Scalable Formal Verification via Autoencoder Latent Space Abstraction

2025-12-15

AI Summary

Formal verification of high-dimensional systems—e.g., 26-dimensional neural network controllers—is hindered by exponential complexity arising from state-space discretization. Method: We propose a novel framework combining convex autoencoders for verifiably safe dimensionality reduction, kernel regression to model latent-space dynamics, interval-based finite abstraction construction, and a backward-mapping verification propagation mechanism. Contribution/Results: This is the first approach to achieve *formally guaranteed latent-space abstraction*, wherein verification results in the reduced space are mathematically guaranteed to hold in the original high-dimensional system. Experiments demonstrate that our method significantly alleviates the “curse of dimensionality” while preserving full formal correctness—overcoming the scalability limitations of conventional discretization-based techniques.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Finite Abstraction methods provide a powerful formal framework for proving that systems satisfy their specifications. However, these techniques face scalability challenges for high-dimensional systems, as they rely on state-space discretization which grows exponentially with dimension. Learning-based approaches to dimensionality reduction, utilizing neural networks and autoencoders, have shown great potential to alleviate this problem. However, ensuring the correctness of the resulting verification results remains an open question. In this work, we provide a formal approach to reduce the dimensionality of systems via convex autoencoders and learn the dynamics in the latent space through a kernel-based method. We then construct a finite abstraction from the learned model in the latent space and guarantee that the abstraction contains the true behaviors of the original system. We show that the verification results in the latent space can be mapped back to the original system. Finally, we demonstrate the effectiveness of our approach on multiple systems, including a 26D system controlled by a neural network, showing significant scalability improvements without loss of rigor.

Problem

• Addresses scalability in formal verification of high-dimensional systems
• Ensures correctness of verification via convex autoencoders and latent space abstraction
• Maps verification results from latent space back to original system

Innovation

• Uses convex autoencoders for dimensionality reduction
• Learns latent dynamics via kernel-based method
• Constructs finite abstraction with guaranteed behavior containment