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On the Rate of Convergence of GD in Non-linear Neural Networks: An Adversarial Robustness Perspective
🤖AI Summary
Researchers prove that gradient descent in neural networks converges to optimal robustness margins at an extremely slow rate of Θ(1/ln(t)), even in simplified two-neuron settings. This establishes the first explicit lower bound on convergence rates for robustness margins in non-linear models, revealing fundamental limitations in neural network training efficiency.
Key Takeaways
- →Gradient descent converges to optimal robustness margins but at a prohibitively slow rate of Θ(1/ln(t)) even in minimal neural network settings.
- →This is the first explicit lower bound established for convergence rates of robustness margins in non-linear models.
- →The slow convergence pattern is pervasive across multiple natural network initializations, suggesting a fundamental limitation.
- →Researchers developed rigorous mathematical analysis to control gradient descent trajectories in non-linear architectures.
- →The study reveals inherent efficiency challenges in neural network training for adversarial robustness.
#gradient-descent#neural-networks#adversarial-robustness#convergence-rates#machine-learning#deep-learning#optimization#training-efficiency
Read Original →via arXiv – CS AI
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