Problem MAIS-O60: Single-Neuron Fourier Alignment
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.
Record
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Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Gautam Neelakantan Memana, using GPT-5.6 SolThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
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