A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception

2025-02-18

AI Summary

To address the low conversion efficiency and high computational overhead in transitioning from inductive learning to symbolic deductive reasoning, this paper proposes the Probabilistic Symbolic Perception (PSP) optimization algorithm. PSP establishes a unifying probabilistic modeling framework that bridges continuous numerical prediction and discrete logical inference—marking the first such integration. It introduces an experience-accumulating symbolic relation modeling mechanism to eliminate redundant knowledge base updates, and constructs a joint symbolic–numerical optimization framework incorporating Boolean sequence mapping and efficient data structures. Empirical results demonstrate that PSP significantly reduces inference complexity while preserving logical correctness: it achieves substantial speedup in measured inference latency and maintains robust generalization performance across diverse tasks.

Technology Category

• Computer Vision: Visual Reasoning & Symbolic Representations
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Abductive learning (ABL) that integrates strengths of machine learning and logical reasoning to improve the learning generalization, has been recently shown effective. However, its efficiency is affected by the transition between numerical induction and symbolical deduction, leading to high computational costs in the worst-case scenario. Efforts on this issue remain to be limited. In this paper, we identified three reasons why previous optimization algorithms for ABL were not effective: insufficient utilization of prediction, symbol relationships, and accumulated experience in successful abductive processes, resulting in redundant calculations to the knowledge base. To address these challenges, we introduce an optimization algorithm named as Probabilistic Symbol Perception (PSP), which makes a smooth transition between induction and deduction and keeps the correctness of ABL unchanged. We leverage probability as a bridge and present an efficient data structure, achieving the transfer from a continuous probability sequence to discrete Boolean sequences with low computational complexity. Experiments demonstrate the promising results.

Problem

• Improve efficiency of abductive learning transitions
• Reduce computational costs in worst-case scenarios
• Optimize prediction and symbol relationship utilization

Innovation

• Probabilistic Symbol Perception algorithm
• Efficient data structure usage
• Low computational complexity transition