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Curto et al.'s Minimality Conjecture for Threshold-Linear Networks

Differential equations · posed by Carina Curto et al., 2024 · disproved

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Statement

Curto et al. (Advances in Applied Mathematics, 2024) conjectured that every stable fixed point of a threshold-linear network is minimal. Disproved: an explicit competitive 3-neuron TLN has a stable fixed point whose support strictly contains another's, and 3 neurons is proven smallest possible.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Jesse Geneson, using GPT-5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    "We used GPT-5 to find the 3-neuron counterexample and to draft some of the expository text." The minimality of the construction and the expansions to larger networks are the author's.

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