Search space is a key consideration for neural architecture search. Recently, Xie et al. (2019) found that randomly generated networks from the same distribution perform similarly, which suggests we should search for random graph distributions instead of graphs. We propose graphon as a new search space. A graphon is the limit of Cauchy sequence of graphs and a scale-free probabilistic distribution, from which graphs of different number of nodes can be drawn. By utilizing properties of the graphon space and the associated cut-distance metric, we develop theoretically motivated techniques that search for and scale up small-capacity stage-wise graphs found on small datasets to large-capacity graphs that can handle ImageNet. The scaled stage-wise graphs outperform DenseNet and randomly wired Watts-Strogatz networks, indicating the benefits of graphon theory in NAS applications.
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