COLEP: CERTIFIABLY ROBUST LEARNING-REASONING CONFORMAL PREDICTION VIA PROBABILISTIC CIRCUITS

Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations during the inference can violate the exchangeability assumption, challenge the coverage guarantees, and result in a subsequent decline in prediction coverage. In this work, we propose the first certifiably robust learning-reasoning conformal prediction framework (COLEP) via probabilistic circuits, which comprises a data-driven learning component that trains statistical models to learn different semantic concepts, and a reasoning component that encodes knowledge and characterizes the relationships among the statistical knowledge models for logic reasoning. To achieve exact and efficient reasoning, we employ probabilistic circuits (PCs) to construct the reasoning component. Theoretically, we provide end-to-end certification of prediction coverage for COLEP under ℓ₂ bounded adversarial perturbations. We also provide certified coverage considering the finite size of the calibration set. Furthermore, we prove that COLEP achieves higher prediction coverage and accuracy over a single model as long as the utilities of knowledge models are non-trivial. Empirically, we show the validity and tightness of our certified coverage, demonstrating the robust conformal prediction of COLEP on various datasets.