The world sees a proliferation of machine learning/deep learning (ML) models and their wide adoption in different application domains recently. This has made the profiling and characterization of ML models an increasingly pressing task for both hardware designers and system providers, as they would like to offer the best possible computing system to serve ML models with the desired latency, throughput, and energy requirements while maximizing resource utilization. Such an endeavor is challenging as the characteristics of an ML model depend on the interplay between the model, framework, system libraries, and the hardware (or the HW/SW stack). A thorough characterization requires understanding the behavior of the model execution across the HW/SW stack levels. Existing profiling tools are disjoint, however, and only focus on profiling within a particular level of the stack. This paper proposes a leveled profiling design that leverages existing profiling tools to perform across-stack profiling. The design does so in spite of the profiling overheads incurred from the profiling providers. We coupled the profiling capability with an automatic analysis pipeline to systematically characterize 65 state-of-the-art ML models. Through this characterization, we show that our across-stack profiling solution provides insights (which are difficult to discern otherwise) on the characteristics of ML models, ML frameworks, and GPU hardware.