Title: Causal Neural Probabilistic Circuits

Original: arXiv:2603.01372v2 Announce Type: replace-cross

Abstract: Concept Bottleneck Models (CBMs) improve the interpretability of end-to-end neural networks by inserting an intermediate layer of concepts, from which class labels are predicted based on concept predictions. A significant advantage of CBMs is their capacity for interventions, allowing domain experts to manually correct mispredicted concept values during testing to boost final accuracy. Nevertheless, standard CBMs typically handle interventions by replacing only the corrected concept value while keeping other predictions static, thereby neglecting causal relationships between concepts. To overcome this limitation, we introduce the Causal Neural Probabilistic Circuit (CNPC). This approach integrates a neural attribute predictor with a causal probabilistic circuit derived from a causal graph. The circuit enables exact and computationally feasible causal inference, naturally accounting for causal dependencies. When interventions occur, CNPC determines the class distribution by combining the attribute predictor’s predictive distribution with the interventional marginals calculated by the circuit, using a Product of Experts (PoE) framework. We provide a theoretical analysis of CNPC’s compositional interventional error relative to its components and specify the conditions under which CNPC approximates the true interventional class distribution. Evaluations on five benchmark datasets, covering both in-distribution and out-of-distribution scenarios, demonstrate that CNPC outperforms five baseline models in task accuracy across varying numbers of intervened attributes.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC