GEARS: Geometric Expansion with Adaptive Routing and Scaffolds - A Graph-Navigation Architecture as an Alternative to Self-Attention

This paper introduces GEARS (Geometric Expansion with Adaptive Routing and Scaffolds), a proposed neural network architecture that takes a different approach to language processing. Instead of comparing every token with every other token through standard attention, GEARS is designed to move through a structured graph of concepts. The model organizes information across several levels, starting from a shared 3D semantic core and extending to higher-dimensional levels such as 6D, 12D, and 24D. The first three coordinates are preserved at every level, allowing any representation to collapse back to this core in constant time. Concepts are placed on precomputed geometric lattices using learnable classifiers trained end-to-end, without requiring manually defined target positions. Connections between levels ("wormholes") provide shortcuts, support context-sensitive routing, help stabilize newly emerging concepts, and allow the architecture to expand to new levels over time. The local structure of the graph can also adapt to different types of data by automatically forming hyperbolic or spherical geometric regions based on Ricci curvature analysis. GEARS also includes a separate sequence module for handling word order and morphology. Its design is motivated by a two-level model of language processing in the brain proposed by Casto, Fedorenko et al. (arXiv:2511.19757). In this design, semantic content and sentence structure are treated as partly distinct problems: the concept graph represents meaning, while the sequence module manages grammatical form and ordering. This separation is intended to make the architecture more flexible across languages with different word-order and morphological patterns. The architecture is also designed with continual learning in mind. It includes top-down and bottom-up concept placement, together with a six-phase training procedure that allows the graph to grow gradually as new structure is learned. Status: architectural proposal / preprint. Experimental validation on standard benchmarks is ongoing. This publication establishes architectural priority and provides a complete formal specification of GEARS.