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Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models
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Proposes COCOCO, a post-hoc conformal prediction framework for NeSy concept-based models that jointly conformalizes concepts and labels and reconciles them with one deduction-abduction revision step, plus e-value-based size budgets.
Problem
NeSy concept-based models (DeepProbLog, LTN) are overconfident, and existing conformal methods for them fail to jointly guarantee logical consistency between concept and label sets, coverage, and conciseness of prediction sets.
Approach
Conformalize concept and label sets separately, then revise both with a single joint deduction-abduction step (intersect the label set with the deductive image of the concept set and vice versa), which yields the largest mutually consistent pair; e-values allow user-specified size budgets without Bonferroni inflation.
Key results
- On Chest-Xrays, COCOCO reduces concept set size from 5.30 (RPB) to 2.90 at concept consistency 1.00, with label coverage 0.88.
- On MNIST-EvenOdd, COCOCO shrinks concept sets from 100 (RPB) to 12.13 with consistency 1.00 versus 0.12 for RPB.
- On RIVAL-10, COCOCO raises concept consistency from 0.94 to 1.00 and reduces concept set size from 6.33 to 5.85, but concept coverage drops from 0.92 to 0.84.
Surprising findings
- Concept coverage of COCOCO is systematically 7-10 points below RPB's, a trade-off for consistency and smaller sets.
Limitations
- Enumerating abduction/deduction images and the cross-product concept set scales poorly with many concepts.
- Coverage lower bound degrades with abductive/deductive soundness failures under incomplete knowledge.
- Assumes conditional independence of concepts when using the product construction.
Experimental setup
Datasets: Chest-Xrays CeBaB RIVAL-10 MNIST-EvenOdd MNIST-Add CIFAR
Benchmarks: Chest-Xrays CeBaB RIVAL-10 MNIST-EvenOdd
Metrics: coverage set size consistency
Baselines: Task Only (TO) Task plus Abduction (TAb) Concepts Only (CO) Concepts plus Deduction (CDe) RPB
Builds on: conformal prediction conformal e-predictions DeepProbLog Logic Tensor Networks reasoning shortcuts
Closest papers by meaning
- Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible (ICML 2025 · similarity 0.88)
- NeSyCoCo: A Neuro-Symbolic Concept Composer for Compositional Generalization (AAAI 2025 · similarity 0.88)
- Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens (NeurIPS 2025 · similarity 0.87)
- Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees (AAAI 2024 · similarity 0.87)
- Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI (NeurIPS 2025 · similarity 0.87)
- A learnability analysis on neuro-symbolic learning (NeurIPS 2025 · similarity 0.87)
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