Predicting the Generalization Gap in Deep Networks with Margin Distributions (1810.00113v2)

Abstract: As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should be predicted from the training data and network parameters. In this paper, we propose such a measure, and conduct extensive empirical studies on how well it can predict the generalization gap. Our measure is based on the concept of margin distribution, which are the distances of training points to the decision boundary. We find that it is necessary to use margin distributions at multiple layers of a deep network. On the CIFAR-10 and the CIFAR-100 datasets, our proposed measure correlates very strongly with the generalization gap. In addition, we find the following other factors to be of importance: normalizing margin values for scale independence, using characterizations of margin distribution rather than just the margin (closest distance to decision boundary), and working in log space instead of linear space (effectively using a product of margins rather than a sum). Our measure can be easily applied to feedforward deep networks with any architecture and may point towards new training loss functions that could enable better generalization.

• The paper introduces a multilayer margin distribution measure to predict the generalization gap of deep networks.
• It employs empirical evaluation on CIFAR-10/100, showing that networks with wider margins achieve higher test accuracies.
• The study offers a linear regression framework leveraging margin statistics, outperforming traditional complexity-based bounds.

Predicting Generalization Gap in Deep Networks

The paper "Predicting the Generalization Gap in Deep Networks with Margin Distributions" by Yiding Jiang et al. addresses a fundamental problem in machine learning: understanding and predicting the generalization gap of deep neural networks. The generalization gap is the discrepancy between training and test accuracy, revealing how well a model will perform on unseen data. This research focuses on developing a robust measure to predict this gap based on margin distributions at various network layers.

Concept Overview

The paper introduces a novel measure leveraging margin distributions, extending beyond the traditional margin definition used in support vector machines (SVMs). In deep networks, margin distribution refers to the distance of training points from the decision boundary. The authors argue that margin distributions, assessed across various network layers, correlate strongly with the generalization gap. This shift from focusing solely on the output layer margin distinguishes their approach from previous methodologies.

Empirical Evaluation

The paper presents extensive empirical evidence supporting the efficacy of the proposed measure. Their experiments, conducted on CIFAR-10 and CIFAR-100 datasets, demonstrate a significant correlation between margin distribution characteristics and generalization performance. Particularly, their measure outperforms theoretical bounds reliant on network complexity and weight norms.

For these experiments, several network architectures were utilized, including convolutional neural networks and residual networks. The paper varied hyperparameters such as network width, normalization techniques, dropout levels, data augmentation, and regularization strengths, ensuring a robust dataset for analysis. Results show that networks achieving higher test accuracies also tended to have margin distributions located further from the decision boundary.

Contributions and Implications

The paper makes several notable contributions:

1. Multilayer Margin Utilization: Demonstrates that using margin information at multiple layers significantly enhances the predictive accuracy for generalization gaps compared to using only the output layer margin.
2. Normalized Margin Distributions: Introduces normalization techniques for margin distributions to mitigate scale effects, bolstering the reliability of the measure.
3. Analytical Framework: Offers a simple yet powerful linear regression framework utilizing margin distribution statistics (quartiles and moments) as features, surprisingly effective across diverse network architectures and datasets.
4. Comparative Analysis: Empirical evidence suggests that this multilayer margin distribution approach yields better predictive accuracy than existing theoretical bounds, setting a new baseline for future studies in understanding deep network generalization.

Future Directions

The findings present several avenues for future research. Directly, the paper suggests further exploring the role of hidden layers in capturing generalization properties and considers how these insights might be utilized to design improved training objectives that inherently promote better generalization. Moreover, advancing theoretical frameworks to more deeply integrate margin distributions across layers could yield new insights into the principles governing deep learning generalization.

This work stands as a testament to the importance of understanding deep learning models beyond superficial performance metrics, aiming for robust, reliable deployment in increasingly complex real-world scenarios.