Challenge: Existing methods for dynamic quantization are hardware-unfriendly and often lead to large quantization errors in static scenarios.
Approach: They propose a Static Hierarchical Mix-precision Quantization method which quantifies both inter-layer and intra-layer sensitivity through unified derivations involving Hessian.
Outcome: The proposed method achieves 75.58% on zero-shot reasoning tasks while yielding average speedup of 2.86.

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PTQ1.61: Push the Real Limit of Extremely Low-Bit Post-Training Quantization Methods for Large Language Models (2025.acl-long)

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Challenge: Existing methods for sub 2-bit quantization introduce an extra 1-bit or more per weight.
Approach: They propose a sub 2-bit post-training quantization method that enables weight quantization to 1.61-bit for the first time.
Outcome: The proposed method reduces the upper bound of quantization error to 1.61-bit for the first time.
CoopQ: Cooperative Game Inspired Layerwise Mixed Precision Quantization for LLMs (2026.findings-acl)

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Challenge: Existing methods for large language models struggle when the average precision drops below four bits, limiting deployment on resourceconstrained devices such as mobiles, edge sensors, or standard GPUs.
Approach: They propose a game-like game-inspired mixed-precision quantization method which translates these Shapley estimates into a binary quadratic optimization formulation, assigning either 2 or 4-bit precision to layers under strict memory constraints.
Outcome: The proposed method reduces Perplexity by 20 – 80 % across average precisions spanning 4 bit down to 2 bit, compared to methods relying on isolated metrics.
Layer-Wise High-Impact Parameter Ratio Optimization in Post-Training Quantization for Large Language Models (2026.acl-long)

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Challenge: Existing methods to quantize large language models suffer from significant accuracy loss at low bit-widths due to high-impact parameters.
Approach: They propose a quadratic optimization framework that quantizes high-impact parameters to moderate bit-widths while quantizing low bit-wideths.
Outcome: The proposed framework preserves high-impact parameters while preserving memory usage.
Can Post-Training Quantization Benefit from an Additional QLoRA Integration? (2025.naacl-industry)

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Challenge: Large language models require considerable computing resources, which can be costly and often unavailable.
Approach: They propose to integrate 4-bit Post-training Quantization with QLoRA to address these issues . they demonstrate that the integration outperforms standard quantization and fine-tuning .
Outcome: The proposed integration outperforms standard PTQ and 16-bit full-parameter fine-tuning on LLMs.
Benchmarking Post-Training Quantization of Large Language Models under Microscaling Floating Point Formats (2026.acl-long)

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Challenge: Microscaling Floating-Point (MXFP) is a low-precision format for large language models (LLMs).
Approach: They conduct systematic evaluations of PTQ under Microscaling Floating-Point (MXFP) . they find that MXFP8 consistently achieves near-lossless performance .
Outcome: The proposed method achieves near-lossless performance while MXFP4 introduces substantial accuracy degradation and remains challenging.
ACBQ: Adaptive Cross-Block Quantization of Large Language Models (2026.acl-long)

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Challenge: Existing methods for post-training quantization struggle to support weight–activation joint quantization and extreme low-bit weight quantization.
Approach: They propose a framework that addresses weight–activation joint quantization and extreme weight quantization.
Outcome: The proposed framework achieves superior performance under both W4A4 and highly aggressive W2 settings while incurring negligible additional computational overhead.
FAQ: Mitigating Quantization Error via Regenerating Calibration Data with Family-Aware Quantization (2026.findings-acl)

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Challenge: representativeness and universality of calibration data remain a bottleneck in quantization accuracy.
Approach: They propose a framework that leverages prior knowledge from LLMs to generate calibration samples . their framework reduces accuracy loss by up to 28.5% compared to baseline .
Outcome: Experiments show that family-aware quantization reduces accuracy loss by up to 28.5% compared to baseline data.
MLWQ: Efficient Small Language Model Deployment via Multi-Level Weight Quantization (2025.emnlp-main)

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Challenge: Existing methods for efficient deployment of small language models face inefficient bit-width allocation and insufficient fine-grained quantization adjustments.
Approach: They propose a weight quantization technique that facilitates efficient deployment of SLMs . they propose to combine inter-layer loss and intra-layer salience to achieve better allocation .
Outcome: Experimental results show that multi-level weight quantization achieves competitive performance compared to state-of-the-art methods.
LRQuant: Learnable and Robust Post-Training Quantization for Large Language Models (2024.acl-long)

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Challenge: Existing methods for post-training quantization (PTQ) are limited by the complexity of the quantization parameter and performance degradations when tested on unseen datasets.
Approach: They propose a learnable smooth-based PTQ framework that allows for rapid adaptation during testing.
Outcome: The proposed framework improves performance on unseen datasets and reduces memory constraints.
LRQ: Optimizing Post-Training Quantization for Large Language Models by Learning Low-Rank Weight-Scaling Matrices (2025.naacl-long)

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Challenge: Existing methods for quantizing weights and activations of large language models suffer from non-negligible accuracy drops, especially on massive multitask language understanding.
Approach: They propose a weight-activation quantization method that reconstructs the outputs of an intermediate Transformer block by leveraging low-rank weight-scaling matrices.
Outcome: The proposed method reduces the complexity of the weight-activation quantization techniques while achieving high throughput and reducing inference costs.

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