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This paper advances the theoretical understanding of deep transformers by modeling them as mean-field interacting systems capable of distributed inference through internal "function vectors." The research demonstrates how architectural depth enables these models to adaptively infer latent context variables at finer scales than previously theorized, offering new insights into their in-context learning capabilities.
Adaptive inference and function vectors in deep transformers
arXiv:2606.16694v1 Announce Type: new Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious. We introduce a theory of a deep transformer as a mean-field interacting system that implements distributed inference, subject to constraints on communication, locality and depth. We show that such a system can exploit internal state representations ('function vectors') to infer a latent context variable at increasingly finer scales over its layers. In an in-context regression task, the theory predicts a non-trivial relationship between non-Gaussian, hierarchical structure in the latent context variable, and transformer depth. Predictions are tested using constrained linear attention transformers and demonstrate adaptive inference in deep architectures. Feedforward blocks and depth enable transformers to implement a much richer class of in-context learning algorithms than previously described.
Abstract:Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious. We introduce a theory of a deep transformer as a mean-field interacting system that implements distributed inference, subject to constraints on communication, locality and depth. We show that such a system can exploit internal state representations ('function vectors') to infer a latent context variable at increasingly finer scales over its layers. In an in-context regression task, the theory predicts a non-trivial relationship between non-Gaussian, hierarchical structure in the latent context variable, and transformer depth. Predictions are tested using constrained linear attention transformers and demonstrate adaptive inference in deep architectures. Feedforward blocks and depth enable transformers to implement a much richer class of in-context learning algorithms than previously described.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Applied Physics (physics.app-ph); Neurons and Cognition (q-bio.NC)
arXiv:2606.16694 [cs.LG]
(or arXiv:2606.16694v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.16694 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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