Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention

Haitz Sáez de Ocáriz Borde

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arXiv · 2507.02944

Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention

Haitz Sáez de Ocáriz Borde

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Abstract

Multi-head attention powers Transformer networks, the primary deep learning architecture behind the success of large language models (LLMs). Yet, the theoretical advantages of multi-head versus single-head attention, beyond mere parallel processing, remain underexplored. In this paper, we reframe multi-head attention as a system of potentially synergistic computational graphs, where each head functions as a feedforward directed acyclic graph (DAG) with a common sink state. We provide intuition and preliminary theoretical analysis of mixing time and minimax fidelity in this framework. Our results show that multi-head attention can synergistically enhance information propagation, yielding faster mixing times and minimax fidelity amplification under specific head-diversity conditions. Finally, we train single-head and multi-head Transformers, each with the same total number of parameters, on sequence manipulation tasks and empirically verify the predicted effects. The code is available at https://github.com/haitzsaezdeocariz/beyondparallelism.

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BibTeX RIS

Haitz Sáez de Ocáriz Borde. 2025-11-09. Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention. https://arxiv.org/abs/2507.02944

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