A Complexity Map of Probabilistic Reasoning for Neurosymbolic Classification Techniques

2024-04-12

AI Summary

Scalability of probabilistic inference in neural-symbolic AI remains unresolved for multi-label classification tasks. Method: This paper introduces the first unified formal framework for probabilistic inference in neural-symbolic classification, systematically characterizing the asymptotic complexity (P/NP/#P-equivalence classes) of four core inference problems and constructing the inaugural probabilistic inference complexity map. The approach integrates formal semantic modeling, computational complexity analysis, probabilistic logic compilation, and prior knowledge injection. Contributions/Results: (1) The first unified complexity map covering diverse inference problems; (2) Identification of a dual constraint mechanism—where expressivity of knowledge representation languages and classification scale jointly limit scalability; (3) Theoretical scalability criteria for mainstream systems (e.g., ProbLog, DLV2+BN, NeuroSAT), precisely delineating their applicability boundaries. The work consolidates and extends over ten decidability results, enabling principled selection and design of neural-symbolic systems.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of neurosymbolic AI which studies how to leverage prior knowledge to improve neural classification systems. Recently, a family of neurosymbolic techniques for informed classification based on probabilistic reasoning has gained significant traction. Unfortunately, depending on the language used to represent prior knowledge, solving certain probabilistic reasoning problems can become prohibitively hard when the number of classes increases. Therefore, the asymptotic complexity of probabilistic reasoning is of cardinal importance to assess the scalability of such techniques. In this paper, we develop a unified formalism for four probabilistic reasoning problems. Then, we compile several known and new tractability results into a single complexity map of probabilistic reasoning. We build on top of this complexity map to characterize the domains of scalability of several techniques. We hope this work will help neurosymbolic AI practitioners navigate the scalability landscape of probabilistic neurosymbolic techniques.

Problem

• Probabilistic Reasoning
• Neuro-Symbolic AI
• Multi-Label Classification

Innovation

• Probabilistic Reasoning
• Neural-Symbolic AI
• Complexity Landscape