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Where Do Large Learning Rates Lead Us? (2410.22113v1)

Published 29 Oct 2024 in cs.LG and stat.ML

Abstract: It is generally accepted that starting neural networks training with large learning rates (LRs) improves generalization. Following a line of research devoted to understanding this effect, we conduct an empirical study in a controlled setting focusing on two questions: 1) how large an initial LR is required for obtaining optimal quality, and 2) what are the key differences between models trained with different LRs? We discover that only a narrow range of initial LRs slightly above the convergence threshold lead to optimal results after fine-tuning with a small LR or weight averaging. By studying the local geometry of reached minima, we observe that using LRs from this optimal range allows for the optimization to locate a basin that only contains high-quality minima. Additionally, we show that these initial LRs result in a sparse set of learned features, with a clear focus on those most relevant for the task. In contrast, starting training with too small LRs leads to unstable minima and attempts to learn all features simultaneously, resulting in poor generalization. Conversely, using initial LRs that are too large fails to detect a basin with good solutions and extract meaningful patterns from the data.

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Authors (5)
  1. Ildus Sadrtdinov (4 papers)
  2. Maxim Kodryan (6 papers)
  3. Eduard Pokonechny (1 paper)
  4. Ekaterina Lobacheva (17 papers)
  5. Dmitry Vetrov (84 papers)

Summary

Understanding the Influence of Initial Learning Rates in Neural Networks Training

The paper titled "Where Do Large Learning Rates Lead Us?" by Sadrtdinov et al. presents an in-depth empirical analysis of the role and impact of large initial learning rates (LRs) in training neural networks. The paper challenges and refines existing conventions within deep learning practice, specifically focusing on the desired size of initial LRs for optimal neural network performance.

Key Findings

The research confronts the ambiguous stance toward large LRs, by posing two prominent questions: 1) determining the appropriate range of large initial LRs for optimal results, and 2) identifying the distinguishing features of models trained with different LRs. The paper classifies LR behaviors into three regimes: convergence, chaotic equilibrium, and divergence.

  1. Empirical Boundary for Learning Rates: It is determined that optimal generalization is achieved by employing initial LRs slightly exceeding the threshold required for network convergence. This strategically positions the learning process in the chaotic equilibrium regime. This finding challenges the prevailing wisdom that emphasizes only the necessity of large LRs, but not the specific quantitative considerations of their magnitude.
  2. Landscape of Solutions: Models initialized with these optimal LRs tend to locate loss landscape basins that house high-quality minima. This significant insight reveals that severe large LRs lead models into broad, high-error basins, whereas slightly larger-than-convergence LRs identify regions densely packed with effective solutions.
  3. Sparse Feature Learning: Training networks with the optimal range of LRs modifies feature learning dynamics. The results exhibit model specialization with sparse sets of features leading to more focused architectures capable of improved generalization. This contrasts with non-optimal LRs which either disperse feature activation too widely or fail to leverage meaningful feature patterns.
  4. Practical Implications for Image Classification: Extending empirical findings from synthetic data to real-world data sets, such as CIFAR-10, reveals similar feature-learning dynamics, confirming the transferability of results. Frequency analysis indicates that networks trained with fine-tuned LRs focus substantially on mid-frequency features beneficial for classification tasks.

Implications and Future Directions

The findings provide profound implications for optimization strategies in neural network training. They suggest that meticulous selection and tuning of initial LRs can avert poor generalization outcomes even when computational resources remain constant. Furthermore, understanding these dynamics may serve theoretical understanding of non-convex optimization landscapes, signaling potential paths for robust architecture design.

Nevertheless, this paper uncovers the need for more research into the relationship between dynamic feature learning and landscape geometry. The sparsification phenomenon raises questions about the inherent trade-offs in interpretability and model robustness that merit further theoretical exploration. Additionally, future research could extend these empirical investigations to other model architectures and data domains, hence broadening the foundational knowledge of large-LR effects in neural network training.

In conclusion, this work propels the discourse on neural network optimization considerably forward, providing invaluable clarity into an often-overlooked aspect of model training—precisely calibrated learning rates. Through rigorous empirical methodology, it lays the groundwork for evolving best practices in model training and architecture design, enhancing both generalization and efficiency in deep learning.

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