Application profiling is an indispensable technique for many software development tasks, such as code and memory layout optimizations, where optimization decisions are tailored to specific program profiles. Unfortunately, modern applications codebases exhibit highly variant behavior across different inputs, creating challenges for conventional profiling approaches that rely on a single representative execution instance. In this paper, we propose \textbf{Phaedrus}, a new \textit{compiler-assisted deep learning framework} designed to predict dynamic program behaviors across varied execution instances, specifically focusing on dynamic function call prediction.Such predicted call sequences are then used for producing optimized code pertinent to a given input. Traditional profile-guided optimization methods struggle with the input-dependent variability of modern applications, where profiling on different inputs yields divergent application behaviors. To address this, Phaedrus proposes two new approaches: \textit{Application Behavior Synthesis}, a profile-less approach where Large Language Models (LLMs) directly infer dynamic functions based on source code \& static compiler analysis, bypassing the need for traditional profiling, and \textit{Application Profile Generalization}, which uses generative models trained on compressed and augmented \textit{Whole Program Path} (WPP) based function profiles to predict application behavior under unseen inputs. Our experiments show that \textit{Phaedrus} can achieve upto $10^7X$ reduction in WPP function profile sizes, can predict most frequently executed functions that cover upto 85-99\% of the execution time, along with an average of 13.68\% (upto 65\%) reduction in application binary size, and an average of 2.8\% performance improvement over the traditional profile-guided optimization.
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