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While neural networks have acted as a strong unifying force in the design of modern AI systems, the neural network architectures themselves remain highly heterogeneous due to the variety of tasks to be solved. In this chapter, we explore…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Endowing robots with human-like physical reasoning abilities remains challenging. We argue that existing methods often disregard spatio-temporal relations and by using Graph Neural Networks (GNNs) that incorporate a relational inductive…

Time series forecasting has received a lot of attention, with recurrent neural networks (RNNs) being one of the widely used models due to their ability to handle sequential data. Previous studies on RNN time series forecasting, however,…

We propose a method combining relational-logic representations with neural network learning. A general lifted architecture, possibly reflecting some background domain knowledge, is described through relational rules which may be handcrafted…

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…

Neural population activity in sensory cortex is organized on low-dimensional manifolds, but why such manifolds arise and what determines their geometry remain unclear. We model cortical populations as recurrent circuits driven by…

Machine learning architectures, including transformers and recurrent neural networks (RNNs) have revolutionized forecasting in applications ranging from text processing to extreme weather. Notably, advanced network architectures, tuned for…

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

Preserving geometric structure is important in learning. We propose a unified class of geometry-aware architectures that interleave geometric updates between layers, where both projection layers and intrinsic exponential map updates arise…

Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…

6DOF camera relocalization is an important component of autonomous driving and navigation. Deep learning has recently emerged as a promising technique to tackle this problem. In this paper, we present a novel relative geometry-aware Siamese…

Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying…

Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. However, it remains unclear what aspects of neural activity contribute to these computational…

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and…

The growing use of deep learning necessitates efficient network design and deployment, making neural predictors vital for estimating attributes such as accuracy and latency. Recently, Graph Neural Networks (GNNs) and transformers have shown…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…