Candidate Retention for Abductive Learning

2026-09-30

AI Summary

This study addresses the pseudo-label noise arising from conflicting explanations in abductive learning, where either selecting a single explanation or weighting all candidates introduces supervision bias. We propose a candidate retention mechanism that optimizes training signal quality by balancing supervision sharpness with model coverage. Methodologically, our approach integrates neural perception with symbolic reasoning to evaluate candidates via posterior probabilities and uncertainty quantification. We derive an error bound dependent on uncertainty and dropout quality, and design a greedy algorithm to dynamically filter effective candidate sets. Experimental results demonstrate that, on majority-aggregation modular addition tasks, the proposed method achieves significantly higher concept accuracy than both single-candidate baselines and the A3BL approach.

Abstract

Abductive learning combines neural perception with symbolic reasoning, using explanations generated by abduction to supervise the perception model. Multiple valid explanations of the same symbolic target can assign conflicting labels to the same inputs. Common policies select a single candidate as a pseudo-label, which may reinforce mistaken assignments, or weight all candidates, which may spread supervision across competing labels. These risks motivate selecting a retained subset to balance supervision sharpness and model-mass coverage. To guide this choice, we bound the coordinate-level supervision error using retained uncertainty, discarded model mass, and model mismatch. For a fixed model and training pair, only the first two terms depend on the retained set. We propose Abductive Candidate Retention (ACR), which uses these terms to guide greedy additions, accepting a candidate when its recovered mass exceeds the increase in retained uncertainty. Experiments show that ACR improves concept accuracy over single-candidate baselines and A3BL in most evaluated aggregated mod-addition settings. Objective ablations support the joint use of uncertainty and posterior mass.

Problem

• Abductive Learning
• Candidate Retention
• Pseudo-labeling
• Supervision Conflict
• Neuro-symbolic AI

Innovation

• Abductive Learning
• Candidate Retention
• Pseudo-labeling
• Retained Uncertainty
• Greedy Selection