# III: Small: Neural Probabilistic Circuits: Towards Compositional and Interpretable Neuro-Symbolic AI

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Illinois at Urbana-Champaign (IL) · $500,000

## Abstract

Despite the superior performance achieved by end-to-end deep neural networks, many of them are black-box models composed of complex operators with massive number of parameters, making it hard to interpret and understand how a decision is made. Existing methods often provide post-hoc explanations to explain the black-box model, but they are not reliable as the explanation model used to elucidate the black-box model may not be an accurate representation. In light of the above challenges, this project proposes an interpretable neuro-symbolic model, dubbed Neural Probabilistic Circuits, that decomposes the black-box prediction into a more transparent process by integrating neural networks for pattern recognition and probabilistic circuits for tractable reasoning. The project aims to build a theoretical foundation for neural probabilistic circuits, and investigate its robustness under both distribution shifts and adversarial attacks. The proposed research will have a significant impact on the design of interpretable neuro-symbolic AI systems, which are crucial for many high-stakes real-world applications. The outcomes of this project will be integrated into both undergraduate and graduate courses in artificial intelligence and machine learning to bolster the technical course material, available to all the students.

Neural probabilistic circuits consist of two modules, a neural module implemented by deep neural networks to recognize different high-level physical attributes from 

## Key facts

- **NSF award ID:** 2504555
- **Awardee organization:** University of Illinois at Urbana-Champaign (IL)
- **SAM.gov UEI:** Y8CWNJRCNN91
- **PI:** Han Zhao
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** SMALL PROJECT, INFO INTEGRATION & INFORMATICS
- **Estimated total:** $500,000
- **Funds obligated:** $500,000
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2504555

## Citation

> US National Science Foundation, Award 2504555, III: Small: Neural Probabilistic Circuits: Towards Compositional and Interpretable Neuro-Symbolic AI. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2504555. Licensed CC0.

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