Optimal Learning Rates for Deep Networks Are Data-Dependent
Key takeaways
- Optimal learning rate scaling in deep networks is fundamentally data-dependent.
- Data-agnostic scaling rules may not generalize across different network depths.
- Data-dependent scaling can lead to stable, depth-independent convergence rates.
- This insight could inform the design of more effective optimization algorithms for deep learning.
Who benefits
Summary
This note demonstrates that in deep scalar linear networks, the optimal depth-wise learning rate scaling is dependent on the data, unlike data-agnostic rules. With data-dependent scaling, learning dynamics become data-independent and weakly depth-dependent, achieving a constant linear convergence rate across all depths.
Why it matters
Understanding how optimal learning rates depend on data can lead to more effective and stable training of deep neural networks, potentially improving convergence speed and model performance, especially in complex real-world applications.
How to implement this in your domain
- 1Re-evaluate current learning rate scheduling strategies, considering data characteristics rather than purely architectural ones.
- 2Explore adaptive learning rate optimizers that can implicitly or explicitly account for data-dependent dynamics.
- 3Conduct experiments with simplified linear models to gain intuition about data-dependent learning rate effects before applying to complex networks.
- 4Investigate techniques for dynamically adjusting learning rates based on data statistics or properties during training.
Original post by Yedi Zhang, Peter E. Latham, Leena Chennuru Vankadara, Andrew Saxe
"arXiv:2607.07884v1 Announce Type: new Abstract: In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth. We show that even in this minimal model, the o…"
View on XOriginally posted by Yedi Zhang, Peter E. Latham, Leena Chennuru Vankadara, Andrew Saxe on X · view source
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