arXiv:2603.10277v3 Announce Type: replace Abstract: In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs). For efficient deployment of GNNs, we introduce a graph feature construction with $\mathrm{O}(\mathrm{nnz} + n)$ complexity, where $\mathrm{nnz}$ is the number of non-zero elements in the matrix and $n$ denotes the matrix dimension. We propose two schemes for estimating the matrix condition number using GNNs; One follows by decomposing the condition number and predicts the relatively more computationally intensive
The increasing complexity and scale of machine learning models and large-scale scientific computing necessitate more efficient methods for numerical stability analysis, which estimating condition numbers addresses.
This development offers a faster, more scalable approach to assess numerical stability in large sparse matrix computations, crucial for advancing AI and scientific applications.
The ability to quickly estimate condition numbers using GNNs changes how researchers and engineers can analyze and optimize the numerical stability of their algorithms and models.
- · AI researchers
- · High-performance computing sector
- · Scientific computing
- · GNN developers
- · Traditional numerical analysis methods that are computationally intensive
Faster development and deployment cycles for AI models and scientific simulations due to improved numerical stability insights.
Reduced computational costs and resource consumption for tasks requiring condition number estimation.
Enabling more sophisticated and stable large-scale AI applications and scientific discoveries where numerical precision is critical.
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Read at arXiv cs.LG