Semantic Probabilistic Layers for Neuro-Symbolic Learning

Kareem Ahmed, Stefano Teso, Kai-Wei Chang, Guy Van den Broeck, Antonio Vergari

Abstract: 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 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 show SPLs outperform such competitors in terms of accuracy on challenging SOP tasks including hierarchical multi-label classification, pathfinding and preference learning, while retaining perfect constraint satisfaction.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2206.00426/code)