  Recent efforts to scale Transformer models have demonstrated rapid progress
across a wide range of tasks (Wei et al., 2022). However, fine-tuning these
models for downstream tasks is expensive due to their large parameter counts.
Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable
alternative by allowing us to fine-tune models by updating only a small number
of parameters. In this work, we propose a general framework for parameter
efficient fine-tuning (PEFT), based on structured unrestricted-rank matrices
(SURM) which can serve as a drop-in replacement for popular approaches such as
Adapters and LoRA. Unlike other methods like LoRA, SURMs provides more
flexibility in finding the right balance between compactness and
expressiveness. This is achieved by using low displacement rank matrices
(LDRMs), which hasn't been used in this context before. SURMs remain
competitive with baselines, often providing significant quality improvements
while using a smaller parameter budget. SURMs achieve 5-7% accuracy gains on
various image classification tasks while replacing low-rank matrices in LoRA.
It also results in up to 12x reduction of the number of parameters in adapters
(with virtually no loss in quality) on the GLUE benchmark.
