Blockwise Hadamard high-Rank Adaptation for Parameter-Efficient LLM Fine-Tuning

Parameter-efficient fine-tuning (PEFT) methods must be resource-efficient yet handle heterogeneous reasoning transformations, and classical low-rank adaptation (LoRA) is constrained by the nominal rank $r$. Hadamard-style extensions like HiRA raise the nominal rank but couple every update to the global energy pattern of the frozen weight matrix, while ABBA trades this inductive bias for fully learned dense intermediates. To address the limitation of global modulation, we propose Block Hadamard high-Rank Adaptation (BHRA), which partitions each weight matrix and applies HiRA-style multiplicative modulation independently within every block, preserving the PEFT parameter footprint while unlocking localized rank amplification. Our empirical analyses reveal that this blockwise design maintains rich spectra across rank budgets, mitigating the collapse induced by global modulation. Across eight commonsense reasoning tasks and two arithmetic benchmarks with Llama-3.2 1B/3B, Mistral-7B, and Gemma-2 9B, BHRA consistently surpasses strong PEFT baselines under matched parameter budgets.