A Statistical Theory of Gated Attention through the Lens of Hierarchical Mixture of Experts

Self-attention has greatly contributed to the success of the widely used Transformer architecture by enabling learning from data with long-range dependencies. In an effort to improve performance, a gated attention model that leverages a gating mechanism within the multi-head self-attention has recently been proposed as a promising alternative. Gated attention has been empirically demonstrated to increase the expressiveness of low-rank mapping in standard attention and even to eliminate the attention sink phenomenon. Despite its efficacy, a clear theoretical understanding of gated attention's benefits remains lacking in the literature. To close this gap, we rigorously show that each entry in a gated attention matrix or a multi-head self-attention matrix can be written as a hierarchical mixture of experts. By recasting learning as an expert estimation problem, we demonstrate that gated attention is more sample-efficient than multi-head self-attention. In particular, while the former needs only a polynomial number of data points to estimate an expert, the latter requires exponentially many data points to achieve the same estimation error. Furthermore, our analysis also provides a theoretical justification for why gated attention yields higher performance when a gate is placed at the output of the scaled dot product attention or the value map rather than at other positions in the multi-head self-attention architecture.

DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks

Parameter-efficient fine-tuning (PEFT) methods have become the standard paradigm for adapting large-scale models. Among these techniques, Weight-Decomposed Low-Rank Adaptation (DoRA) has been shown to improve both the learning capacity and training stability of the vanilla Low-Rank Adaptation (LoRA) method by explicitly decomposing pre-trained weights into magnitude and directional components. In this work, we propose DoRAN, a new variant of DoRA designed to further stabilize training and boost the sample efficiency of DoRA. Our approach includes two key stages: (i) injecting noise into the denominator of DoRA's weight decomposition, which serves as an adaptive regularizer to mitigate instabilities; and (ii) replacing static low-rank matrices with auxiliary networks that generate them dynamically, enabling parameter coupling across layers and yielding better sample efficiency in both theory and practice. Comprehensive experiments on vision and language benchmarks show that DoRAN consistently outperforms LoRA, DoRA, and other PEFT baselines. These results underscore the effectiveness of combining stabilization through noise-based regularization with network-based parameter generation, offering a promising direction for robust and efficient fine-tuning of foundation models.

HoRA: Cross-Head Low-Rank Adaptation with Joint Hypernetworks

Low-Rank Adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) technique that adapts large pre-trained models by adding low-rank matrices to their weight updates. However, in the context of fine-tuning multi-head self-attention (MHA), LoRA has been employed to adapt each attention head separately, thereby overlooking potential synergies across different heads. To mitigate this issue, we propose a novel Hyper-shared Low-Rank Adaptation (HoRA) method, which utilizes joint hypernetworks to generate low-rank matrices across attention heads. By coupling their adaptation through a shared generator, HoRA encourages cross-head information sharing, and thus directly addresses the aforementioned limitation of LoRA. By comparing LoRA and HoRA through the lens of hierarchical mixture of experts, our theoretical findings reveal that the latter achieves superior sample efficiency to the former. Furthermore, through extensive experiments across diverse language and vision benchmarks, we demonstrate that HoRA outperforms LoRA and other PEFT methods while requiring only a marginal increase in the number of trainable parameters.