Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses
Researchers have analyzed the parameterized complexity of testing stationarity for continuous piecewise-affine functions, a core task in nonsmooth optimization. Their findings reveal fixed-dimensional tractability for certain aspects and W[1]-hardness for others, with lower bounds suggesting algorithms cannot efficiently scale with the instance size relative to dimension. These results also extend to testing local minimality for PA functions and have implications for analyzing shallow ReLU CNN training losses. AI
IMPACT Provides theoretical insights into the computational complexity of training certain neural network architectures.