I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory
arXiv:2606.29675v1 Announce Type: new Abstract: Bogomolny, Bohigas and Schmit (BBS) found that the spectrum of the pairwise distance matrix on N points sampled from a smooth d-dimensional manifold encodes a signature of the underlying geometry. We develop I-BBS (Inference-BBS), a coordinate-free method that identifies a low-dimensional latent sub-manifold embedded in a high-dimensional ambient distance matrix alone, without accessing an ambient high-dimensional vector space. It therefore applies even when that space is only partly observable or undefined. We model the ambient embedding by two
The continuous advancements in machine learning and data science, coupled with increasingly complex datasets, are driving the need for more efficient and robust methods of dimensionality reduction and data interpretation.
This development offers a coordinate-free method for uncovering latent structures in high-dimensional data, which is critical for understanding complex systems where full observability or well-defined vector spaces are lacking.
The ability to infer low-dimensional sub-manifolds from distance matrices alone provides new tools for AI, potentially expanding its application to areas with partially observable or undefined ambient spaces.
- · AI researchers and developers
- · Data scientists
- · Sectors with complex, high-dimensional data
- · Developers of AI agents
- · Traditional dimensionality reduction methods in specific applications
Improved performance and applicability of AI models in scenarios with incomplete or non-Euclidean data.
Acceleration of research into novel AI architectures that can exploit these coordinate-free understandings of data topology.
Potential for new forms of 'dark matter' discovery in scientific fields by identifying previously hidden latent structures.
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