mlsanityData to 14 Oct 2026

The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm

arXiv 2508.01077 ↗First posted 1 Aug 2025cs.LG cs.AIcited by 9

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Abstract (arXiv)

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.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 4 of its 9 references that are in the map. First posted on arXiv 1 Aug 2025.

Builds on

4 of 9 references.

References · 4

  1. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  2. 2022Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruningcited by 322
  3. 2025Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantizationcited by 28
  4. 2025The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithmcited by 20

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 9.

9 papers.

  1. 2026WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantizationcited by 7
  2. 2026High-Rate Quantized Matrix Multiplication IIcited by 4
  3. 2026GPTQ-2D: Cubic-Time Two-Sided Adaptive Roundingcited by 2
  4. 2026Price of metric universality in vector quantization is at most 0.11 bitcited by 1
  5. 2026FastKron: Efficient Quantization with Kronecker-Factored Hessianscited by 1
  6. 2026WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessianscited by 0
  7. 2026Generalization behavior of OPTQ and the role of regularizationcited by 0
  8. 2026Product-Aware Deterministic Rounding for Quantized Matrix Multiplicationcited by 0
  9. 2026Revisiting Error Feedback for Model Quantizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Gradient Based Method for the Fusion of Lattice Quantizers
  2. 2021A Survey of Quantization Methods for Efficient Neural Network Inference
  3. 2025DiscQuant: A Quantization Method for Neural Networks Inspired by Discrepancy Theory
  4. 2022Why Quantization Improves Generalization: NTK of Binary Weight Neural Networks
  5. 2021Neural Network Quantization for Efficient Inference: A Survey
  6. 2022Post-training Quantization for Neural Networks with Provable Guarantees
  7. 2021Training Quantized Neural Networks to Global Optimality via Semidefinite Programming
  8. 2026OJBKQ: Objective-Joint Babai-Klein Quantization