Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter

2025-10-27

AI Summary

Neural networks for eigenvalue computation suffer from heavy reliance on large-scale labeled operator-eigenvalue pairs and inefficient data generation. Method: This paper proposes an operator-similarity-based acceleration framework for eigenvalue dataset construction. It introduces a novel clustering scheme leveraging spectral distribution similarity among operators, combined with truncated FFT-based sorting; further, it designs a ranking-aware Chebyshev subspace filter to reuse historical eigenpairs for cross-problem knowledge transfer, eliminating redundant eigenvalue computations. The method requires no additional training—only precomputation and filtering suffices. Contribution/Results: Experiments demonstrate up to 3.5× speedup over conventional numerical solvers while preserving numerical accuracy. To the best of our knowledge, this is the first dedicated acceleration framework tailored specifically for eigenvalue dataset generation.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Eigenvalue problems are among the most important topics in many scientific disciplines. With the recent surge and development of machine learning, neural eigenvalue methods have attracted significant attention as a forward pass of inference requires only a tiny fraction of the computation time compared to traditional solvers. However, a key limitation is the requirement for large amounts of labeled data in training, including operators and their eigenvalues. To tackle this limitation, we propose a novel method, named Sorting Chebyshev Subspace Filter (SCSF), which significantly accelerates eigenvalue data generation by leveraging similarities between operators -- a factor overlooked by existing methods. Specifically, SCSF employs truncated fast Fourier transform sorting to group operators with similar eigenvalue distributions and constructs a Chebyshev subspace filter that leverages eigenpairs from previously solved problems to assist in solving subsequent ones, reducing redundant computations. To the best of our knowledge, SCSF is the first method to accelerate eigenvalue data generation. Experimental results show that SCSF achieves up to a $3.5 imes$ speedup compared to various numerical solvers.

Problem

• Accelerating eigenvalue dataset generation for neural methods
• Reducing redundant computations in eigenvalue problem solving
• Leveraging operator similarities to improve data generation efficiency

Innovation

• Grouping operators with similar eigenvalue distributions
• Constructing Chebyshev subspace filter from solved problems
• Reducing redundant computations via truncated Fourier sorting