EEG is the most common signal source for noninvasive BCI applications. For such applications, the EEG signal needs to be decoded and translated into appropriate actions. A recently emerging EEG decoding approach is deep learning with Convolutional or Recurrent Neural Networks (CNNs, RNNs) with many different architectures already published. Here we present a novel framework for the large-scale evaluation of different deep-learning architectures on different EEG datasets. This framework comprises (i) a collection of EEG datasets currently comprising 100 examples (recording sessions) from six different classification problems, (ii) a collection of different EEG decoding algorithms, and (iii) a wrapper linking the decoders to the data as well as handling structured documentation of all settings and (hyper-) parameters and statistics, designed to ensure transparency and reproducibility. As an applications example we used our framework by comparing three publicly available CNN architectures: the Braindecode Deep4 ConvNet, Braindecode Shallow ConvNet, and EEGNet. We also show how our framework can be used to study similarities and differences in the performance of different decoding methods across tasks. We argue that the deep learning EEG framework as described here could help to tap the full potential of deep learning for BCI applications.

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives of a given order are subject to inequality or equality constraints. We then characterize the posterior distribution over model and constraint parameters through stochastic variational inference. As a result, the proposed approach allows for accurate and scalable uncertainty quantification on the predictions and on all parameters. We demonstrate the application of equality constraints in the challenging problem of parameter inference in ordinary differential equation models, while we showcase the application of inequality constraints on the problem of monotonic regression of count data. The proposed approach is extensively tested in several experimental settings, leading to highly competitive results in challenging modeling applications, while offering high expressiveness, flexibility and scalability.

Mode connectivity is a recently introduced frame- work that empirically establishes the connected- ness of minima by finding a high accuracy curve between two independently trained models. To investigate the limits of this setup, we examine the efficacy of this technique in extreme cases where the input models are trained or initialized differently. We find that the procedure is resilient to such changes. Given this finding, we propose using the framework for analyzing loss surfaces and training trajectories more generally, and in this direction, study SGD with cosine annealing and restarts (SGDR). We report that while SGDR moves over barriers in its trajectory, propositions claiming that it converges to and escapes from multiple local minima are not substantiated by our empirical results.

Persistence diagrams are important feature descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in Machine Learning have been done through kernel methods, i.e., embeddings of persistence diagrams into Reproducing Kernel Hilbert Spaces (RKHS), in which all computations can be performed easily. Since persistence diagrams enjoy theoretical stability guarantees for the diagram distances, the {\em metric properties} of a kernel $k$, i.e., the relationship between the RKHS distance $d_k$ and the diagram distances, are of central interest for understanding if the persistence diagram guarantees carry over to the embedding. In this article, we study the possibility of embedding persistence diagrams into RKHS with bi-Lipschitz maps. In particular, we show that when the RKHS is infinite dimensional, any lower bound must depend on the cardinalities of the persistence diagrams, and that when the RKHS is finite dimensional, finding a bi-Lipschitz embedding is impossible, even when restricting the persistence diagrams to have bounded cardinalities.

Inverse reinforcement learning is the problem of inferring the reward function of an observed agent, given its policy or behavior. Researchers perceive IRL both as a problem and as a class of methods. By categorically surveying the current literature in IRL, this article serves as a reference for researchers and practitioners in machine learning to understand the challenges of IRL and select the approaches best suited for the problem on hand. The survey formally introduces the IRL problem along with its central challenges which include accurate inference, generalizability, correctness of prior knowledge, and growth in solution complexity with problem size. The article elaborates how the current methods mitigate these challenges. We further discuss the extensions of traditional IRL methods: (i) inaccurate and incomplete perception, (ii) incomplete model, (iii) multiple rewards, and (iv) non-linear reward functions. This discussion concludes with some broad advances in the research area and currently open research questions.

