arXiv:2606.16990v1 Announce Type: new Abstract: While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered by high dimensionality and the ``varying length'' problem across different filtration scales. We propose a compact spectral representation that distills the persistent Laplacian into three mathematically grounded invariants: Betti numbers, the spectral gap, and analytic torsion. Across benchmark datasets including MNIST, QM-3D, and SKEMPI WT, we demonstrate that this red
The paper was published now, proposing a new methodology for representing persistent Laplacians, which are critical in analyzing complex data geometries.
This research offers a more efficient and powerful way to extract meaningful features from data, potentially enhancing the performance and applicability of AI and machine learning across various domains.
The ability to distill complex geometric data into simpler, invariant representations could significantly improve the interpretability, efficiency, and robustness of advanced machine learning models.
- · AI/ML researchers
- · Data scientists
- · Healthcare (drug discovery)
- · Materials science
- · Traditional dimensionality reduction techniques
- · Inefficient geometric deep learning approaches
Improved performance and reduced computational cost for AI models dealing with complex topological data.
Accelerated discovery and design cycles in fields like chemistry, materials science, and biology due to better data representation.
New classes of AI applications become feasible as models can process and understand more intricate data structures efficiently.
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Read at arXiv cs.LG