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Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs (1802.10026v4)

Published 27 Feb 2018 in stat.ML, cs.AI, and cs.LG

Abstract: The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet.

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Authors (5)
  1. Timur Garipov (13 papers)
  2. Pavel Izmailov (26 papers)
  3. Dmitrii Podoprikhin (2 papers)
  4. Dmitry Vetrov (84 papers)
  5. Andrew Gordon Wilson (133 papers)
Citations (684)

Summary

  • The paper reveals that connected local optima exist in DNN loss surfaces, challenging the notion of isolated minima.
  • It introduces Fast Geometric Ensembling (FGE), a method that takes small steps in weight space to form robust ensembles.
  • FGE delivers practical performance gains, achieving a 0.56% top-1 error reduction on ImageNet and enhanced accuracy on CIFAR benchmarks.

Insights into Loss Surfaces and Fast Ensembling of DNNs

The paper "Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs" explores the geometric intricacies of the loss surfaces of deep neural networks (DNNs). The authors provide novel insights into the connectivity of local optima in DNNs and introduce a fast ensembling method inspired by these findings. This work has profound implications for optimization and model ensembling in neural networks.

Connection of Local Optima

Central to the paper is the discovery that the optima of complex DNN loss functions are not isolated but rather can be connected by simple curves. By employing an approach to identify these high-accuracy paths, the authors show that paths in the form of polygonal chains or Bezier curves can achieve nearly constant training and test accuracy. This finding challenges the long-standing notion that local optima are isolated in the high-dimensional parameter space of DNNs.

Fast Geometric Ensembling (FGE)

Building on the understanding of mode connectivity, the authors propose the Fast Geometric Ensembling (FGE) method. FGE is a novel ensembling approach that quickly generates high-performing ensembles by taking small steps in weight space, exploring different but near-equivalent regions corresponding to different trained models. Remarkably, FGE achieves improved performance over traditional methods like Snapshot Ensembles, particularly on key image classification benchmarks such as CIFAR-10, CIFAR-100, and ImageNet.

Empirical Evaluation and Numerical Strength

The evaluation demonstrates the efficacy of FGE compared to other ensembling techniques. On CIFAR-100, FGE improves test accuracy when compared to both Snapshot Ensembles and independently trained networks. Even with a limited training budget, FGE effectively balances performance and efficiency. For instance, FGE achieves a 0.56% improvement in top-1 error rate over a ResNet-50 model on ImageNet in just five epochs, highlighting its practical advantage.

Theoretical and Practical Implications

The practical implications of this research are substantial. By revealing simple connective structures between local optima, this work could pave the way for more robust optimization techniques, improving both the convergence and generalization capabilities of DNNs. The potential to exploit these pathways for more nuanced posterior approximations can inspire advancements in Bayesian deep learning.

From a theoretical perspective, the findings suggest a reevaluation of the landscape of DNN loss functions—viewing them not as isolated basins but as connected valleys. These insights may lead to more intuitive and effective model training and ensemble generation methods, providing a richer understanding of over-parameterized model behaviors.

Future Directions

Future research could explore the potential of leveraging these insights for developing adaptive optimization algorithms, enhancing the stability and speed of convergence. Additionally, the existence of such pathways could be harnessed to design models more secure against adversarial attacks or to inform novel visualization techniques that capture the connectivity of DNN landscapes.

In conclusion, this paper makes significant contributions to the understanding of DNN loss surfaces and opens new avenues for efficient model ensembling and optimization. Its blend of theoretical insight and practical application sets a foundation for advancing both aspects of deep learning research.

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