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Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection

Wen-Chao Hu, Wang-Zhou Dai, Yuan Jiang, Zhi-Hua Zhou

TL;DR

This work tackles the mismatch between neural outputs and domain knowledge in Neuro-Symbolic AI by introducing Abductive Reflection (ABL-Refl). Building on Abductive Learning, ABL-Refl replaces expensive consistency optimization with a knowledge-driven reflection vector that flags potential errors and triggers targeted abduction, yielding KB-consistent outputs with greater efficiency. Empirical results on symbolic and visual Sudoku, as well as graph-based optimization, show superior accuracy, reduced training resources, and faster inference compared to state-of-the-art NeSy methods and symbolic solvers. The approach demonstrates strong adaptability across data modalities and knowledge representations, with potential applications to large language models and broader domains demanding reliable, knowledge-aligned reasoning.

Abstract

Neuro-Symbolic (NeSy) AI could be regarded as an analogy to human dual-process cognition, modeling the intuitive System 1 with neural networks and the algorithmic System 2 with symbolic reasoning. However, for complex learning targets, NeSy systems often generate outputs inconsistent with domain knowledge and it is challenging to rectify them. Inspired by the human Cognitive Reflection, which promptly detects errors in our intuitive response and revises them by invoking the System 2 reasoning, we propose to improve NeSy systems by introducing Abductive Reflection (ABL-Refl) based on the Abductive Learning (ABL) framework. ABL-Refl leverages domain knowledge to abduce a reflection vector during training, which can then flag potential errors in the neural network outputs and invoke abduction to rectify them and generate consistent outputs during inference. ABL-Refl is highly efficient in contrast to previous ABL implementations. Experiments show that ABL-Refl outperforms state-of-the-art NeSy methods, achieving excellent accuracy with fewer training resources and enhanced efficiency.

Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection

TL;DR

This work tackles the mismatch between neural outputs and domain knowledge in Neuro-Symbolic AI by introducing Abductive Reflection (ABL-Refl). Building on Abductive Learning, ABL-Refl replaces expensive consistency optimization with a knowledge-driven reflection vector that flags potential errors and triggers targeted abduction, yielding KB-consistent outputs with greater efficiency. Empirical results on symbolic and visual Sudoku, as well as graph-based optimization, show superior accuracy, reduced training resources, and faster inference compared to state-of-the-art NeSy methods and symbolic solvers. The approach demonstrates strong adaptability across data modalities and knowledge representations, with potential applications to large language models and broader domains demanding reliable, knowledge-aligned reasoning.

Abstract

Neuro-Symbolic (NeSy) AI could be regarded as an analogy to human dual-process cognition, modeling the intuitive System 1 with neural networks and the algorithmic System 2 with symbolic reasoning. However, for complex learning targets, NeSy systems often generate outputs inconsistent with domain knowledge and it is challenging to rectify them. Inspired by the human Cognitive Reflection, which promptly detects errors in our intuitive response and revises them by invoking the System 2 reasoning, we propose to improve NeSy systems by introducing Abductive Reflection (ABL-Refl) based on the Abductive Learning (ABL) framework. ABL-Refl leverages domain knowledge to abduce a reflection vector during training, which can then flag potential errors in the neural network outputs and invoke abduction to rectify them and generate consistent outputs during inference. ABL-Refl is highly efficient in contrast to previous ABL implementations. Experiments show that ABL-Refl outperforms state-of-the-art NeSy methods, achieving excellent accuracy with fewer training resources and enhanced efficiency.

Paper Structure

This paper contains 31 sections, 5 equations, 5 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Abductive Reflection
  4. Problem Setting
  5. Brief Introduction to Abductive Learning
  6. Challenge.
  7. Architecture
  8. Benefits.
  9. Training Paradigm
  10. Experiments
  11. Solving Sudoku
  12. Dataset and Setting.
  13. Compared Methods and Results.
  14. Comparing to Symbolic Solvers.
  15. Solving Visual Sudoku
  16. ...and 16 more sections

Figures (5)

  • Figure 1: Abductive Learning (ABL) framework.
  • Figure 2: Architecture of Abductive Reflection (ABL-Refl). It replaces the external consistency optimization module with an efficient reflection mechanism, which is abduced directly from $\mathcal{KB}$.
  • Figure 3: Consistency measurements.
  • Figure 4: Training curve on solving Sudoku and visual Sudoku.
  • Figure 5: A case study in the solving Sudoku experiment.