Testing approximate first-order stationarity for continuous PA functions is XP-tractable but W[1]-hard (with ETH lower bounds) when parameterized by dimension d, and the same parameterized complexity classification holds for stationarity testing in shallow ReLU CNN weight space.
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Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses
Testing approximate first-order stationarity for continuous PA functions is XP-tractable but W[1]-hard (with ETH lower bounds) when parameterized by dimension d, and the same parameterized complexity classification holds for stationarity testing in shallow ReLU CNN weight space.