Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models

2026-05-18

AI Summary

This work addresses the challenge of reliably quantifying prediction uncertainty in Neural-Symbolic Concept-Based Models (NeSy-CBMs), which often suffer from overconfidence and fail to simultaneously satisfy logical consistency, coverage guarantees, and output conciseness. To this end, the authors propose COCOCO, a novel post-hoc framework that, for the first time, integrates conformal prediction into NeSy-CBMs. COCOCO jointly calibrates concept and label predictions and incorporates a single deductive-abductive refinement step to achieve all three desiderata. The method allows users to specify desired prediction set sizes and is robust to imperfect background knowledge. Extensive experiments across eight datasets demonstrate that COCOCO provides distribution-free coverage guarantees while significantly outperforming existing baselines, achieving a superior trade-off between prediction set compactness and model performance.

Abstract

Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction-abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.

Problem

• Neuro-Symbolic Concept-based Models
• Conformal Prediction
• overconfidence
• trustworthiness
• coverage guarantees

Innovation

• Conformal Prediction
• Neuro-Symbolic Models
• Concept-Based Models
• Deduction-Abduction Revision
• Distribution-Free Coverage