Parameter-Efficient Fine-Tuning (PEFT) has become the standard approach for adapting large language models (LLMs). However, despite reducing trainable parameter counts, many PEFT methods remain memory-bound by token-level activation intermediates that scale linearly with sequence length, limiting their practicality for long-context and on-device adaptation. Unlike prior memory-efficient PEFT approaches that preserve token-level adapter activations, LARS (Low-memory Activation-Rank Subspace) reduces the sequence-length scaling of stored adapter activation intermediates from O(BSRL) to O(BRL) by performing adaptation within a sequence-level low-rank subspace. Through pooled feature extraction, low-rank subspace modulations, and residual projection, LARS reduces the overall memory footprint by 23% on GPUs and 47.8% on CPUs relative to LoRA at S = 1024, with relative savings increasing with context length. Experiments across reasoning, understanding, long-context, retrieval, and token-level tasks show that LARS maintains competitive performance relative to LoRA while substantially improving memory efficiency. Beyond GPUs, LARS also reduces average CPU power and energy consumption per optimisation step by 22.43% and 22.06%, respectively. These results demonstrate that activation-efficient adaptation provides a practical path toward resource-constrained and on-device fine-tuning of LLMs.

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