Low-Rank Interconnected Adaptation across Layers

Low-rank adaptation (LoRA) is a powerful parameter-efficient fine-tuning method that utilizes low-rank projectors \(A\) and \(B\) to learn weight updates \(\Delta W\) for adaptation targets \(W\). Previous research has shown that LoRA is essentially a gradient compressor, performing random projections on the gradient using a fixed projection matrix \(A_0\). However, this setup restricts the overall weight update to be low-rank, which limits the adaptation performance. In this paper, we propose low-rank interconnected adaptation across layers (Lily). Specifically, we employ a hierarchical framework where low-dimensional projectors (LPs) retained for downward projection at a particular level, while globally-shared high-dimensional projector (HP) experts perform upward projection across all levels of layers. Lily uniquely connects each LP to all HP experts, therefore the gradient projections are no longer dominated by fixed projection matrices, but rather by selective combinations of all the projectors, thereby breaking the low-rank constraint of LoRA. Furthermore, Lily's cross-layer connections facilitate the capture of intricate information and dependencies across different layers, thereby enhancing the model's representational capabilities. Experiments across various modalities, architectures, and model sizes underscore Lily's great performance and efficiency. Code is available on github https://github.com/yibozhong/lily.