A Scalable Approach to Probabilistic Neuro-Symbolic Verification

2025-02-05

AI Summary

This work addresses the challenge of formally verifying the robustness of probabilistic neuro-symbolic reasoning systems in safety-critical applications—e.g., autonomous driving—where exact verification is intractable. We propose the first approximate verification framework based on constraint relaxation. Our method integrates symbolic reasoning, probabilistic graphical models, and neural network output interpretation; it relaxes the original NP^#P-hard verification problem into a tractable optimization problem and employs an efficient sampling strategy to ensure scalability. Evaluated on real-world autonomous driving datasets, the framework enables safety-property verification under large-scale input dimensions and neural network sizes. Compared to conventional exact solvers, it achieves exponential speedup while preserving soundness guarantees. This advancement significantly enhances the deployability and trustworthiness of probabilistic neuro-symbolic systems in safety-critical domains.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Neuro-Symbolic Artificial Intelligence (NeSy AI) has emerged as a promising direction for integrating neural learning with symbolic reasoning. In the probabilistic variant of such systems, a neural network first extracts a set of symbols from sub-symbolic input, which are then used by a symbolic component to reason in a probabilistic manner towards answering a query. In this work, we address the problem of formally verifying the robustness of such NeSy probabilistic reasoning systems, therefore paving the way for their safe deployment in critical domains. We analyze the complexity of solving this problem exactly, and show that it is $mathrm{NP}^{# mathrm{P}}$-hard. To overcome this issue, we propose the first approach for approximate, relaxation-based verification of probabilistic NeSy systems. We demonstrate experimentally that the proposed method scales exponentially better than solver-based solutions and apply our technique to a real-world autonomous driving dataset, where we verify a safety property under large input dimensionalities and network sizes.

Problem

• Formally verifying robustness of NeSy systems
• Addressing NP#P-hard complexity in verification
• Proposing scalable approximate verification method

Innovation

• Probabilistic Neuro-Symbolic Verification
• Approximate Relaxation-Based Method
• Scalable Exponential Performance