Title: Energy-Aware Neural Architecture Optimization with Fast Splitting Steepest Descent. Abstract: Designing energy-efficient networks is of critical importance for enabling state-of-the-art deep learning in mobile and edge settings where the computation and energy budgets are highly limited. Recently, Wu et al. (2019) framed the search of efficient neural architectures into a continuous splitting process: it iteratively splits existing neurons into multiple off-springs to achieve progressive loss minimization,  thus finding novel architectures by gradually growing the neural network. However, this method was not specifically tailored for designing energy-efficient networks, and is computationally expensive on large-scale benchmarks.  In this work, we substantially improve Wu et al. (2019) in two significant ways:  1) we incorporate the energy cost of splitting different neurons to better guide the splitting process, thereby discovering more energy-efficient network architectures; 2) we substantially speed up the splitting process of Wu et al. (2019), which requires expensive eigen-decomposition, by proposing a highly scalable Rayleigh-quotient stochastic gradient algorithm.  Our fast algorithm allows us to reduce the computational cost of splitting to the same level of typical back-propagation updates and enables efficient implementation on GPU. Extensive empirical results show that our method can train highly accurate and energy-efficient networks on challenging datasets such as ImageNet,  improving a variety of baselines,  including the pruning-based methods and expert-designed architectures.