Related papers: Geometric and Topological Inference for Deep Repre…

The thesis explores the role machine learning methods play in creating intuitive computational models of neural processing. Combined with interpretability techniques, machine learning could replace human modeler and shift the focus of human…

The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to…

Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…

Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…

Human intelligence relies in part on our brains' ability to create abstract mental models that succinctly capture the hidden blueprint of our reality. Such abstract world models notably allow us to rapidly navigate novel situations by…

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

One of the most crucial tasks in the future will be to understand what is going on in neural networks, as they will become even more powerful and widely deployed. This work aims to use TDA methods to analyze neural representations. We…

To tackle increasingly complex tasks, it has become an essential ability of neural networks to learn abstract representations. These task-specific representations and, particularly, the invariances they capture turn neural networks into…

Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…

In neuroimaging, extensive post-processing of resting-state functional MRI (rfMRI) data is necessary for its application and investigation in relation to brain-behavior associations. Such post-processing is used to derive brain…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot…

Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…

Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.…

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on…