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• W2963325933 abstract "Although neural networks are routinely and successfully trained in practice using simple gradient-based methods, most existing theoretical results are negative, showing that learning such networks is difficult, in a worst-case sense over all data distributions. In this paper, we take a more nuanced view, and consider whether specific assumptions on the niceness of the input distribution, or niceness of the target function (e.g. in terms of smoothness, non-degeneracy, incoherence, random choice of parameters etc.), are sufficient to guarantee learnability using gradient-based methods. We provide evidence that neither class of assumptions alone is sufficient: On the one hand, for any member of a class of nice target functions, there are difficult input distributions. On the other hand, we identify a family of simple target functions, which are di_cult to learn even if the input distribution is nice. To prove our results, we develop some tools which may be of independent interest, such as extending Fourier-based hardness techniques developed in the context of statistical queries (Blum et al., 1994), from the Boolean cube to Euclidean space and to more general classes of functions." @default.
• W2963325933 created "2019-07-30" @default.
• W2963325933 creator A5017753135 @default.
• W2963325933 date "2018-01-01" @default.
• W2963325933 modified "2023-09-27" @default.
• W2963325933 title "Distribution-specific hardness of learning neural networks" @default.
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