TLoRA: Tri-Matrix Low-Rank Adaptation of Large Language Models

We propose TLoRA, a novel tri-matrix low-rank adaptation method that decomposes weight updates into three matrices: two fixed random matrices and one trainable matrix, combined with a learnable, layer-wise scaling factor. This tri-matrix design enables TLoRA to achieve highly efficient parameter adaptation while introducing minimal additional computational overhead. Through extensive experiments on the GLUE benchmark, we demonstrate that TLoRA achieves comparable performance to existing low-rank methods such as LoRA and Adapter-based techniques, while requiring significantly fewer trainable parameters. Analyzing the adaptation dynamics, we observe that TLoRA exhibits Gaussian-like weight distributions, stable parameter norms, and scaling factor variability across layers, further highlighting its expressive power and adaptability. Additionally, we show that TLoRA closely resembles LoRA in its eigenvalue distributions, parameter norms, and cosine similarity of updates, underscoring its ability to effectively approximate LoRA's adaptation behavior. Our results establish TLoRA as a highly efficient and effective fine-tuning method for LLMs, offering a significant step forward in resource-efficient model adaptation.