aiqbench analysis
This research investigates the theoretical convergence properties of transformer architectures over long generation horizons, demonstrating that even minimal models can fail to stabilize without specific temperature constraints. The study reveals a fundamental limitation where no single global temperature threshold guarantees convergence across all transformer configurations, highlighting inherent instability in standard attention mechanisms.
Asymptotic Behavior of Transformers
arXiv:2610.19358v1 Announce Type: new Abstract: In this paper we study the behavior of transformer networks generating text over long periods of time. We show that even a three-token, single-layer attention-only transformer can fail to converge. We then study a rich class of transformers with arbitrary finite depth, layer normalization, MLPs, RoPE encodings, and an arbitrary mix of local and global layers. Every transformer in this class has a softmax temperature threshold above which its empirical cache distribution converges to a unique limit, independent of initial conditions. We show further that, while each transformer has a temperature threshold, the supremum of this set is infinite, so there is no global minimal temperature that forces all transformers to converge.
Abstract:In this paper we study the behavior of transformer networks generating text over long periods of time. We show that even a three-token, single-layer attention-only transformer can fail to converge. We then study a rich class of transformers with arbitrary finite depth, layer normalization, MLPs, RoPE encodings, and an arbitrary mix of local and global layers. Every transformer in this class has a softmax temperature threshold above which its empirical cache distribution converges to a unique limit, independent of initial conditions. We show further that, while each transformer has a temperature threshold, the supremum of this set is infinite, so there is no global minimal temperature that forces all transformers to converge.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Statistics Theory (math.ST)
arXiv:2610.19358 [cs.LG]
(or arXiv:2610.19358v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.19358 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 212 words
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