SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization

• URL: http://arxiv.org/abs/2604.07663v2
• Date: Wed, 15 Apr 2026 21:35:18 GMT
• Title: SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization
• Abstract summary: We propose SAGE (Sign Adaptive GradiEnt) to replace AdamW in hybrid structures.<n>SAGE combines a Lion-style update direction with a new, memory-efficient $O(d)$ adaptive scale.<n>On Llama models up to 1.3B parameters, our SAGE-based hybrid achieves new state-of-the-art perplexity, outperforming all baselines.
• Score: 1.675857332621569
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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