Can a Python program be executed statement-by-statement by neural networks composed according to the source code? We formulate the Neuro-Symbolic Execution Problem and introduce Neural Interpretation (NI), the first neural model for the execution of generic source code that allows missing definitions. NI preserves source code structure, where every variable has a vector encoding, and every function executes a neural network. NI is a novel neural model of computers with a compiler architecture that can assemble neural layers "programmed" by source code. NI is the first neural model capable of executing Py150 dataset programs, including library functions without concrete inputs, and it can be trained with flexible code understanding objectives. We demonstrate white-box execution without concrete inputs for variable misuse localization and repair.

The ability to generalize out-of-domain (OOD) is an important goal for deep neural network development, and researchers have proposed many high-performing OOD generalization methods from various foundations. While many OOD algorithms perform well in various scenarios, these systems are evaluated as ``black-boxes''. Instead, we propose a flexible framework that evaluates OOD systems with finer granularity using a probing module that predicts the originating domain from intermediate representations. We find that representations always encode some information about the domain. While the layerwise encoding patterns remain largely stable across different OOD algorithms, they vary across the datasets. For example, the information about rotation (on RotatedMNIST) is the most visible on the lower layers, while the information about style (on VLCS and PACS) is the most visible on the middle layers. In addition, the high probing results correlate to the domain generalization performances, leading to further directions in developing OOD generalization systems.