Challenge: Existing methods for large language models constrain update to low-rank subspaces, limiting expressiveness and performance.
Approach: They propose a distributed PEFT approach that initializes adapters across different devices and aggregates their delta updates collectively on (W) Empirically, HD-PiSSA provides 16 higher effective updated ranks than data-parallel LoRA or PiSSA when fine-tuning on 8 GPUs with the same per-device adapter rank.
Outcome: Empirically, HD-PiSSA outperforms LoRA and PiSSA in math, code, and multi-task learning tasks.

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