This paper presents a novel approach to vehicle positioning that operates without reliance on the global navigation satellite system (GNSS). Traditional GNSS approaches are vulnerable to interference in certain environments, rendering them unreliable in situations such as urban canyons, under flyovers, or in low reception areas. This study proposes a vehicle positioning method based on learning the road signature from accelerometer and gyroscope measurements obtained by an inertial measurement unit (IMU) sensor. In our approach, the route is divided into segments, each with a distinct signature that the IMU can detect through the vibrations of a vehicle in response to subtle changes in the road surface. The study presents two different data-driven methods for learning the road segment from IMU measurements. One method is based on convolutional neural networks and the other on ensemble random forest applied to handcrafted features. Additionally, the authors present an algorithm to deduce the position of a vehicle in real-time using the learned road segment. The approach was applied in two positioning tasks: (i) a car along a$6 \ [km]$route in a dense urban area; (ii) an e-scooter on a$1 \ [km]$route that combined road and pavement surfaces. The mean error between the proposed method’s position and the ground truth was approximately$50 \ [m] $for the car and$30 \ [m]$for the e-scooter. Compared to a solution based on time integration of the IMU measurements, the proposed approach has a mean error of more than 5 times better for e-scooters and 20 times better for cars.

Many problems in machine learning (ML) can be cast as learning functions from sets to graphs, or more generally to hypergraphs; in short, Set2Graph functions. Examples include clustering, learning vertex and edge features on graphs, and learning features on triplets in a collection. A natural approach for building Set2Graph models is to characterize all linear equivariant set-to-hypergraph layers and stack them with non-linear activations. This posses two challenges: (i) the expressive power of these networks is not well understood; and (ii) these models would suffer from high, often intractable computational and memory complexity, as their dimension grows exponentially. This paper advocates a family of neural network models for learning Set2Graph functions that is both practical and of maximal expressive power (universal), that is, can approximate arbitrary continuous Set2Graph functions over compact sets. Testing these models on different machine learning tasks, mainly an application to particle physics, we find them favorable to existing baselines.

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation we are able to quickly adapt successful CNN models to the surface setting. The surface-image representation is based on a covering map from the image domain to the surface. Namely, the map wraps around the surface several times, making sure that every part of the surface is well represented in the image. Differently from previous surface-to-image representations, we provide a low distortion coverage of all surface parts in a single image. Specifically, for the use case of learning spherical signals, our representation provides a low distortion alternative to several popular spherical parameterizations used in deep learning. We have used the surface-to-image representation to apply standard CNN architectures to 3D models including spherical signals. We show that our method achieves state of the art or comparable results on the tasks of shape retrieval, shape classification and semantic shape segmentation.

Constraining linear layers in neural networks to respect symmetry transformations from a group $G$ is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a fundamental question that has received very little attention to date: Can these networks approximate any (continuous) invariant function? We tackle the rather general case where $G\leq S_n$ (an arbitrary subgroup of the symmetric group) that acts on $\R^n$ by permuting coordinates. This setting includes several recent popular invariant networks. We present two main results: First, $G$-invariant networks are universal if high-order tensors are allowed. Second, there are groups $G$ for which higher-order tensors are unavoidable for obtaining universality. $G$-invariant networks consisting of only first-order tensors are of special interest due to their practical value. We conclude the paper by proving a necessary condition for the universality of $G$-invariant networks that incorporate only first-order tensors. Lastly, we propose a conjecture stating that this condition is also sufficient.