Finite Brains Generalize Without Bound: Spatial Memory as a Universal Computer

Summary

The paper proposes that finite neural systems can generalize to arbitrary input lengths by relying on coincidences (e.g., equality) rather than coordinates (e.g., position, count, time). It introduces a memory architecture based on cycles, grid modules, place cells, and a hippocampal index, which enables a machine to compute Turing-computable functions. Trained on strings up to 40 symbols, the model achieves at least 99% accuracy on lengths 41–500 for nine of fifteen benchmark tasks, including five that LSTMs and Transformers fail, and can reverse strings of 15,015 symbols without error when given new cycles.

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Why it matters by industry

• Artificial intelligence

  This work directly addresses the 'Reasoning' and 'Models' subtopics by proposing a novel neural architecture that achieves length generalization, a key challenge in AI reasoning and model design.