In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g.

Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g.

However, these videos are limited in both quantity and diversity compared to dash cam videos, which are more widely used across various types of vehicles and capture a broader range of scenarios.

When the neural network's output is a single scalar, we prove that these

Rooftop 3D reconstruction using UAV-based photogrammetry offers a promising solution for infrastructure assessment, but existing methods often require high percentages of image overlap and extended flight times to ensure model accuracy when using autonomous flight paths. This study systematically evaluates key flight parameters-ground sampling distance (GSD) and image overlap-to optimize the 3D reconstruction of complex rooftop infrastructure. Controlled UAV flights were conducted over a multi-segment rooftop at Queen's University using a DJI Phantom 4 Pro V2, with varied GSD and overlap settings. The collected data were processed using Reality Capture software and evaluated against ground truth models generated from UAV-based LiDAR and terrestrial laser scanning (TLS). Experimental results indicate that a GSD range of 0.75-1.26 cm combined with 85% image overlap achieves a high degree of model accuracy, while minimizing images collected and flight time. These findings provide guidance for planning autonomous UAV flight paths for efficient rooftop assessments.

When the neural network's output is a single scalar, we prove that these

In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g.

Segway's all-new Navimow X350 robot lawn mower is a big step up from its earlier Navimow I- and H-series, which remain available. Segway's all-new Navimow X3 series of robot lawn mowers boasts enhanced navigation savvy and onboard AI. The Navimow X350 reviewed here is a big step up from the Navimow i110n mower I reviewed in 2024. The Navimow i110n's navigation was the best in its class at the time, and its cutting performance is fantastic. That said, I found the older mower--which will continue to be available for sale--to be underpowered, and it had an uncanny ability to find its way onto the street during my review period due to its poor cliff detection.

Studying the interplay between the geometry of the loss landscape and the optimization trajectories of simple neural networks is a fundamental step for understanding their behavior in more complex settings.This paper reveals the presence of topological obstruction in the loss landscape of shallow ReLU neural networks trained using gradient flow. We discuss how the homogeneous nature of the ReLU activation function constrains the training trajectories to lie on a product of quadric hypersurfaces whose shape depends on the particular initialization of the network's parameters. When the neural network's output is a single scalar, we prove that these quadrics can have multiple connected components, limiting the set of reachable parameters during training. We analytically compute the number of these components and discuss the possibility of mapping one to the other through neuron rescaling and permutation. In this simple setting, we find that the non-connectedness results in a topological obstruction, which, depending on the initialization, can make the global optimum unreachable.