arXiv:2605.24390v1 Announce Type: new Abstract: The eigendecomposition of the Laplace--Beltrami Operator (LBO) is fundamental to geometric analysis, yet computing its low-frequency eigenmodes remains a significant bottleneck due to the high cost of iterative solvers on large-scale data. To amortize this cost, we introduce the Neural Eigenspace Operator (NEO), a feed-forward framework designed to predict the spectrum directly from point clouds. Crucially, NEO circumvents the ill-posed nature of standard eigenvector regression, which suffers from intrinsic sign flips and rotation ambiguities, by
Advances in neural operators and the growing need for efficient geometric analysis in large-scale data environments are driving research into faster computational methods.
Efficiently computing Laplace-Beltrami eigenmodes is fundamental for various AI applications, including shape analysis, computer graphics, and physics simulations, significantly impacting the performance and scalability of these systems.
The development of methods like NEO could reduce the computational bottleneck associated with geometric analysis, potentially accelerating research and development in fields reliant on these calculations.
- · AI researchers
- · Computer graphics industry
- · Robotics
- · Computational science
- · Traditional iterative solvers for LBO
Faster processing of complex geometric data will become feasible.
New applications in real-time 3D reconstruction and high-fidelity simulations could emerge.
The widespread adoption of such operators could lead to more nuanced and responsive AI systems interacting with physical environments.
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Read at arXiv cs.LG