 of 45 references.

References · 31

  1. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  2. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,386
  3. 2023AWQ: Activation-aware Weight Quantization for LLM Compression and Accelerationcited by 1,298
  4. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 634
  5. 2024SpinQuant: LLM quantization with learned rotationscited by 471
  6. 2023OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Modelscited by 424
  7. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 414
  8. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 378
  9. 2024Extreme Compression of Large Language Models via Additive Quantizationcited by 232
  10. 2024Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Lawscited by 144
  11. 2024FlatQuant: Flatness Matters for LLM Quantizationcited by 131
  12. 2024QTIP: Quantization with Trellises and Incoherence Processingcited by 91
19 more
  1. 2024An empirical study of LLaMA3 quantization: from LLMs to MLLMscited by 64
  2. 2024PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compressioncited by 61
  3. 2025How much do language models memorize?cited by 61
  4. 2025ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantizationcited by 46
  5. 2025Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scalingcited by 35
  6. 2025GuidedQuant: Large Language Model Quantization via Exploiting End Loss Guidancecited by 32
  7. 2025Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantizationcited by 28
  8. 2025NestQuant: Nested Lattice Quantization for Matrix Products and LLMscited by 23
  9. 2025Model-Preserving Adaptive Roundingcited by 23
  10. 2025QuEST: Stable Training of LLMs with 1-Bit Weights and Activationscited by 22
  11. 2025The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithmcited by 20
  12. 2025Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronoscited by 16
  13. 2025Ecco: Improving Memory Bandwidth and Capacity for LLMs via Entropy-aware Cache Compressioncited by 14
  14. 2025Outlier-Safe Pre-Training for Robust 4-Bit Quantization of Large Language Modelscited by 13
  15. 2025The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithmcited by 9
  16. 2025any4: Learned 4-bit Numeric Representation for LLMscited by 5
  17. 2025Not All Bits Are Equal: Scale-Dependent Memory Optimization Strategies for Reasoning Modelscited by 4
  18. 2025Microbenchmarking NVIDIA's Blackwell Architecture: An in-depth Architectural Analysiscited by 3
  19. 2026Float8@2bits: Entropy Coding Enables Data-Free Model Compressioncited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 7.

7 papers.

  1. 2026HARP: Hadamard-Preconditioned Adaptive Rotation Processor for Extreme LLM Quantizationcited by 5
  2. 2026High-Rate Quantized Matrix Multiplication IIcited by 4
  3. 2026SoftWater: Class-Aware Rate Allocation for Softmax Quantizationcited by 2
  4. 2026Pricing the Risk of Runtime Compression: Anytime-Valid Admission and a Served-Output Law for Compressed Serving Statecited by 0
  5. 2026WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessianscited by 0
  6. 2026OSFP4: Joint Optimization of Diagonal Smoothing and Block Scales for NVFP4 Quantizationcited by 0
  7. 2026When Does Compensating Inherited Quantization Error Help? Mean-Square Guarantees for Layer-Wise Quantization and Their Limitscited by 0

Similar, not cited

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  1. 2026High-Rate Quantized Matrix Multiplication I
  2. 2024decoupleQ: Towards 2-bit Post-Training Uniform Quantization via decoupling Parameters into Integer and Floating Points
  3. 2026GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling
  4. 2026Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape
  5. 2026Price of metric universality in vector quantization is at most 0.11 bit
  6. 2025InfoQ: Mixed-Precision Quantization via Global Information Flow
  7. 2026GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation
  8. 2026BCJR-QAT: A Differentiable Relaxation of Trellis-Coded Weight Quantization