MixUp as Locally Linear Out-Of-Manifold Regularization (1809.02499v3)

Abstract: MixUp is a recently proposed data-augmentation scheme, which linearly interpolates a random pair of training examples and correspondingly the one-hot representations of their labels. Training deep neural networks with such additional data is shown capable of significantly improving the predictive accuracy of the current art. The power of MixUp, however, is primarily established empirically and its working and effectiveness have not been explained in any depth. In this paper, we develop an understanding for MixUp as a form of "out-of-manifold regularization", which imposes certain "local linearity" constraints on the model's input space beyond the data manifold. This analysis enables us to identify a limitation of MixUp, which we call "manifold intrusion". In a nutshell, manifold intrusion in MixUp is a form of under-fitting resulting from conflicts between the synthetic labels of the mixed-up examples and the labels of original training data. Such a phenomenon usually happens when the parameters controlling the generation of mixing policies are not sufficiently fine-tuned on the training data. To address this issue, we propose a novel adaptive version of MixUp, where the mixing policies are automatically learned from the data using an additional network and objective function designed to avoid manifold intrusion. The proposed regularizer, AdaMixUp, is empirically evaluated on several benchmark datasets. Extensive experiments demonstrate that AdaMixUp improves upon MixUp when applied to the current art of deep classification models.

• The paper positions MixUp as a form of out-of-manifold regularization, revealing manifold intrusion as a key limitation.
• It introduces AdaMixUp, an adaptive method that dynamically learns mixing policies to avoid conflicts between synthetic and true labels.
• Empirical evaluations demonstrate significant performance gains, including a 30.67% error reduction on the SVHN dataset.

MixUp as Locally Linear Out-Of-Manifold Regularization

The presented paper investigates the inner workings and theoretical framework underpinning MixUp, a recently developed data augmentation scheme. MixUp enhances the performance of deep neural networks by linearly interpolating both data and labels from random training pairs. This approach, though effective, has largely been supported by empirical evidence rather than a solid theoretical understanding.

Contribution and Insights

The paper positions MixUp as a form of out-of-manifold regularization, introducing the notion of imposing local linearity constraints beyond the existing data manifold. This theoretical analysis leads to the identification of a significant limitation within MixUp, termed "manifold intrusion." This phenomenon refers to underfitting caused by conflicts between interpolated synthetic labels and existing training labels when parameters controlling MixUp are not optimally fine-tuned.

To mitigate this issue, the paper proposes AdaMixUp, an adaptive variation of MixUp where mixing policies are dynamically learned from the data. An additional neural network and objective function are integrated to avoid manifold intrusion actively. The paper rigorously tests AdaMixUp across several benchmark datasets, reporting that AdaMixUp consistently outperforms standard MixUp, enhancing deep classification models.

Results and Implications

The empirical evaluations demonstrate that potentially detrimental manifold intrusion can be addressed using AdaMixUp. Strong numerical results indicate improved predictive performance across datasets, with notable error reductions, such as a 30.67% improvement in SVHN dataset error rates.

The advancement from MixUp to AdaMixUp not only offers practical benefits for contemporary image recognition and classification models but also enriches the theoretical understanding of regularization in neural networks. By considering regions outside the standard data manifold, AdaMixUp provides a fresh perspective on data augmentation.

Future Directions

The paper hints at broader implications for this line of paper, suggesting that MixUp's localized linearity mechanisms open a pathway to new regularization paradigms. There exists potential for exploring more complex mixing strategies beyond linear interpolation and developing a quantitative framework for assessing generalization capabilities stemming from out-of-manifold constraints.

In summary, by framing MixUp within a formalized regularization technique, this research marks a stepping stone in bridging empirical findings with robust theoretical foundations, paving the way for further advancements in AI model enhancement strategies.