Related papers: A geometry of information, I: Nerves, posets and d…

Neural models learn data representations that lie on low-dimensional manifolds, yet modeling the relation between these representational spaces is an ongoing challenge. By integrating spectral geometry principles into neural modeling, we…

We discuss the Pistone-Sempi exponential manifold on the finite-dimensional Gaussian space. We consider the role of the entropy, the continuity of translations, Poincar\'e-type inequalities, the generalized differentiability of probability…

Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…

The human brain represents objects in a way that is both invariant across instances and flexible enough to support different contexts and tasks. Yet it remains unknown how object representations are dynamically remapped as the same object…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure"…

Disentangled representation learning offers useful properties such as dimension reduction and interpretability, which are essential to modern deep learning approaches. Although deep learning techniques have been widely applied to…

We present a method that learns a spatiotemporal neural irradiance field for dynamic scenes from a single video. Our learned representation enables free-viewpoint rendering of the input video. Our method builds upon recent advances in…

Explainability of deep neural networks is one of the most challenging and interesting problems in the field. In this study, we investigate the topic focusing on the interpretability of deep learning-based registration methods. In…

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…

This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…

Deep learning approaches to generic (non-semantic) segmentation have so far been indirect and relied on edge detection. This is in contrast to semantic segmentation, where DNNs are applied directly. We propose an alternative approach called…

Dynamic graphs (DG) describe dynamic interactions between entities in many practical scenarios. Most existing DG representation learning models combine graph convolutional network and sequence neural network, which model spatial-temporal…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…

Extracting structured representations from raw visual data is an important and long-standing challenge in machine learning. Recently, techniques for unsupervised learning of object-centric representations have raised growing interest. In…

Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This…