Research map / Adversarial robustness and security / Certified and empirical robustness
COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuits
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Proposes COLEP, a certifiably robust conformal prediction framework that combines learned concept models with probabilistic-circuit-based logical reasoning, and certifies coverage under l2-bounded adversarial perturbations.
Problem
Conformal prediction coverage guarantees break under test-time adversarial perturbations that violate exchangeability, and purely data-driven models struggle to keep certified coverage high.
Approach
Augment a main classifier with knowledge (concept) models and a reasoning component built from probabilistic circuits that encode implication rules; the PC-corrected class probabilities are bounded via randomized smoothing and used to build worst-case non-conformity scores, yielding end-to-end certified coverage and provable gains over a single model.
Key results
- COLEP consistently achieves higher certified coverage than RSCP under l2-bounded perturbations, with a large margin at delta=0.5.
- Under PGD attack (delta=0.25), standard CP's marginal coverage falls below the 0.9 nominal level while COLEP stays above it, with smaller set size than RSCP.
- The paper proves COLEP achieves higher marginal coverage and accuracy than a single main model with high probability when knowledge utilities are non-trivial.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add knowledge-enabled probabilistic-circuit reasoning to the main model (COLEP) | COLEP vs. RSCP · GTSRB, CIFAR-10, and AwA2 under bounded perturbations | certified coverage | Helped |
| Add knowledge-enabled probabilistic-circuit reasoning to the main model (COLEP) | COLEP vs. RSCP · GTSRB, CIFAR-10, and AwA2 under PGD attack (δ=0.25) | marginal coverage | Helped |
| Add knowledge-enabled probabilistic-circuit reasoning to the main model (COLEP) | COLEP vs. RSCP · GTSRB, CIFAR-10, and AwA2 under PGD attack (δ=0.25) | averaged set size | Helped |
| Apply a PGD attack at δ=0.25 | Standard conformal prediction (CP) · GTSRB, CIFAR-10, and AwA2 | marginal coverage | Hurt |
| Add knowledge-enabled probabilistic-circuit reasoning, assuming non-trivial knowledge-model and rule utility | COLEP vs. a single main model · Adversarial setting | marginal coverage | Helped |
| Add knowledge-enabled probabilistic-circuit reasoning, assuming non-trivial knowledge-model and rule utility | COLEP vs. a single main model · Benign and adversarial mixture distribution | prediction accuracy | Helped |
Limitations
- Requires pretraining multiple knowledge models, adding computational cost.
- Knowledge rules must be designed by domain experts; not fully automatic.
- Assumes knowledge rules are clean and fixed at inference time; contaminated knowledge is left for future work.
Experimental setup
Datasets: GTSRB CIFAR-10 AwA2
Benchmarks: GTSRB CIFAR-10 AwA2
Metrics: certified coverage marginal coverage average prediction set size prediction accuracy
Baselines: CP RSCP
Builds on: conformal prediction randomized smoothing RSCP probabilistic circuits semantic loss
Closest papers by meaning
- Conformal Prediction with Learned Features (ICML 2024 · similarity 0.86)
- Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models (ICML 2026 · similarity 0.85)
- Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models (NeurIPS 2026 · similarity 0.85)
- Pause and Reflect: Conformal Aggregation for Chain-of-Thought Reasoning (NeurIPS 2026 · similarity 0.84)
- Provably Reliable Conformal Prediction Sets in the Presence of Data Poisoning (ICLR 2025 · similarity 0.84)
- Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models (NeurIPS 2025 · similarity 0.84)
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