Problem MAIS-O60: Single-Neuron Fourier Alignment
Does a single ReLU neuron trained on modular addition align to one Fourier frequency? Open Problem MAIS-O60, itself posed by Claude Fable 5 under the direction of Lionel Levine, is answered negatively: an explicit construction reaches a frozen state whose Fourier energy is spread equally across all nonzero frequency classes, on an open set of initial conditions.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Neural network training dynamics
- Posed by
- Claude Fable 5 (directed by Lionel Levine)
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-08-05
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Gautam Neelakantan Memana
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The main counterexample is the author's, with GPT-5.6 Sol assisting the literature review and problem clarification. The strengthened results in Appendix A were developed through conversations with GPT-5.6 Sol, which also produced the appendix's initial draft. A rare full loop: the problem was posed by one model and its strengthening drafted by another.