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

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curto-minimal-fixed-pointsDifferential equationsposed by Carina Curto et al., 2024recorded: disproved

1 attempt · no person has looked

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.

Context

A 2024 published conjecture from the Curto school of combinatorial neural network dynamics; recent, with a small but active audience.

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  • #1

    Attempt 1

    constructionGPT-5 with Jesse Geneson ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5
    people
    Jesse Geneson

    "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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