topology and geometry
RoadGen: Generating Road Scenarios for Autonomous Vehicle Testing
Yang, Fan, Lu, You, Chen, Bihuan, Qin, Peng, Peng, Xin
With the rapid development of autonomous vehicles, there is an increasing demand for scenario-based testing to simulate diverse driving scenarios. However, as the base of any driving scenarios, road scenarios (e.g., road topology and geometry) have received little attention by the literature. Despite several advances, they either generate basic road components without a complete road network, or generate a complete road network but with simple road components. The resulting road scenarios lack diversity in both topology and geometry. To address this problem, we propose RoadGen to systematically generate diverse road scenarios. The key idea is to connect eight types of parameterized road components to form road scenarios with high diversity in topology and geometry. Our evaluation has demonstrated the effectiveness and usefulness of RoadGen in generating diverse road scenarios for simulation.
The Topology and Geometry of Neural Representations
Lin, Baihan, Kriegeskorte, Nikolaus
A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.