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This is an early-stage theoretical preprint that proposes a geometric framework for deriving attention mechanisms. It claims to recover standard, causal, linear, tensor attention and RNNs from a common formalism, then introduces new geometric spaces as possible inspiration for architectures. Readers should treat the unifying view as a conceptual lens rather than a demonstrated performance gain, since the abstract reports no experiments, and the proposed architectures remain speculative until they are benchmarked.
Geometric knowledge spaces, Attention pairing and Architectures
arXiv:2610.29526v1 Announce Type: new Abstract: In this paper, we propose a geometric approach to deriving attention mechanisms and exploring potential new transformer architectures. We begin by formalizing the notions of knowledge worlds and attention pairings, then demonstrate how this framework naturally leads to the architectures of standard attention, causal attention, linear attention, tensor attention, and recurrent neural networks. Finally, we introduce several new geometric spaces that may inspire novel neural network architectures.
Abstract:In this paper, we propose a geometric approach to deriving attention mechanisms and exploring potential new transformer architectures. We begin by formalizing the notions of knowledge worlds and attention pairings, then demonstrate how this framework naturally leads to the architectures of standard attention, causal attention, linear attention, tensor attention, and recurrent neural networks. Finally, we introduce several new geometric spaces that may inspire novel neural network architectures.
Machine Learning (cs.LG); Algebraic Geometry (math.AG); General Topology (math.GN)
arXiv:2610.29526 [cs.LG]
(or arXiv:2610.29526v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.29526 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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