Mapping is crucial for spatial reasoning, planning and robot navigation.
Existing approaches range from metric, which require precise geometry-based
optimization, to purely topological, where image-as-node based graphs lack
explicit object-level reasoning and interconnectivity. In this paper, we
propose a novel topological representation of an environment based on "image
segments", which are semantically meaningful and open-vocabulary queryable,
conferring several advantages over previous works based on pixel-level
features. Unlike 3D scene graphs, we create a purely topological graph with
segments as nodes, where edges are formed by a) associating segment-level
descriptors between pairs of consecutive images and b) connecting neighboring
segments within an image using their pixel centroids. This unveils a
"continuous sense of a place", defined by inter-image persistence of segments
along with their intra-image neighbours. It further enables us to represent and
update segment-level descriptors through neighborhood aggregation using graph
convolution layers, which improves robot localization based on segment-level
retrieval. Using real-world data, we show how our proposed map representation
can be used to i) generate navigation plans in the form of "hops over segments"
and ii) search for target objects using natural language queries describing
spatial relations of objects. Furthermore, we quantitatively analyze data
association at the segment level, which underpins inter-image connectivity
during mapping and segment-level localization when revisiting the same place.
Finally, we show preliminary trials on segment-level `hopping' based zero-shot
real-world navigation. Project page with supplementary details:
oravus.github.io/RoboHop/

基于图像片段的拓扑表示，通过图卷积层的邻域聚合改进机器人定位，并能够生成导航计划和通过自然语言查询搜索目标对象。

RoboHop: 基于分段拓扑地图的开放世界视觉导航

RoboHop: Segment-based Topological Map Representation for Open-World  Visual Navigation

The rise of Artificial Intelligence (AI) recently empowered researchers to
investigate hard mathematical problems which eluded traditional approaches for
decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields
laying the foundations of modern mathematics -- is still completely unexplored.
This work proposes the first use of AI to investigate UA's conjectures with an
equivalent equational and topological characterization. While topological
representations would enable the analysis of such properties using graph neural
networks, the limited transparency and brittle explainability of these models
hinder their straightforward use to empirically validate existing conjectures
or to formulate new ones. To bridge these gaps, we propose a general algorithm
generating AI-ready datasets based on UA's conjectures, and introduce a novel
neural layer to build fully interpretable graph networks. The results of our
experiments demonstrate that interpretable graph networks: (i) enhance
interpretability without sacrificing task accuracy, (ii) strongly generalize
when predicting universal algebra's properties, (iii) generate simple
explanations that empirically validate existing conjectures, and (iv) identify
subgraphs suggesting the formulation of novel conjectures.

人工智能应用于通用代数领域的推测性预测，通过等式表达和拓扑表示来增强透明度和可解释性，验证现有猜想并提出新的猜想。