Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed. We propose GAP, a Generalizable Approximate Partitioning framework that takes a deep learning approach to graph partitioning. We define a differentiable loss function that represents the partitioning objective. Unlike baselines that redo the optimization per graph, GAP is capable of generalization, allowing us to train models that produce performant partitions at inference time, even on unseen graphs. Furthermore, because we learn the representation of the graph while jointly optimizing for the partitioning loss function, GAP can be easily tuned for a variety of graph structures. We evaluate the performance of GAP on graphs of varying sizes and structures, including graphs of widely used machine learning models (e.g., ResNet, VGG, and Inception-V3), scale-free graphs, and random graphs.