Semantic Probabilistic Layers for Neuro-Symbolic Learning
This addresses the problem of integrating logical constraints into neural networks for structured-output tasks, offering a modular solution with broad applicability in neuro-symbolic learning.
The authors tackled structured-output prediction by designing a Semantic Probabilistic Layer that ensures predictions satisfy symbolic constraints, achieving higher accuracy than competitors on tasks like hierarchical classification while maintaining perfect constraint satisfaction.
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer (SPL) can model intricate correlations, and hard constraints, over a structured output space all while being amenable to end-to-end learning via maximum likelihood. SPLs combine exact probabilistic inference with logical reasoning in a clean and modular way, learning complex distributions and restricting their support to solutions of the constraint. As such, they can faithfully, and efficiently, model complex SOP tasks beyond the reach of alternative neuro-symbolic approaches. We empirically demonstrate that SPLs outperform these competitors in terms of accuracy on challenging SOP tasks including hierarchical multi-label classification, pathfinding and preference learning, while retaining perfect constraint satisfaction.