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Certified Continual Learning for Neural Network Regression

Long H. Pham, Jun Sun

TL;DR

The paper tackles preserving verified neural-network properties during continual learning by attaching certificates to verified properties and guiding retraining with three lightweight mechanisms: certificate-based data augmentation, a certificate-based regularizer, and model clipping (with Craig interpolation for relaxation). The method, implemented in the Socrates framework and validated on ACAS Xu, MNIST, CIFAR10, and Census, maintains 100% of the verified properties across experiments while incurring minimal overhead and sometimes improving accuracy. Key contributions include formalizing certificates across layers, integrating augmentation and regularization to respect these certificates, and introducing a clipping-plus-relaxation pathway to restore properties when broken. The work demonstrates that certified continual learning can effectively balance adaptation to new data with preservation of crucial safety and fairness properties, offering practical value for safety-critical deployments.

Abstract

On the one hand, there has been considerable progress on neural network verification in recent years, which makes certifying neural networks a possibility. On the other hand, neural networks in practice are often re-trained over time to cope with new data distribution or for solving different tasks (a.k.a. continual learning). Once re-trained, the verified correctness of the neural network is likely broken, particularly in the presence of the phenomenon known as catastrophic forgetting. In this work, we propose an approach called certified continual learning which improves existing continual learning methods by preserving, as long as possible, the established correctness properties of a verified network. Our approach is evaluated with multiple neural networks and on two different continual learning methods. The results show that our approach is efficient and the trained models preserve their certified correctness and often maintain high utility.

Certified Continual Learning for Neural Network Regression

TL;DR

The paper tackles preserving verified neural-network properties during continual learning by attaching certificates to verified properties and guiding retraining with three lightweight mechanisms: certificate-based data augmentation, a certificate-based regularizer, and model clipping (with Craig interpolation for relaxation). The method, implemented in the Socrates framework and validated on ACAS Xu, MNIST, CIFAR10, and Census, maintains 100% of the verified properties across experiments while incurring minimal overhead and sometimes improving accuracy. Key contributions include formalizing certificates across layers, integrating augmentation and regularization to respect these certificates, and introducing a clipping-plus-relaxation pathway to restore properties when broken. The work demonstrates that certified continual learning can effectively balance adaptation to new data with preservation of crucial safety and fairness properties, offering practical value for safety-critical deployments.

Abstract

On the one hand, there has been considerable progress on neural network verification in recent years, which makes certifying neural networks a possibility. On the other hand, neural networks in practice are often re-trained over time to cope with new data distribution or for solving different tasks (a.k.a. continual learning). Once re-trained, the verified correctness of the neural network is likely broken, particularly in the presence of the phenomenon known as catastrophic forgetting. In this work, we propose an approach called certified continual learning which improves existing continual learning methods by preserving, as long as possible, the established correctness properties of a verified network. Our approach is evaluated with multiple neural networks and on two different continual learning methods. The results show that our approach is efficient and the trained models preserve their certified correctness and often maintain high utility.
Paper Structure (11 sections, 1 theorem, 13 equations, 2 figures, 5 tables, 2 algorithms)

This paper contains 11 sections, 1 theorem, 13 equations, 2 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Neural Network Verification
  4. Continual Learning
  5. Problem Definition
  6. Our Approach
  7. Evaluation
  8. Experimental Subjects
  9. Research Questions and Answers
  10. Related Work
  11. Conclusion

Key Result

Theorem 4.2

All the remaining certificates after the model clipping are valid.

Figures (2)

  • Figure 1: An example of model initialization
  • Figure 2: The accuracy on different values of $K$

Theorems & Definitions (10)

  • Definition 3.1: Neural Networks
  • Example 3.1
  • Definition 3.2: Neural Network Certificate
  • Example 3.2
  • Example 3.3
  • Example 4.1
  • Example 4.2
  • Definition 4.1: Craig interpolation
  • Example 4.3
  • Theorem 4.2: Soundness