TerMeZO: Ternary Sparse Zeroth-Order Optimization for Fine-tuning BitNet Models at the Edge

Abstract

Fine-tuning anguage models (LLMs) with first-order optimizers requires a memory several times larger than that required for inference. Memory-efficient zeroth-order optimization (MeZO) sidesteps this cost by estimating gradients from forward passes only. However, for BitNet architectures, a family of LLMs with ternary {-1,0,1\} weights and 8-bit activations, fine-tuning requires updating full-precision latent weights, and thus the memory footprint of MeZO no longer matches that of inference. A promising solution is to finetune only a subset of the latent weights, but existing sparse zeroth-order (ZO) methods either ignore the ternary structure or require first-order gradient information to build a sparse mask, which is at odds with the purpose of ZO fine-tuning. We propose TerMeZO, a sparse MeZO scheme that exploits the geometry of the ternary quantizer itself to identify the latent weights that are more likely to change values during fine-tuning, at no additional data or memory cost. Our convergence analysis shows that TerMeZO can converge faster than full-parameter MeZO, owing to its optimized reduction of the fine-tuning effective dimension. We run extensive experiments on BitNet models ranging from 1B to 3B parameters, spanning classification, instruction-following, and mathematical reasoning tasks. TerMeZO matches or exceeds the performance of full-parameter MeZO while substantially reducing the fine-tuning memory footprint.