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arXiv Machine Learning By Xiaoyu Li, Lequan Lin, Dai Shi, Jiaojiao Jiang, Junbin Gao, Andi Han

The Ball and the Box: Two Geometries of Computation in Superposition

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The paper investigates how neural representations that use superposition can encode more features than their dimensionality. It derives sharp dimension thresholds for computing Boolean gates with a single threshold layer, distinguishing between two error criteria: a vanishing expected error count and high‑probability correctness of every output. The study reveals that the expected‑count threshold follows a ball geometry, while joint reliability follows a box geometry, and provides explicit thresholds for conjunction, disjunction, and majority gates, including a transition analysis for pairwise conjunction.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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