Problem MAIS-O60: Single-Neuron Fourier Alignment
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Statement
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.
Context
A machine-posed 2026 problem from a curated open-problems list; real and documented, with no accumulated literature.
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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.
Reviews
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