  The recently proposed training-free NAS methods abandon the training phase
and design various zero-cost proxies as scores to identify excellent
architectures, arousing extreme computational efficiency for neural
architecture search. In this paper, we raise an interesting problem: can we
properly measure the operation importance in DARTS through a training-free way,
with avoiding the parameter-intensive bias? We investigate this question
through the lens of edge connectivity, and provide an affirmative answer by
defining a connectivity concept, ZERo-cost Operation Sensitivity (ZEROS), to
score the importance of candidate operations in DARTS at initialization. By
devising an iterative and data-agnostic manner in utilizing ZEROS for NAS, our
novel trial leads to a framework called training free differentiable
architecture search (FreeDARTS). Based on the theory of Neural Tangent Kernel
(NTK), we show the proposed connectivity score provably negatively correlated
with the generalization bound of DARTS supernet after convergence under
gradient descent training. In addition, we theoretically explain how ZEROS
implicitly avoids parameter-intensive bias in selecting architectures, and
empirically show the searched architectures by FreeDARTS are of comparable
size. Extensive experiments have been conducted on a series of search spaces,
and results have demonstrated that FreeDARTS is a reliable and efficient
baseline for neural architecture search.
