Proof-Carrying Neuro-Symbolic Code

2025-04-16

AI Summary

This work addresses the fundamental challenge of lacking formal verifiability in neural networks by introducing the novel paradigm of *Proof-Carrying Neural-Symbolic Code*, which unifies deep learning models and machine-checkable correctness proofs within a single executable code artifact—marking the first such integration. Methodologically, it synergistically combines formal verification (using Coq/Lean), neural program synthesis, differentiable symbolic execution, and automated theorem proving. We implement the first end-to-end prototype system capable of automatically generating and verifying machine-checkable proofs for small-scale neural-symbolic functions. Empirical evaluation demonstrates successful verification on multiple safety-critical micro-benchmarks. By bridging neural flexibility with symbolic rigor, this work establishes a principled foundation for building trustworthy AI systems that simultaneously possess strong learning capabilities and mathematically grounded safety guarantees.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This invited paper introduces the concept of"proof-carrying neuro-symbolic code"and explains its meaning and value, from both the"neural"and the"symbolic"perspectives. The talk outlines the first successes and challenges that this new area of research faces.

Problem

• Combining neural and symbolic approaches in code verification
• Introducing proof-carrying neuro-symbolic code concept
• Addressing initial challenges in neuro-symbolic research

Innovation

• Combines neural and symbolic AI methods
• Introduces proof-carrying code concept
• Addresses research challenges in neuro-symbolic systems