One-Shot Localisation of the Global Minimum of a Noisy One-Dimensional Function: An Iterative Neural Minimizer Compared with Set Transformers and Classical Estimators

arXiv:2604.03614v4 Announce Type: replace-cross Abstract: We study a passive form of global optimisation: from twenty noisy samples of an unknown one-dimensional function, predict where its global minimum lies, with no further queries. We introduce the Neural Function Minimizer (NFM), an iterative model that walks a position across the domain and, at every step, reads the samples near that position and attends to all twenty of them, and we compare it with two Set Transformers of the same size trained on the same data, one that answers with a single point and one that answers with a mixture of

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