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.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Mathematical neuroscience
- Posed by
- Carina Curto et al.
- Year posed
- 2024
- Years open
- 1y
- Solved
- 2025-10-26
- Model
- GPT-5
- Vendor
- OpenAI
- Collaborators
- Jesse Geneson
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 8 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
"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.