Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization

Layer-wise post-training quantization has emerged as a widely used technique for compressing large language models (LLMs) without retraining. However, recent progress in this line of research is saturating, underscoring the need to revisit its core limitation and explore further improvements. This study identifies a critical bottleneck in existing layer-wise PTQ methods: the accumulation of quantization errors across layers significantly degrades performance, particularly in low-bit regimes. To address this, we propose Quantization Error Propagation (QEP), a lightweight and general framework that enhances layer-wise PTQ by explicitly propagating the quantization error which enable compensating for accumulated quantization errors. Additionally, we introduce a tunable propagation mechanism that allows for control over both propagation strength and computational overhead, making the framework adaptable to various architectures and resource constraints. Empirical evaluation on LLaMA2 models (7B, 13B, 70B) demonstrate that incorporating QEP into standard layer-wise PTQ pipelines outperforms standard PTQ methods. Notably, QEP yields substantial performance improvements under extreme low-bit quantization settings.

Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling

Learning-based methods have gained attention as general-purpose solvers because they can automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face challenges with scalability. To address these issues, the improved Sampling algorithm for Combinatorial Optimization (iSCO) using discrete Langevin dynamics has been proposed, demonstrating better performance than several learning-based solvers. This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA). QQA smoothly transitions the objective function from a simple convex form, where half-integral solutions dominate, to the original objective function, where the variables are restricted to 0 or 1. Furthermore, we incorporate parallel run communication leveraging GPUs, enhancing exploration capabilities and accelerating convergence. Numerical experiments demonstrate that our approach is a competitive general-purpose solver, achieving comparable performance to iSCO across various benchmark problems. Notably, our method exhibits superior trade-offs between speed and solution quality for large-scale instances compared to iSCO, commercial solvers, and specialized algorithms.