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Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models which optimise one of many disparate disentanglement metrics. Symmetry Based Disentangled Representation learning introduced a robust mathematical framework that defined precisely what is meant by a "linear disentangled representation". This framework determined that such representations would depend on a particular decomposition of the symmetry group acting on the data, showing that actions would manifest through irreducible group representations acting on independent representational subspaces. Caselles-Dupre et al [2019] subsequently proposed the first model to induce and demonstrate a linear disentangled representation in a VAE model. In this work we empirically show that linear disentangled representations are not generally present in standard VAE models and that they instead require altering the loss landscape to induce them. We proceed to show that such representations are a desirable property with regard to classical disentanglement metrics. Finally we propose a method to induce irreducible representations which forgoes the need for labelled action sequences, as was required by prior work. We explore a number of properties of this method, including the ability to learn from action sequences without knowledge of intermediate states and robustness under visual noise. We also demonstrate that it can successfully learn 4 independent symmetries directly from pixels.

Mixed Sample Data Augmentation (MSDA) has received increasing attention in recent years, with many successful variants such as MixUp and CutMix. By studying the mutual information between the function learned by a VAE on the original data and on the augmented data we show that MixUp distorts learned functions in a way that CutMix does not. We further demonstrate this by showing that MixUp acts as a form of adversarial training, increasing robustness to attacks such as Deep Fool and Uniform Noise which produce examples similar to those generated by MixUp. We argue that this distortion prevents models from learning about sample specific features in the data, aiding generalisation performance. In contrast, we suggest that CutMix works more like a traditional augmentation, improving performance by preventing memorisation without distorting the data distribution. However, we argue that an MSDA which builds on CutMix to include masks of arbitrary shape, rather than just square, could further prevent memorisation whilst preserving the data distribution in the same way. To this end, we propose FMix, an MSDA that uses random binary masks obtained by applying a threshold to low frequency images sampled from Fourier space. These random masks can take on a wide range of shapes and can be generated for use with one, two, and three dimensional data. FMix improves performance over MixUp and CutMix, without an increase in training time, for a number of models across a range of data sets and problem settings, obtaining a new single model state-of-the-art result on CIFAR-10 without external data. Finally, we show that a consequence of the difference between interpolating MSDA such as MixUp and masking MSDA such as FMix is that the two can be combined to improve performance even further. Code for all experiments is provided at https://github.com/ecs-vlc/FMix ., Comment: Code available at https://github.com/ecs-vlc/FMix

We introduce torchbearer, a model fitting library for pytorch aimed at researchers working on deep learning or differentiable programming. The torchbearer library provides a high level metric and callback API that can be used for a wide range of applications. We also include a series of built in callbacks that can be used for: model persistence, learning rate decay, logging, data visualization and more. The extensive documentation includes an example library for deep learning and dynamic programming problems and can be found at http://torchbearer.readthedocs.io. The code is licensed under the MIT License and available at https://github.com/ecs-vlc/torchbearer., Comment: 5 pages