  While neural architecture search (NAS) has enabled automated machine learning
(AutoML) for well-researched areas, its application to tasks beyond computer
vision is still under-explored. As less-studied domains are precisely those
where we expect AutoML to have the greatest impact, in this work we study NAS
for efficiently solving diverse problems. Seeking an approach that is fast,
simple, and broadly applicable, we fix a standard convolutional network (CNN)
topology and propose to search for the right kernel sizes and dilations its
operations should take on. This dramatically expands the model's capacity to
extract features at multiple resolutions for different types of data while only
requiring search over the operation space. To overcome the efficiency
challenges of naive weight-sharing in this search space, we introduce DASH, a
differentiable NAS algorithm that computes the mixture-of-operations using the
Fourier diagonalization of convolution, achieving both a better asymptotic
complexity and an up-to-10x search time speedup in practice. We evaluate DASH
on ten tasks spanning a variety of application domains such as PDE solving,
protein folding, and heart disease detection. DASH outperforms state-of-the-art
AutoML methods in aggregate, attaining the best-known automated performance on
seven tasks. Meanwhile, on six of the ten tasks, the combined search and
retraining time is less than 2x slower than simply training a CNN backbone that
is far less accurate.
