Phase 3: Robust Training & Practical Implementation

Building and Evaluating Robust Networks

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This phase bridges theory and practice by focusing on practical workflows for building and evaluating robust neural networks. You’ll learn how to write formal specifications, understand the complementary roles of falsifiers and verifiers, explore standard benchmarks for evaluation, master hands-on robustness testing strategies, and study robust training approaches including regularization-based methods and certified adversarial training. This phase emphasizes practical application of verification concepts.

What You’ll Learn

This phase covers practical implementation: from writing formal specifications and benchmarking to hands-on robustness testing and certified training methods that bake verification into the training process.

Guides in This Phase

1️⃣ Formal Specifications

How to write precise safety properties and correctness specifications

Formal Specifications

2️⃣ Falsifiers & Verifiers

Understanding the roles and complementarity of attack-based falsifiers and certifiers

Falsifiers and Verifiers

3️⃣ Verification Benchmarks

Standard datasets, evaluation metrics, and competition results

Verification Benchmarks

4️⃣ Robustness Testing Guide

Practical strategies for testing neural network robustness without formal verification

Robustness Testing Guide

5️⃣ Regularization Training

Lipschitz regularization, TRADES, and margin maximization for robustness

Regularization-Based Robust Training

6️⃣ Certified Adversarial Training

Training with verified bounds using IBP, CROWN, and relaxation-based methods

Certified Adversarial Training

Next Phase

After learning practical implementation, explore Phase 4: Advanced Topics & Frontiers for advanced topics and research frontiers.

Zhongkui Ma · GitHub · Homepage

Last Updated: January 03, 2026