Learning Differentiable Logic Programs for Abstract Visual Reasoning

TL;DR

This paper introduces NEUMANN, a graph-based differentiable reasoner that efficiently performs abstract visual reasoning by learning explanatory programs, surpassing existing neural and symbolic methods in complex scene understanding.

Contribution

The paper presents NEUMANN, a memory-efficient, graph-based differentiable reasoner capable of learning and applying abstract programs for visual reasoning tasks.

Findings

NEUMANN outperforms neural, symbolic, and neuro-symbolic baselines in visual reasoning tasks.

It efficiently handles structured programs with functors and complex visual scenes.

The approach enables reasoning about unseen scenes through learned abstract programs.

Abstract

Visual reasoning is essential for building intelligent agents that understand the world and perform problem-solving beyond perception. Differentiable forward reasoning has been developed to integrate reasoning with gradient-based machine learning paradigms. However, due to the memory intensity, most existing approaches do not bring the best of the expressivity of first-order logic, excluding a crucial ability to solve abstract visual reasoning, where agents need to perform reasoning by using analogies on abstract concepts in different scenarios. To overcome this problem, we propose NEUro-symbolic Message-pAssiNg reasoNer (NEUMANN), which is a graph-based differentiable forward reasoner, passing messages in a memory-efficient manner and handling structured programs with functors. Moreover, we propose a computationally-efficient structure learning algorithm to perform explanatory program induction on complex visual scenes. To evaluate, in addition to conventional visual reasoning tasks, we propose a new task, visual reasoning behind-the-scenes, where agents need to learn abstract programs and then answer queries by imagining scenes that are not observed. We empirically demonstrate that NEUMANN solves visual reasoning tasks efficiently, outperforming neural, symbolic, and neuro-symbolic baselines.