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AI Research
arXiv CS.AI·3d ago·5 min read
On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective
TL;DR
Gradient Descent (GD) in a simple two-neuron ReLU network converges to an optimal robustness margin, but at a very slow rate of Θ(1/ln(t)). This study establishes the first explicit lower bound on this convergence rate in non-linear models.
✦ Why It Matters
Consider adjusting your training strategies to account for slow convergence rates in non-linear neural networks.
Key Takeaways
- Understand the implications of slow convergence rates in neural networks.
- Explore alternative optimization techniques to improve training speed.
- Consider robustness margins when designing binary classification tasks.
- Utilize empirical simulations to validate convergence behavior in your models.
How It Works
The study analyzes the dynamics of Gradient Descent in a two-neuron ReLU network by examining the trajectories of the decision boundary. By controlling the system's dynamics, the authors derive a lower bound on the convergence rate, revealing how the non-linear architecture affects the optimization process.