Scalable Neural-Probabilistic Answer Set Programming

TL;DR

This paper introduces SLASH, a scalable neural-probabilistic answer set programming framework that integrates neural models with probabilistic logic programming, enabling comprehensive joint probability estimation and efficient reasoning.

Contribution

SLASH combines neural probabilistic predicates with answer set programming, allowing flexible probabilistic queries and scalable inference in neuro-symbolic AI systems.

Findings

SLASH effectively performs probabilistic reasoning on complex tasks.

It scales well by pruning insignificant parts of the program.

Demonstrated on MNIST addition and VQA benchmarks.

Abstract

The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic programming to be carried out via the probability estimations of deep neural networks. However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel $+/-$ notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on a variety of different tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).