Paper Detail
Jichao Jiang, Cristian McGee, El Houcine Bergou, Hanqin Cai, Aritra Dutta
Full-parameter fine-tuning of large language models (LLMs) incurs substantial optimizer state memory overhead, limiting the model sizes that fit on modern GPUs. Existing approaches either compress optimizer state, abandon first-order gradients, or change the update geometry while retaining dense state. The recently introduced Muon optimizer reduces optimizer memory through matrix-valued updates. Still, its geometry differs from AdamW and can lead to performance degradation when fine-tuning AdamW-pretrained models. To reduce optimizer memory without sacrificing accuracy or computational efficiency in LLM fine-tuning, we propose Ternary Absolute-max Column-wise One-sparse optimizer, or TACO, which follows Muon's operator-norm steepest-descent view but takes the geometric route further. TACO computes the exact steepest-descent direction under a dimension-normalized $1\to1$ operator norm by selecting the sign of the largest magnitude entry in each column of two-dimensional weight matrices. This retains first-order gradients while making optimizer state memory nearly negligible. Our practical TACO optimizer maintains only a small set of low precision gradient components per column, reducing persistent optimizer state by $174\times$ relative to AdamW8bit (from 27.7 GB to 0.16 GB) and peak training memory by $2.9\times$ (from 80.6 GB to 27.5 GB) on OPT-13B, while achieving comparable accuracy and runtime. TACO further enables full-parameter fine-tuning of 30-32B-parameter models on a single 80 GB H100 GPU across multiple model families and tasks.
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@article{jiang2026taco,
title = {TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning},
author = {Jichao Jiang and Cristian McGee and El Houcine Bergou and Hanqin Cai and Aritra Dutta},
year = {2026},
abstract = {Full-parameter fine-tuning of large language models (LLMs) incurs substantial optimizer state memory overhead, limiting the model sizes that fit on modern GPUs. Existing approaches either compress optimizer state, abandon first-order gradients, or change the update geometry while retaining dense state. The recently introduced Muon optimizer reduces optimizer memory through matrix-valued updates. Still, its geometry differs from AdamW and can lead to performance degradation when fine-tuning AdamW},
url = {https://arxiv.org/abs/2610.02199},
keywords = {cs.LG, math.OC, Computer science, Ternary operation, Limiting, Algorithm, Set (abstract data type)},
eprint = {2610.02199},
archiveprefix = {arXiv},
}
{}