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    <abstract>The AdamW optimizer, while standard for LLM pretraining, is a critical memory bottleneck, consuming optimizer states equivalent to twice the model’s size. Although light-state optimizers like SinkGD attempt to address this issue, we identify the embedding layer dilemma: these methods fail to handle the sparse, high-variance gradients inherent to embeddings, forcing a hybrid design that reverts to AdamW and partially negates the memory gains. We propose SAGE (Sign Adaptive GradiEnt), a novel optimizer that resolves this dilemma by replacing AdamW in this hybrid structure. SAGE combines a Lion-style update direction with a new, memory-efficient O(d) adaptive scale. This scale acts as a “safe damper,” provably bounded by 1.0, which tames high-variance dimensions more effectively than existing methods. This superior stability allows SAGE to achieve better convergence. On Llama models up to 1.3B parameters, our SAGE-based hybrid achieves new state-of-the-art perplexity, outperforming all baselines, including SinkGD hybrid, while significantly reducing optimizer state memory.</abstract>
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%0 Conference Proceedings
%T SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization
%A Lee, Wooin
%A Kim, Hyun-Tae
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F lee-kim-2026-sage
%X The AdamW optimizer, while standard for LLM pretraining, is a critical memory bottleneck, consuming optimizer states equivalent to twice the model’s size. Although light-state optimizers like SinkGD attempt to address this issue, we identify the embedding layer dilemma: these methods fail to handle the sparse, high-variance gradients inherent to embeddings, forcing a hybrid design that reverts to AdamW and partially negates the memory gains. We propose SAGE (Sign Adaptive GradiEnt), a novel optimizer that resolves this dilemma by replacing AdamW in this hybrid structure. SAGE combines a Lion-style update direction with a new, memory-efficient O(d) adaptive scale. This scale acts as a “safe damper,” provably bounded by 1.0, which tames high-variance dimensions more effectively than existing methods. This superior stability allows SAGE to achieve better convergence. On Llama models up to 1.3B parameters, our SAGE-based hybrid achieves new state-of-the-art perplexity, outperforming all baselines, including SinkGD hybrid, while significantly reducing optimizer state memory.
%R 10.18653/v1/2026.findings-acl.923
%U https://aclanthology.org/2026.findings-acl.923/
%U https://doi.org/10.18653/v1/2026.findings-acl.923
%P 18525-18537

Markdown (Informal)

[SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization](https://aclanthology.org/2026.findings-acl.923/) (Lee & Kim, Findings 2026)

• SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization (Lee & Kim, Findings 2026)

ACL

• Wooin Lee and Hyun-Tae Kim. 2026. SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization. In Findings of the Association for Computational Linguistics: ACL 2026, pages 18525–18537, San Diego, California, United States. Association for Computational Linguistics.