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.

设计了一个语义概率层，可以将其插入到任何神经网络中，保证其预测与一组预先定义的符号约束一致，以此来预测结构化输出，它能够模拟复杂的相关性和硬约束，实现最大似然的端到端学习，对于其他神经符号方法无法处理的结构化输出任务，SPL 的效果要好得多，并且能够满足完美的约束条件。