Jim Portegies

Pim Otte, Dick Arends, Raul Sánchez Flores et al.

Waterproof Editor provides an educational environment specifically targeted to teaching with proof assistants or programming languages. It arose from Waterproof, educational software targeted at helping students acquire the skill of giving mathematical proofs. Its original features such as enabling rich formatting and providing clear input areas are now abstracted away in an npm package and can be used in different educational contexts. We invite interested parties to use this component in their educational software, and offer to assist with this.

Bram Grooten, Jelle Wemmenhove, Maurice Poot et al.

In pursuit of enhanced multi-agent collaboration, we analyze several on-policy deep reinforcement learning algorithms in the recently published Hanabi benchmark. Our research suggests a perhaps counter-intuitive finding, where Proximal Policy Optimization (PPO) is outperformed by Vanilla Policy Gradient over multiple random seeds in a simplified environment of the multi-agent cooperative card game. In our analysis of this behavior we look into Hanabi-specific metrics and hypothesize a reason for PPO's plateau. In addition, we provide proofs for the maximum length of a perfect game (71 turns) and any game (89 turns). Our code can be found at: https://github.com/bramgrooten/DeepRL-for-Hanabi

Bart Smets, Jim Portegies, Erik Bekkers et al.

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these networks to be designed with built-in symmetries such as rotation in addition to the standard translation equivariance of CNNs. Having all the desired symmetries included in the design obviates the need to include them by means of costly techniques such as data augmentation. We will discuss our PDE-based G-CNNs (PDE-G-CNNs) in a general homogeneous space setting while also going into the specifics of our primary case of interest: roto-translation equivariance. We solve the PDE of interest by a combination of linear group convolutions and non-linear morphological group convolutions with analytic kernel approximations that we underpin with formal theorems. Our kernel approximations allow for fast GPU-implementation of the PDE-solvers, we release our implementation with this article in the form of the LieTorch extension to PyTorch, available at https://gitlab.com/bsmetsjr/lietorch . Just like for linear convolution a morphological convolution is specified by a kernel that we train in our PDE-G-CNNs. In PDE-G-CNNs we do not use non-linearities such as max/min-pooling and ReLUs as they are already subsumed by morphological convolutions. We present a set of experiments to demonstrate the strength of the proposed PDE-G-CNNs in increasing the performance of deep learning based imaging applications with far fewer parameters than traditional CNNs.

Anatoliy Babic, Harshit Bansal, Gianluca Finocchio et al.

SciSports is a Dutch startup company specializing in football analytics. This paper describes a joint research effort with SciSports, during the Study Group Mathematics with Industry 2018 at Eindhoven, the Netherlands. The main challenge that we addressed was to automatically process empirical football players' trajectories, in order to extract useful information from them. The data provided to us was two-dimensional positional data during entire matches. We developed methods based on Newtonian mechanics and the Kalman filter, Generative Adversarial Nets and Variational Autoencoders. In addition, we trained a discriminator network to recognize and discern different movement patterns of players. The Kalman-filter approach yields an interpretable model, in which a small number of player-dependent parameters can be fit; in theory this could be used to distinguish among players. The Generative-Adversarial-Nets approach appears promising in theory, and some initial tests showed an improvement with respect to the baseline, but the limits in time and computational power meant that we could not fully explore it. We also trained a Discriminator network to distinguish between two players based on their trajectories; after training, the network managed to distinguish between some pairs of players, but not between others. After training, the Variational Autoencoders generated trajectories that are difficult to distinguish, visually, from the data. These experiments provide an indication that deep generative models can learn the underlying structure and statistics of football players' trajectories. This can serve as a starting point for determining player qualities based on such trajectory data.