A Neural Rewriting System to Solve Algorithmic Problems

Modern neural network architectures still struggle to learn algorithmic procedures that require to systematically apply compositional rules to solve out-of-distribution problem instances. In this work, we propose an original approach to learn algorithmic tasks inspired by rewriting systems, a classic framework in symbolic artificial intelligence. We show that a rewriting system can be implemented as a neural architecture composed by specialized modules: the Selector identifies the target sub-expression to process, the Solver simplifies the sub-expression by computing the corresponding result, and the Combiner produces a new version of the original expression by replacing the sub-expression with the solution provided. We evaluate our model on three types of algorithmic tasks that require simplifying symbolic formulas involving lists, arithmetic, and algebraic expressions. We test the extrapolation capabilities of the proposed architecture using formulas involving a higher number of operands and nesting levels than those seen during training, and we benchmark its performance against the Neural Data Router, a recent model specialized for systematic generalization, and a state-of-the-art large language model (GPT-4) probed with advanced prompting strategies.