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This research note investigates the theoretical capacity limits of transformer architectures regarding sequence ordering tasks, specifically demonstrating that two attention heads are required when an output MLP is present, whereas one head suffices without it. The study contributes to the foundational understanding of model expressivity and architectural efficiency within the machine learning community.

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Transformer Heads Looking for Order

arXivSeptember 24, 20261 min read

arXiv:2609.25588v1 Announce Type: new Abstract: In this note, we show that the problem of checking, whether a sequence of bits is ordered, is not doable by 1-head 1-layer transformers but is doable by a 2-head 1-layer transformer. Unlike similar previous results, our results assume the model where transformers have an output MLP.

Abstract:In this note, we show that the problem of checking, whether a sequence of bits is ordered, is not doable by 1-head 1-layer transformers but is doable by a 2-head 1-layer transformer. Unlike similar previous results, our results assume the model where transformers have an output MLP.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2609.25588 [cs.AI]

(or arXiv:2609.25588v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.25588 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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