aiqbench analysis
This paper introduces DAMCHA, a novel attention mechanism that generalizes Multi-Head Attention by learning dynamic, input-dependent Mahalanobis metrics to capture inter-head interactions previously ignored by standard Euclidean similarity. By parameterizing the metric matrix as a function of the data's intrinsic manifold structure, this approach offers a drop-in replacement for existing Transformer architectures with comparable computational overhead but superior expressive power. The work represents a significant theoretical and practical advancement in optimizing the core mechanics of large language models and other sequence modeling tasks.
Data-Adaptive Mahalanobis Metric Learning for Cross-Head Attention in Transformers
arXiv:2610.13261v1 Announce Type: new Abstract: In this paper, we propose Data-Adaptive Mahalanobis Cross-Head Attention (DAMCHA), a simple and effective attention mechanism that generalizes Multi-Head Attention (MHA) through the lens of metric learning. Standard MHA implicitly learns a static, head-wise Euclidean similarity corresponding to the diagonal blocks of a unified cross-head metric matrix, discarding all off-diagonal interactions across heads. DAMCHA addresses this limitation via two key innovations. First, it learns the full cross-head metric matrix, inducing a Mahalanobis-like similarity that explicitly captures inter-head interactions beyond the restricted block-diagonal structure of MHA. Second, it parameterizes the metric matrix as an input-dependent function, enabling the attention geometry to dynamically adapt to the intrinsic manifold structure of the data rather than remaining fixed after training. We further introduce principled regularization strategies, most notably stack-wise parameter sharing, to ensure computational efficiency and stable optimization. DAMCHA serves as a drop-in replacement for MHA and its variants in various Transformer architectures, delivering superior expressive power and learning performance with comparable or reduced computational overhead. Extensive experiments demonstrate that DAMCHA-based Transformers consistently outperform competing baselines across a range of benchmark tasks. Code is available at https://github.com/erwinmsmith/DAMCHA.
Abstract:In this paper, we propose Data-Adaptive Mahalanobis Cross-Head Attention (DAMCHA), a simple and effective attention mechanism that generalizes Multi-Head Attention (MHA) through the lens of metric learning. Standard MHA implicitly learns a static, head-wise Euclidean similarity corresponding to the diagonal blocks of a unified cross-head metric matrix, discarding all off-diagonal interactions across heads. DAMCHA addresses this limitation via two key innovations. First, it learns the full cross-head metric matrix, inducing a Mahalanobis-like similarity that explicitly captures inter-head interactions beyond the restricted block-diagonal structure of MHA. Second, it parameterizes the metric matrix as an input-dependent function, enabling the attention geometry to dynamically adapt to the intrinsic manifold structure of the data rather than remaining fixed after training. We further introduce principled regularization strategies, most notably stack-wise parameter sharing, to ensure computational efficiency and stable optimization. DAMCHA serves as a drop-in replacement for MHA and its variants in various Transformer architectures, delivering superior expressive power and learning performance with comparable or reduced computational overhead. Extensive experiments demonstrate that DAMCHA-based Transformers consistently outperform competing baselines across a range of benchmark tasks. Code is available at this https URL.
Machine Learning (cs.LG)
arXiv:2610.13261 [cs.LG]
(or arXiv:2610.13261v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.13261 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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