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as molecular structures, abstract syntax trees of computer programs, or syntax trees of natural language, by learning the cost function of an edit distance, i.e. the costs of replacing, deleting, or inserting nodes in a tree. However, learning such costs directly may yield an edit distance which violates metric axioms, is challenging to interpret, and may not generalize well. In this contribution, we propose a novel metric learning approach for trees which learns an edit distance indirectly by embedding the tree nodes as vectors, such that the Euclidean distance between those vectors supports class discrimination. We learn such embeddings by reducing the distance to prototypical trees from the same class and increasing the distance to prototypical trees from different classes. In our experiments, we show that our proposed metric learning approach improves upon the state-of-the-art in metric learning for trees on six benchmark data sets, ranging from computer science over biomedical data to a natural-language processing data set containing over 300,000 nodes.

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found generator or classifier. This paper proposes to model GANs explicitly as finite games in mixed strategies, thereby ensuring that every LNE is an NE. With this formulation, we propose a solution method that is proven to monotonically converge to a resource-bounded Nash equilibrium (RB-NE): by increasing computational resources we can find better solutions. We empirically demonstrate that our method is less prone to typical GAN problems such as mode collapse, and produces solutions that are less exploitable than those produced by GANs and MGANs, and closely resemble theoretical predictions about NEs.

We focus on two supervised visual reasoning tasks whose labels encode a semantic relational rule between two or more objects in an image: the MNIST Parity task and the colorized Pentomino task. The objects in the images undergo random translation, scaling, rotation and coloring transformations. Thus these tasks involve invariant relational reasoning. We report uneven performance of various deep CNN models on these two tasks. For the MNIST Parity task, we report that the VGG19 model soundly outperforms a family of ResNet models. Moreover, the family of ResNet models exhibits a general sensitivity to random initialization for the MNIST Parity task. For the colorized Pentomino task, now both the VGG19 and ResNet models exhibit sluggish optimization and very poor test generalization, hovering around 30% test error. The CNN we tested all learn hierarchies of fully distributed features and thus encode the distributed representation prior. We are motivated by a hypothesis from cognitive neuroscience which posits that the human visual cortex is modularized, and this allows the visual cortex to learn higher order invariances. To this end, we consider a modularized variant of the ResNet model, referred to as a Residual Mixture Network (ResMixNet) which employs a mixture-of-experts architecture to interleave distributed representations with more specialized, modular representations. We show that very shallow ResMixNets are capable of learning each of the two tasks well, attaining less than 2% and 1% test error on the MNIST Parity and the colorized Pentomino tasks respectively. Most importantly, the ResMixNet models are extremely parameter efficient: generalizing better than various non-modular CNNs that have over 10x the number of parameters. These experimental results support the hypothesis that modularity is a robust prior for learning invariant relational reasoning.

Gating is a key technique used for integrating information from multiple sources by long short-term memory (LSTM) models and has recently also been applied to other models such as the highway network. Although gating is powerful, it is rather expensive in terms of both computation and storage as each gating unit uses a separate full weight matrix. This issue can be severe since several gates can be used together in e.g. an LSTM cell. This paper proposes a semi-tied unit (STU) approach to solve this efficiency issue, which uses one shared weight matrix to replace those in all the units in the same layer. The approach is termed "semi-tied" since extra parameters are used to separately scale each of the shared output values. These extra scaling factors are associated with the network activation functions and result in the use of parameterised sigmoid, hyperbolic tangent, and rectified linear unit functions. Speech recognition experiments using British English multi-genre broadcast data showed that using STUs can reduce the calculation and storage cost by a factor of three for highway networks and four for LSTMs, while giving similar word error rates to the original models.

The task of Question Answering has gained prominence in the past few decades for testing the ability of machines to understand natural language. Large datasets for Machine Reading have led to the development of neural models that cater to deeper language understanding compared to information retrieval tasks. Different components in these neural architectures are intended to tackle different challenges. As a first step towards achieving generalization across multiple domains, we attempt to understand and compare the peculiarities of existing end-to-end neural models on the Stanford Question Answering Dataset (SQuAD) by performing quantitative as well as qualitative analysis of the results attained by each of them. We observed that prediction errors reflect certain model-specific biases, which we further discuss in this paper.