Spatial Memory as a Universal Computer: How Finite Brains Generalize Without Bound
This paper proposes that generalization beyond training length arises when a learner reads only coincidences (invariant relations) rather than coordinates (position, count, time). It argues that such a learner's memory must be cyclic, linking to grid cells, place cells, and the hippocampal index, and that this architecture achieves Turing-complete computation. The authors report that their machine trained on strings up to 40 symbols achieves at least 99% accuracy on lengths 41-500 for nine of fifteen benchmark tasks, including five that LSTM/Transformer cannot solve, and can reverse strings of 15,015 symbols when given new cycles.
Why it matters: Offers a novel theoretical framework connecting neuroscience to AI generalization, with concrete benchmark results showing advantages over standard sequence models.