mlsanityData to 7 Oct 2026

NestQuant: Nested Lattice Quantization for Matrix Products and LLMs

arXiv 2502.09720 ↗First posted 13 Feb 2025cs.LG cs.AI cs.ITcited by 16

Not on the map. Why?

Abstract (arXiv)

Post-training quantization (PTQ) has emerged as a critical technique for efficient deployment of large language models (LLMs). This work proposes NestQuant, a novel PTQ scheme for weights and activations that is based on self-similar nested lattices. Recent works have mathematically shown such quantizers to be information-theoretically optimal for low-precision matrix multiplication. We implement a practical low-complexity version of NestQuant based on Gosset lattice, making it a drop-in quantizer for any matrix multiplication step (e.g., in self-attention, MLP etc). For example, NestQuant quantizes weights, KV-cache, and activations of Llama-3-8B to 4 bits, achieving perplexity of 6.6 on wikitext2. This represents more than 55% reduction in perplexity gap with respect to unquantized model (perplexity of 6.14) compared to state-of-the-art Metas SpinQuant (perplexity 7.3), OstQuant (7.3) and QuaRot (8.2). Comparisons on bigger models (up to 70B) and on various LLM evaluation benchmarks confirm uniform superiority of NestQuant.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 15 of its 34 references that are in the map. First posted on arXiv 13 Feb 2025.

Builds on

15 of 34 references.

References · 15

  1. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,710
  2. 2019HellaSwag: Can a Machine Really Finish Your Sentence?cited by 4,018
  3. 2016Pointer Sentinel Mixture Modelscited by 2,992
  4. 2019PIQA: Reasoning about Physical Commonsense in Natural Languagecited by 2,818
  5. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,838
  6. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,338
  7. 2022LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scalecited by 881
  8. 2024QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMscited by 598
  9. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 397
  10. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 354
  11. 2022Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruningcited by 317
  12. 2024DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMscited by 165
3 more
  1. 2025OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fittingcited by 94
  2. 2024QTIP: Quantization with Trellises and Incoherence Processingcited by 86
  3. 2020Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transformcited by 79

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 14.

16 papers.

Sort:

By area:

  1. 2025Model-Preserving Adaptive Roundingcited by 20
  2. 2026High-Rate Quantized Matrix Multiplication Icited by 6
  3. 2026WaterSIC: Information-Theoretically (Near) Optimal Linear Layer Quantizationcited by 5
  4. 2025Learning Grouped Lattice Vector Quantizers for Low-Bit LLM Compressioncited by 4
  5. 2026High-Rate Quantized Matrix Multiplication IIcited by 2
  6. 2026LC-QAT: Data-Efficient 2-Bit QAT for LLMs via Linear-Constrained Vector Quantizationcited by 2
  7. 2026SoftWater: Class-Aware Rate Allocation for Softmax Quantizationcited by 2
  8. 2026Price of metric universality in vector quantization is at most 0.11 bitcited by 1
  9. 2026UniSVQ: 2-bit Unified Scalar-Vector Quantizationcited by 1
  10. 2026HyperQuant: A Rate-Distortion-Optimal Quantization Pipeline for Large Language and Diffusion Modelscited by 1
  11. 2026Contraction-Gauge Preconditioning for Quantized Matrix Multiplicationcited by 1
  12. 2026ELMoE-3D: Leveraging Intrinsic Elasticity of MoE for Hybrid-Bonding-Enabled Self-Speculative Decoding in On-Premises Servingcited by 0
4 more
  1. 2026OffQ: Taming Structured Outliers in LLM Quantization by Offsettingcited by 0
  2. 2026CurveFP: Co-Designing Numerical Representation and Product Arithmetic for Language Modelscited by 0
  3. 2026The Asymmetric Harms of LLM Compressioncited by 0
  4. 2026WaterKron and FlipFlop Hessian: Information-Theoretically Grounded Quantization with Kronecker-factored Hessianscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024SpinQuant: LLM quantization with learned rotations
  2. 2025PTQTP: Post-Training Quantization to Trit-Planes for Large Language Models
  3. 2025Gradual Binary Search and Dimension Expansion : A general method for activation quantization in LLMs
  4. 2023FineQuant: Unlocking Efficiency with Fine-Grained Weight-Only Quantization for LLMs
  5. 2023SmoothQuant+: Accurate and Efficient 4-bit Post-Training WeightQuantization for LLM
  6. 2026CurveTQ: Rotation-Free Trellis Quantization of LLM Weights via Curvature-Weighted Search
  7. 2025ParoQuant: Pairwise Rotation Quantization for Efficient Reasoning LLM Inference
  8. 2026Multi-Scale Dequant: Eliminating Dequantization Bottleneck via Activation Decomposition for Efficient LLM Inference