Large Margin Deep Networks for Classification (1803.05598v2)

Abstract: We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm).

• The paper introduces a flexible large margin loss function deployable across any network layer to enhance classification robustness.
• It employs l_p-norm margin approximations via a first-order linearization technique, enabling efficient computation in deep architectures.
• Empirical results on MNIST, CIFAR-10, and ImageNet show up to 21% improvement under adversarial conditions, underscoring practical benefits.

Large Margin Deep Networks for Classification: A Comprehensive Review

Introduction

The notion of large margins has long been central to the classification task within machine learning, offering advantages such as enhanced generalization and robustness to perturbations. Yet, the practical integration of large margin principles into deep neural networks has remained an underexplored domain, predominantly due to the complexity of computing margins in the context of deep architectures. This paper proposes an innovative approach to incorporate large margins in deep networks, extending beyond just the output layer and introducing a novel margin-based loss function applicable to any set of layers within the network. The proposed framework theoretically and empirically bridges the gap by integrating $l_p$-norm-based margin calculations across different network layers.

Methodology

The authors introduce a loss function that approximates large margins through a first-order framework, capable of being deployed across any layer within a network. This flexibility regarding layer selection and $l_p$-norm choice ($p \geq 1$) provides a more generalized and potentially robust classification paradigm across various tasks and datasets.

The loss function is defined using a linearization technique to approximate margins for deep networks, thereby bypassing the intractability associated with exact computation. By employing distance metrics like $l_1$, $l_2$, and $l_\infty$, the paper demonstrates how this method facilitates a more robust decision boundary than conventional cross-entropy loss.

Empirical Findings

Extensive empirical evaluation is conducted on datasets such as MNIST, CIFAR-10, and ImageNet, demonstrating the superiority of the proposed large margin loss function in domains like adversarial robustness, generalization with limited data, and learning from noisy labels. Remarkably, the proposed method presents strong numerical improvements, such as outperforming conventional models by up to 21% on the MNIST dataset under adversarial perturbations, and similarly significant gains are observed on CIFAR-10 and ImageNet as well. These results underscore the potential of large-margin deep networks to substantially outperform standard loss functions in terms of accuracy and robustness.

Related Work and Contributions

Unlike preceding research that primarily focused on the output layer, this work presents a novel solution by maximizing the margin on multiple intermediate layers. It offers a flexible solution applicable across architecture types, including convolutions and residual networks, independent of the specific domain or data type. This flexibility contrasts with the limitations of earlier approaches, such as those relying on the traditional hinge loss or cross-entropy loss combined with additional margin-encouraging terms at the output layer only.

Implications and Prospective Developments

The findings suggest significant theoretical and practical implications for improving generalizability and robustness in deep systems through large-margin techniques. Moreover, by dedicating attention to hidden layers, this research paves the way for further explorations into architectural efficiency and the impact of intermediate representations on model robustness and generalization.

The proposed method highlights a tangible pathway toward more resilient AI models capable of maintaining performance even under challenging scenarios, such as adversarial attacks or data scarcity. Future research could build upon this foundational work by exploring margin definitions and adaptations in different network architectures, potentially sparking a wave of resilient model training practices within the machine learning community.

Conclusion

In summation, the introduction of a large margin-based loss function for deep networks represents a significant stride in marrying traditional margin-based classifiers with contemporary deep learning models. By validating this method over prominent datasets and numerous scenarios, the work demonstrates both the feasibility and advantages of such an approach, setting a precedent for more robust and generalizable AI systems.