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Distributional Smoothing with Virtual Adversarial Training (1507.00677v9)

Published 2 Jul 2015 in stat.ML and cs.LG

Abstract: We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as virtual adversarial training (VAT). The LDS of a model at an input datapoint is defined as the KL-divergence based robustness of the model distribution against local perturbation around the datapoint. VAT resembles adversarial training, but distinguishes itself in that it determines the adversarial direction from the model distribution alone without using the label information, making it applicable to semi-supervised learning. The computational cost for VAT is relatively low. For neural network, the approximated gradient of the LDS can be computed with no more than three pairs of forward and back propagations. When we applied our technique to supervised and semi-supervised learning for the MNIST dataset, it outperformed all the training methods other than the current state of the art method, which is based on a highly advanced generative model. We also applied our method to SVHN and NORB, and confirmed our method's superior performance over the current state of the art semi-supervised method applied to these datasets.

Citations (453)

Summary

  • The paper presents Virtual Adversarial Training (VAT) which regularizes neural networks by enforcing local distributional smoothness without relying on label information.
  • VAT efficiently computes worst-case perturbations using KL divergence and power iteration, reducing overhead to at most three forward and backward propagations.
  • Experimental results on MNIST, SVHN, and NORB demonstrate that VAT outperforms traditional regularization methods in both supervised and semi-supervised learning scenarios.

Virtual Adversarial Training: Enhancing Neural Network Robustness

The paper presents a novel approach to regularizing neural networks, termed Virtual Adversarial Training (VAT), aimed at improving model smoothness and mitigating overfitting. VAT is grounded in the concept of Local Distributional Smoothness (LDS), a regularization technique designed to enhance the robustness of model predictions against input perturbations without relying on label information. This allows its application in both supervised and semi-supervised learning contexts.

Methodology and Implementation

Local Distributional Smoothness (LDS) is defined using the Kullback-Leibler (KL) divergence to measure the sensitivity of the model distribution to input perturbations. The authors conceptualize the worst-case scenario for input perturbation, similar to adversarial training, but uniquely without label reliance, thus the term "virtual" adversarial direction. This virtual adversarial direction is computed efficiently via a second-order Taylor expansion and power iteration method, reducing computational overhead to a feasible level, requiring at most three forward and backward propagations in neural networks.

The proposed VAT distinguishes itself with largely invariant performance under different parameterizations, owing to its construction, which remains steadfast across reparametrizations. This contrasts with traditional L2 regularization, which lacks this invariant property and fails to address local input-output specificities effectively.

Experimental Evaluation

The paper provides extensive experimental validation across several benchmarks, including MNIST, SVHN, and NORB. For the MNIST dataset, VAT demonstrated superior performance in supervised settings, closely rivaling the ladder network, which is one of the state-of-the-art generative model approaches. Notably, VAT outshone other contemporary regularization methods such as adversarial training, dropout, and random perturbation training.

In semi-supervised settings, VAT's efficacy was particularly profound. It surpassed existing methods not reliant on generative models for the SVHN and NORB datasets. These outcomes highlight VAT's robustness in leveraging unlabeled data to improve generalization, an area where many traditional methods fall short.

Implications and Future Directions

VAT introduces a paradigm shift in regularization approaches by minimizing dependency on label information, thereby offering a scalable solution for semi-supervised learning. Its computational simplicity and minimal hyperparameter tuning render it an attractive option for large-scale applications where data labeling is constrained.

The theoretical implications suggest potential integrations with manifold learning or other geometric approaches to further enhance model robustness against adversarial perturbations. Additionally, integrating VAT with generative models might yield even more pronounced performance enhancements, given the complementary strengths of the two paradigms.

Future work could explore extending VAT to broader model architectures and more complex datasets, further testing its versatility and adaptability in various AI contexts.

In summary, VAT is a promising development, contributing significantly to the ongoing discourse on making neural networks robust and efficient, especially in semi-supervised learning scenarios.