Quantized Evolution Strategies: High-precision Fine-tuning of Quantized LLMs at Low-precision Cost

Post-Training Quantization (PTQ) is essential for deploying Large Language Models (LLMs) on memory-constrained devices, yet it renders models static and difficult to fine-tune. Standard fine-tuning paradigms, including Reinforcement Learning (RL), fundamentally rely on backpropagation and continuous weights to compute gradients. Thus they cannot be used on quantized models, where the parameter space is discrete and non-differentiable. While Evolution Strategies (ES) offer a backpropagation-free alternative, optimization of the quantized parameters can still fail due to vanishing or inaccurate gradient estimation. This paper introduces Quantized Evolution Strategies (QES), an optimization paradigm that performs full-parameter fine-tuning directly in the quantized space. QES is based on two innovations: (1) it integrates accumulated error feedback to preserve high-precision weight updating signals, and (2) it utilizes a stateless seed replay to reduce memory usage to low-precision inference levels. QES significantly outperforms the state-of-the-art zeroth-order fine-tuning methods on a variety of tasks, making direct fine-tuning for quantized models possible. It therefore opens up the possibility for scaling up LLMs entirely in the quantized space. The source code is available at https://github.com/dibbla/Quantized-Evolution-Strategies .