Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have significantly reduced the number of trainable parameters needed in fine-tuning large language models (LLMs).The developments of LoRA-style adapters have considered two main directions: (1) enhancing model expressivity with high-rank adapters, and (2) aiming for further parameter reduction, as exemplified by vector-based methods.However, these approaches come with a trade-off, as achieving the expressivity of high-rank weight updates typically comes at the cost of sacrificing the extreme parameter efficiency offered by vector-based techniques.To address this issue, we propose a vector-based random Tensor network for high-Rank Adaptation (TeRA), a novel PEFT method that achieves high-rank weight updates while retaining the parameter efficiency of vector-based PEFT adapters.This is achieved by parametrizing the tensorized weight update matrix as a Tucker-like tensor network (TN), whereby large randomly initialized factors are frozen and shared across layers, while only small layer-specific scaling vectors, corresponding to diagonal entries of factor matrices, are trained.Comprehensive experiments demonstrate that TeRA matches or even outperforms existing high-rank adapters, while requiring as few trainable parameters as vectorbased methods.Theoretical analysis and ablation studies validate the effectiveness of the proposed TeRA method.The code is available at https://github.com/guyuxuan9/TeRA.

The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not efficiently utilise the Multi-head Attention (MHA) block, which is the core of transformer architectures. To address this issue, we propose a novel intuitive framework that, at its very core, performs MHA compression through a multi-head tensorisation process and the Tucker decomposition. This enables both higher-dimensional structured denoising and compression of the MHA weights, by enforcing a shared higher-dimensional subspace across the weights of the multiple attention heads. We demonstrate that this approach consistently enhances the reasoning capabilities of LLMs across multiple benchmark datasets, and for both encoder-only and decoder-only architectures, while achieving compression rates of up to ~ 250 times in the MHA weights, all without requiring any additional data, training, or fine-tuning. Furthermore, we show that the proposed method can be seamlessly combined with existing FFN-only-based denoising techniques to achieve further improvements in LLM reasoning performance.1