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With the growing workload of inference tasks on mobile devices, state-of-the-art neural architectures (NAs) are typically designed through Neural Architecture Search (NAS) to identify NAs with good tradeoffs between accuracy and efficiency (e.g., latency). Since measuring the latency of a huge set of candidate architectures during NAS is not scalable, approaches are needed for predicting end-to-end inference latency on mobile devices. Such predictions are challenging due to hardware heterogeneity, optimizations applied by ML frameworks, and the diversity of neural architectures. Motivated by these challenges, in this paper, we first quantitatively assess characteristics of neural architectures and mobile devices that have significant effects on inference latency. Based on this assessment, we propose a latency prediction framework which addresses these challenges by developing operation-wise latency predictors, under a variety of settings and a number of hardware devices, with multi-core CPUs and GPUs, achieving high accuracy in end-to-end latency prediction, as shown by our comprehensive evaluations. To illustrate that our approach does not require expensive data collection, we also show that accurate predictions can be achieved on real-world NAs using only small amounts of profiling data.