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

Haitz Sáez de Ocáriz Borde
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:554-569, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-borde26a, title = {Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention}, author = {Borde, Haitz S\'aez de Oc\'ariz}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {554--569}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/borde26a/borde26a.pdf}, url = {https://proceedings.mlr.press/v282/borde26a.html}, 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.} }
Endnote
%0 Conference Paper %T Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention %A Haitz Sáez de Ocáriz Borde %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-borde26a %I PMLR %P 554--569 %U https://proceedings.mlr.press/v282/borde26a.html %V 282 %X 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.
APA
Borde, H.S.d.O.. (2026). Beyond Parallelism: Synergistic Computational Graph Effects in Multi-Head Attention. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:554-569 Available from https://proceedings.mlr.press/v282/borde26a.html.

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