Post-training quantization (PTQ) of large language models (LLMs) reduces memory usage and accelerates inference while maintaining accuracy. However, it remains unclear how to select a quantization scheme that achieves target accuracy across different model scales. We introduce two parameters to characterize this: the quantization ratio Q_r (proportion of parameters quantized to low precision) and the block size Q_b (number of parameters sharing a scaling factor). Based on extensive experiments across multiple LLM families and scales, we propose a unified scaling law that predicts quantization-induced loss degradation as a function of Q_r, Q_b, and model size. Our scaling law reveals two practical implications: (1) larger models tolerate higher Q_r, making mixed-precision increasingly effective at scale; (2) small Q_b, commonly used in mixed precision, becomes unnecessary for large models, simplifying hardware design without sacrificing accuracy. These findings provide a principled recipe for quantizing LLMs in practical deployment.

Parameter-Efficient Fine-Tuning (PEFT) has gained prominence through low-rank adaptation methods like LoRA. In this paper, we focus on sparsity-based PEFT (SPEFT), which introduces trainable sparse adaptations to the weight matrices in the model, offering greater flexibility in selecting fine-tuned parameters compared to low-rank methods. We conduct the first systematic evaluation of salience metrics for SPEFT, inspired by zero-cost NAS proxies, and identify simple gradient-based metrics is reliable, and results are on par with the best alternatives, offering both computational efficiency and robust performance. Additionally, we compare static and dynamic masking strategies, finding that static masking, which predetermines non-zero entries before training, delivers efficiency without sacrificing performance, while dynamic masking offers no substantial benefits. Across NLP tasks, a simple gradient-based, static SPEFT consistently outperforms other fine-tuning methods for LLMs, providing a simple yet effective baseline for SPEFT. Our work challenges the notion that complexity is necessary for effective PEFT, while our open-source framework establishes a reproducible benchmark for future research.

The inference of Large language models (LLMs) requires immense computation and memory resources. To curtail these costs, quantisation has emerged as a promising solution, but existing LLM quantisation mainly focuses on 8-bit. In this work, we explore the statistical and learning properties of the LLM layer and attribute the bottleneck of LLM quantisation to numerical scaling offsets. To address this, we adapt block quantisations for LLMs, a family of methods that share scaling factors across packed numbers. Block quantisations efficiently reduce the numerical scaling offsets solely from an arithmetic perspective, without additional treatments in the computational path. Our nearly-lossless quantised 6-bit LLMs achieve a 19× higher arithmetic density and 5× memory density than the float32 baseline, surpassing the prior art 8-bit quantisation by 2.5× in arithmetic density and 1.2× in memory density, without requiring any data calibration or re-training. We also share our insights into sub-8-bit LLM quantisation, including the mismatch between activation and weight distributions, optimal fine-tuning strategies, and a lower quantisation granularity inherent in the statistical properties of LLMs. The latter two tricks enable nearly-lossless 4-bit LLMs on downstream tasks. Our code is open-sourced.