Exploring many execution paths in a binary program is essential to discover new vulnerabilities. Dynamic Symbolic Execution (DSE) is useful to trigger complex input conditions and enables an accurate exploration of a program while providing extensive crash replayability and semantic insights. However, scaling this type of analysis to complex binaries is difficult. Current methods suffer from the path explosion problem, despite many attempts to mitigate this challenge (e.g., by merging paths when appropriate). Still, in general, this challenge is not yet surmounted, and most bugs discovered through such techniques are shallow. We propose a novel approach to address the path explosion problem: A smart triaging system that leverages supervised machine learning techniques to replicate human expertise, leading to vulnerable path discovery. Our approach monitors the execution traces in vulnerable programs and extracts relevant features - register and memory accesses, function complexity, system calls - to guide the symbolic exploration. We train models to learn the patterns of vulnerable paths from the extracted features, and we leverage their predictions to discover interesting execution paths in new programs. We implement our approach in a tool called SyML, and we evaluate it on the Cyber Grand Challenge (CGC) dataset - a well-known dataset of vulnerable programs - and on 3 real-world Linux binaries. We show that the knowledge collected from the analysis of vulnerable paths, without any explicit prior knowledge about vulnerability patterns, is transferrable to unseen binaries, and leads to outperforming prior work in path prioritization by triggering more, and different, unique vulnerabilities.