Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning

TL;DR

This paper introduces Neural Probabilistic Circuits (NPCs), a transparent model architecture that combines attribute recognition and logical reasoning to enable interpretable predictions while maintaining competitive performance.

Contribution

The paper proposes NPCs, an inherently interpretable model with a novel three-stage training process and theoretical error bounds, advancing explainability in neural network predictions.

Findings

NPCs achieve competitive accuracy on benchmark datasets.

They provide both most probable and counterfactual explanations.

The model's error is theoretically bounded by module errors.

Abstract

End-to-end deep neural networks have achieved remarkable success across various domains but are often criticized for their lack of interpretability. While post hoc explanation methods attempt to address this issue, they often fail to accurately represent these black-box models, resulting in misleading or incomplete explanations. To overcome these challenges, we propose an inherently transparent model architecture called Neural Probabilistic Circuits (NPCs), which enable compositional and interpretable predictions through logical reasoning. In particular, an NPC consists of two modules: an attribute recognition model, which predicts probabilities for various attributes, and a task predictor built on a probabilistic circuit, which enables logical reasoning over recognized attributes to make class predictions. To train NPCs, we introduce a three-stage training algorithm comprising attribute recognition, circuit construction, and joint optimization. Moreover, we theoretically demonstrate that an NPC's error is upper-bounded by a linear combination of the errors from its modules. To further demonstrate the interpretability of NPC, we provide both the most probable explanations and the counterfactual explanations. Empirical results on four benchmark datasets show that NPCs strike a balance between interpretability and performance, achieving results competitive even with those of end-to-end black-box models while providing enhanced interpretability.