# LFQ: Logit-aware Final-block Quantization for Boosting the Generation Quality of Low-Bit Quantized LLMs

arXiv: https://arxiv.org/abs/2605.29756 · HTML: https://mlsanity.com/paper/2605.29756/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 18 of 18)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [FlexRound: Learnable Rounding based on Element-wise Division for Post-Training Quantization](https://mlsanity.com/paper/2306.00317/) (2023)
- [An Alternative Cross Entropy Loss for Learning-to-Rank](https://mlsanity.com/paper/1911.09798/) (2019)
- [Cluster-Promoting Quantization with Bit-Drop for Minimizing Network Quantization Loss](https://mlsanity.com/paper/2109.02100/) (2021)
- [LRQ: Optimizing Post-Training Quantization for Large Language Models by Learning Low-Rank Weight-Scaling Matrices](https://mlsanity.com/paper/2407.11534/) (2024)
- [RILQ: Rank-Insensitive LoRA-based Quantization Error Compensation for Boosting 2-bit Large Language Model Accuracy](https://mlsanity.com/paper/2412.01129/) (2024)
- [Unifying Uniform and Binary-coding Quantization for Accurate Compression of Large Language Models](https://mlsanity.com/paper/2506.03781/) (2025)

## Built on by (most cited first, 2 of 2)

- [SoftWater: Class-Aware Rate Allocation for Softmax Quantization](https://mlsanity.com/paper/2608.12026/) (2026)
- [Why Does Post-Training Quantization Work?](https://mlsanity.com/paper/2609.11716/) (2026)

## Abstract (arXiv)

As large language models continue to scale, low-bit weight-only post-training quantization (PTQ) offers a practical solution to their memory-efficient deployment. Although block-wise PTQ is capable of matching the full-precision (FP) baseline on basic language modeling and understanding, its quality is degraded for generative tasks -- especially at longer responses and extended chains of thought, which is critical in boosting task accuracy. We attribute this shortfall to two factors: (i) the omission of the unembedding layer (the LM head) in block-wise optimization and (ii) the reliance on the mean squared error (MSE) objective. Both factors cause the token probability distribution of the quantized model to misalign with that of the FP model, yielding notable accuracy drops on text generation benchmarks. To rectify the discrepancy, we introduce Logit-aware Final-block Quantization (LFQ), a simple yet effective enhancement to block-wise PTQ that quantizes the final Transformer block by minimizing the cross-entropy between the logits of the FP model and those of its quantized counterpart. By aligning token probabilities at the logit level in the final block, LFQ consistently improves the accuracy of complex generation tasks over state-of-the-art block-wise PTQ across diverse model families, while maintaining parity with FP baselines on language modeling and understanding.