Challenge: Existing scaling laws focus on general performance, overlooking crucial fine-grained factors and how quantization differentially impacts diverse knowledge capabilities.
Approach: They propose a framework that unifies model size, bit-width, and fine-grained factors into memorization, application, and reasoning.
Outcome: The proposed framework shows strong fit and cross-architecture consistency on 293 different PTQ configurations.

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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.
DL-QAT: Weight-Decomposed Low-Rank Quantization-Aware Training for Large Language Models (2024.emnlp-industry)

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Challenge: Quantization-aware Training (QAT) is a popular technique for reducing memory usage and improving computational efficiency in large language models.
Approach: They propose a weight-decomposed low-rank quantization-aware training approach that integrates QAT with a group-specific quantization magnitude adjustment.
Outcome: The proposed method outperforms the state-of-the-art method on LLaMA and LLama2 models.
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.
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.
A Survey of Post-Training Scaling in Large Language Models (2025.acl-long)

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Challenge: Large language models (LLMs) have demonstrated proficiency in understanding and generating human natural languages.
Approach: They propose a framework for scaling large language models using supervised fine-tuning, RLxF and test-time compute methodologies.
Outcome: The proposed model can be used to understand and generate human natural languages.
A Comprehensive Evaluation of Quantization Strategies for Large Language Models (2024.findings-acl)

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Challenge: Quantization studies have focused on instruction-tuned LLMs, leaving their performance on other benchmarks unclear.
Approach: They propose a framework to evaluate quantized large language models using four dimensions . they propose to reduce the bits needed for model weights or activations with minimal performance loss .
Outcome: The proposed framework can retain comparable performance to non-quantized LLMs on most benchmarks.
Beyond Dynamic Quantization: An Efficient Static Hierarchical Mix-precision Framework for Near-Lossless LLM Compression (2025.emnlp-industry)

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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.
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Revisiting Pruning vs Quantization for Small Language Models (2025.findings-emnlp)

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Challenge: Compressing Small Language Models (SLMs) is particularly suited for resource-constrained devices, but their compression dynamics remain underexplored compared to Large Language Model (LLMs).
Approach: They evaluated post-training pruning and quantization methods across six SLMs from 0.5 to 3.8B, seven languages, and seven downstream tasks.
Outcome: The proposed methods outperform pruning and quantization on six SLMs from 0.5 to 3.8B, seven languages, and seven downstream tasks.
Exploring Layer-wise Information Effectiveness for Post-Training Quantization in Small Language Models (2026.findings-acl)

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Challenge: Large language models with billions of parameters are often over-provisioned . smaller models exhibit lower robustness under extreme low-bit quantization .
Approach: They propose a hardware-native, metric-driven post-training quantization framework that keeps uniform bit-width within each layer while mixing precision across layers.
Outcome: LieQ reduces large accuracy gap observed for large language models with billions of parameters while preserving standard multiplication kernels.
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.

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