A Counterexample to Fourier Alignment in Single-Neuron Modular Addition

We give a negative solution to MAIS-O60. We first construct an example in which an initially active ReLU neuron becomes completely inactive in finite time and thereafter remains frozen at a limit whose Fourier energy is equally distributed among all nonzero real frequency classes. The counterexample holds on an open set of initial conditions and therefore occurs with positive probability under Gaussian initialization. An appendix prepared by GPT-5.6 Sol strengthens the counterexample by showing

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ethics.ai (5 August 2026), “A Counterexample to Fourier Alignment in Single-Neuron Modular Addition,” evidence record 16973, https://ethics.ai/record/16973 (originally published by arXiv cs.LG).

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