Mike Holenderski

Luis Armando Pérez Rey, Giovanni Luca Marchetti, Danica Kragic et al.

We introduce Equivariant Isomorphic Networks (EquIN) -- a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, EquIN is suitable for group actions that are not free, i.e., that stabilize data via nontrivial symmetries. EquIN is theoretically grounded in the orbit-stabilizer theorem from group theory. This guarantees that an ideal learner infers isomorphic representations while trained on equivariance alone and thus fully extracts the geometric structure of data. We provide an empirical investigation on image datasets with rotational symmetries and show that taking stabilizers into account improves the quality of the representations.

Jort de Jong, Mike Holenderski

Semantic segmentation is the task of classifying each pixel in an image. Training a segmentation model achieves best results using annotated images, where each pixel is annotated with the corresponding class. When obtaining fine annotations is difficult or expensive, it may be possible to acquire coarse annotations, e.g. by roughly annotating pixels in an images leaving some pixels around the boundaries between classes unlabeled. Segmentation with coarse annotations is difficult, in particular when the objective is to optimize the alignment of boundaries between classes. This paper proposes a regularization method for models with an encoder-decoder architecture with superpixel based upsampling. It encourages the segmented pixels in the decoded image to be SLIC-superpixels, which are based on pixel color and position, independent of the segmentation annotation. The method is applied to FCN-16 fully convolutional network architecture and evaluated on the SUIM, Cityscapes, and PanNuke data sets. It is shown that the boundary recall improves significantly compared to state-of-the-art models when trained on coarse annotations.

Luis A. Pérez Rey, Loek Tonnaer, Vlado Menkovski et al.

The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by (Higgins et al., 2018) outlines the properties that should characterize a disentangled representation that captures the symmetries of data. However, it is not clear how to measure the degree to which a data representation fulfills these properties. We propose a metric for the evaluation of the level of LSBD that a data representation achieves. We provide a practical method to evaluate this metric and use it to evaluate the disentanglement of the data representations obtained for three datasets with underlying $SO(2)$ symmetries.

Loek Tonnaer, Luis A. Pérez Rey, Vlado Menkovski et al.

The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the notion of linearly disentangled representations, but there is currently no metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and to compare to previous understandings of disentanglement. We propose $\mathcal{D}_\mathrm{LSBD}$, a mathematically sound metric to quantify LSBD, and provide a practical implementation for $\mathrm{SO}(2)$ groups. Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to learn LSBD representations. We demonstrate the utility of our metric by showing that (1) common VAE-based disentanglement methods don't learn LSBD representations, (2) LSBD-VAE as well as other recent methods can learn LSBD representations, needing only limited supervision on transformations, and (3) various desirable properties expressed by existing disentanglement metrics are also achieved by LSBD representations.

Marijn van Knippenberg, Mike Holenderski, Vlado Menkovski

Complex real-life routing challenges can be modeled as variations of well-known combinatorial optimization problems. These routing problems have long been studied and are difficult to solve at scale. The particular setting may also make exact formulation difficult. Deep Learning offers an increasingly attractive alternative to traditional solutions, which mainly revolve around the use of various heuristics. Deep Learning may provide solutions which are less time-consuming and of higher quality at large scales, as it generally does not need to generate solutions in an iterative manner, and Deep Learning models have shown a surprising capacity for solving complex tasks in recent years. Here we consider a particular variation of the Capacitated Vehicle Routing (CVRP) problem and investigate the use of Deep Learning models with explicit memory components. Such memory components may help in gaining insight into the model's decisions as the memory and operations on it can be directly inspected at any time, and may assist in scaling the method to such a size that it becomes viable for industry settings.