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MpSub: A Momentum $p$-Dimensional Subspace Trust-Region Method for Derivative-Free Fine-Tuning of Large Language Models

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

Full-parameter fine-tuning of large language models has substantial memory costs because backpropagation stores activations and gradients. Zeroth-order optimization avoids this by estimating update directions from loss evaluations, but existing methods require tuning a sensitive learning rate for each model and task. We propose the momentum $p$-dimensional subspace trust-region method (MpSub). At each iteration, MpSub searches within a $p$-dimensional subspace: one direction preserves historical momentum from the most recent accepted step, while the remaining directions explore via fresh rando

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