mlsanityData to 14 Oct 2026

BCJR-QAT: A Differentiable Relaxation of Trellis-Coded Weight Quantization

arXiv 2605.10655 ↗First posted 11 May 2026cs.LGcited by 0

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Abstract (arXiv)

Trellis-coded quantization sets the current 2-bit post-training frontier for LLMs (QTIP), but pushing below the PTQ ceiling requires quantization-aware training, and QAT on a trellis is obstructed by the non-differentiable Viterbi argmax. We introduce BCJR-QAT, a relaxation that replaces the argmax with the BCJR forward-backward sum-product algorithm at temperature T, producing a soft codeword equal to the Boltzmann expectation over trellis paths, exactly differentiable, recovering the hard QTIP code as T → 0, and mathematically identical to the transfer-matrix computation for a 1D Ising-like spin chain. We contribute (i) a fused Triton kernel making BCJR tractable on a single consumer GPU (6.57× speedup, fp32 parity); (ii) a quantitative drift-budget theory of when BCJR-QAT can escape the QTIP-PTQ Voronoi basin, verified across four experiments; and (iii) a positive empirical result on Llama-3.2-1B at 2 bpw under end-to-end forward-KL distillation: with the right schedule (skip the high-T phase to avoid an overshoot we diagnose), single-layer BCJR-QAT beats QTIP-PTQ by -0.084 PPL on WikiText-2, and multi-layer compounding is super-additive.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 23 of its 31 references that are in the map. First posted on arXiv 11 May 2026.

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References · 23

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,599
  3. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,886
  4. 2019HellaSwag: Can a Machine Really Finish Your Sentence?cited by 4,100
  5. 2023QLoRA: Efficient Finetuning of Quantized LLMscited by 3,418
  6. 2016Pointer Sentinel Mixture Modelscited by 3,096
  7. 2019PIQA: Reasoning about Physical Commonsense in Natural Languagecited by 2,883
  8. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  9. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,919
  10. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,386
  11. 2024The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scalecited by 1,160
  12. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
11 more
  1. 2023OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Modelscited by 424
  2. 2023QuIP: 2-Bit Quantization of Large Language Models With Guaranteescited by 414
  3. 2024QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebookscited by 378
  4. 2023LLM-QAT: Data-Free Quantization Aware Training for Large Language Modelscited by 324
  5. 2024OLMoE: Open Mixture-of-Experts Language Modelscited by 301
  6. 2024Extreme Compression of Large Language Models via Additive Quantizationcited by 232
  7. 2024EfficientQAT: Efficient Quantization-Aware Training for Large Language Modelscited by 127
  8. 2024QTIP: Quantization with Trellises and Incoherence Processingcited by 91
  9. 2024PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compressioncited by 61
  10. 2026There Will Be a Scientific Theory of Deep Learningcited by 29
  11. 2024LeanQuant: Accurate and Scalable Large Language Model Quantization with Loss-error-aware Gridcited by 22

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