An important goal of neural architecture search (NAS) is to automate-away the design of neural networks on new tasks in under-explored domains. Motivated by this broader vision for NAS, we study the problem of enabling users to discover the right neural operations given data from their specific domain. We introduce a search space of neural operations called XD-Operations that mimic the inductive bias of standard multichannel convolutions while being much more expressive: we prove that XD-operations include many named operations across several application areas. Starting with any standard backbone network such as LeNet or ResNet, we show how to transform it into an architecture search space over XD-operations and how to traverse the space using a simple weight-sharing scheme. On a diverse set of applications--image classification, solving partial differential equations (PDEs), and sequence modeling--our approach consistently yields models with lower error than baseline networks and sometimes even lower error than expert-designed domain-specific approaches.
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