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Application profiling is an indispensable technique for many software development tasks, such as code optimization and memory management, 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 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 scenarios, specifically focusing on dynamic function call prediction. 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 Profile Generalization}, which uses generative models trained on compressed and augmented \textit{Whole Program Path} (WPP) profiles to predict application behavior under unseen inputs, and \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. Our experiments show that \textit{Phaedrus} can achieve upto \(10^7X\) reduction in WPP profile sizes, can predict dynamic hot functions that cover upto 85-99\% of the execution time, along with an average of \textbf{13.46\%} (upto \textbf{65\%}) reduction in application binary size reduction, without profiles.