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

• URL: http://arxiv.org/abs/2507.02944v1
• Date: Sat, 28 Jun 2025 11:35:31 GMT
• Title: Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention
• Authors: Haitz Sáez de Ocáriz Borde,
• Abstract summary: Multi-head attention powers Transformer networks, the primary deep learning architecture behind the success of large language models (LLMs)<n>Yet, the theoretical advantages of multi-head versus single-head attention, beyond mere parallel processing, remain underexplored.<n>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.
• Score: 1.3597551064547502
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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