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differential-equations / Mathematical neuroscience

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

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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differential-equationsOct 26, 2025Significance 8/100Registry: unreviewed

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

Prior state unknown→disproved

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.

Source authenticatedCurto et al.'s Minimality Conjecture for Threshold-Linear Networks →
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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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Curto et al.'s Minimality Conjecture for Threshold-Linear Networks — Mathematical Frontier Network