We address a maximally structured case of the question, “Can you hear your location on a manifold,” posed by Wyman and Xi [Can you hear your location on a manifold?, https://arxiv.org/abs/2304.04659, 2023] for dimension . In short, we show that if a compact surface without a boundary sounds the same at every point, then the surface has a transitive action by the isometry group. In the process, we show that you can hear your location on Klein bottles and that you can hear the lengths and multiplicities of looping geodesics on compact hyperbolic quotients.
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This content will become publicly available on December 1, 2026
Embodied visuomotor representation
Abstract Imagine sitting at your desk, looking at objects on it. You do not know their exact distances from your eye in meters, but you can immediately reach out and touch them. Instead of an externally defined unit, your sense of distance is tied to your action’s embodiment. In contrast, conventional robotics relies on precise calibration to external units, with which vision and control processes communicate. We introduceEmbodied Visuomotor Representation, a methodology for inferring distance in a unit implied by action. With it a robot without knowledge of its size, environmental scale, or strength can quickly learn to touch and clear obstacles within seconds of operation. Likewise, in simulation, an agent without knowledge of its mass or strength can successfully jump across a gap of unknown size after a few test oscillations. These behaviors mirror natural strategies observed in bees and gerbils, which also lack calibration in an external unit.
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- Award ID(s):
- 2020624
- PAR ID:
- 10650603
- Editor(s):
- DeCroon, Guido
- Publisher / Repository:
- NPJ Robotics
- Date Published:
- Journal Name:
- npj Robotics
- Edition / Version:
- 1
- Volume:
- 3
- Issue:
- 1
- ISSN:
- 2731-4278
- Page Range / eLocation ID:
- 1 to 15
- Subject(s) / Keyword(s):
- embodied representation, vision, control
- Format(s):
- Medium: X Size: 2MB Other: pdf
- Size(s):
- 2MB
- Sponsoring Org:
- National Science Foundation
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