  \textit{Differentiable ARchiTecture Search} (DARTS) has recently become the
mainstream of neural architecture search (NAS) due to its efficiency and
simplicity. With a gradient-based bi-level optimization, DARTS alternately
optimizes the inner model weights and the outer architecture parameter in a
weight-sharing supernet. A key challenge to the scalability and quality of the
learned architectures is the need for differentiating through the inner-loop
optimisation. While much has been discussed about several potentially fatal
factors in DARTS, the architecture gradient, a.k.a. hypergradient, has received
less attention. In this paper, we tackle the hypergradient computation in DARTS
based on the implicit function theorem, making it only depends on the obtained
solution to the inner-loop optimization and agnostic to the optimization path.
To further reduce the computational requirements, we formulate a stochastic
hypergradient approximation for differentiable NAS, and theoretically show that
the architecture optimization with the proposed method, named iDARTS, is
expected to converge to a stationary point. Comprehensive experiments on two
NAS benchmark search spaces and the common NAS search space verify the
effectiveness of our proposed method. It leads to architectures outperforming,
with large margins, those learned by the baseline methods.
