Related papers: Geodesic Mode Connectivity
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an…
We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes,…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical…
In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…
Directions and paths, as commonly provided by navigation systems, are usually derived considering absolute metrics, e.g., finding the shortest path within an underlying road network. With the aid of crowdsourced geospatial data we aim at…
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with…
Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and the intricate geometric characteristics of loss landscapes,…
Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not…
This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data.…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…