ZO-Act用激活信息锁定关键子空间，让零阶微调更稳定，在Llama-3和OPT-13B上都比旧方法强，适合显存受限的场景。
ZO-Act提出一种激活感知的零阶微调方法，通过一次性计算输入激活基，将扰动限制在固定低秩子空间中，从而将有效扰动维度降低至系数矩阵大小。该方法在Llama-3-8B、OPT-13B和INT4 Llama-3-8B上实验，在语言理解、问答和常识推理任务中一致超越现有零阶微调基线。分析表明，ZO-Act通过低维系数扰动减少了方差依赖项和有限差分误差，并利用LLM激活和梯度的低秩结构控制子空间近似偏差。
ZO-Act: Efficient Zeroth-Order Fine-Tuning via One-Shot Activation-Informed Low-Rank Subspaces
Zeroth-order (ZO) optimization enables fine-tuning large language models when backpropagation is unavailable or memory-prohibitive, but existing methods often perturb full model weights or randomly constructed low-dimensional subspaces, yielding high-variance estimates and limited performance. We propose ZO-Act, an activation-informed ZO fine-tuning method that restricts perturbations to a fixed low-rank subspace derived from input activations. For each linear layer, ZO-Act computes a small activation basis once at initialization and optimizes only lightweight coefficient matrices using forward-only loss evaluations. This reduces the effective perturbation dimension, exposes explicit trainable variables compatible with momentum-based optimizers such as Adam, and naturally supports quantized LLM fine-tuning by keeping low-bit weights frozen. We analyze ZO-Act as zeroth-order optimization over a restricted coefficient space and show that perturbing the low-dimensional coefficients reduces both the variance-dependent convergence term and the finite-difference error of the ZO estimator, at the cost of a controlled subspace approximation bias that is mitigated by the low-rank structure of LLM activations and gradients. Experiments on Llama-3-8B, OPT-13B, and INT4 Llama-3-8B show consistent gains over strong ZO fine-tuning baselines across language understanding, question answering, and commonsense reasoning.