This paper analyzes the numerical stability of Extreme Learning Machines (ELM) from a spectral perspective, focusing on how the conditioning of the hidden layer matrix affects training reliability. The authors demonstrate that the smallest singular value determines perturbation amplification in output weights, while the condition number quantifies hidden-layer instability.
- SVD-based pseudoinverse computation is identified as the most reliable method under ill-conditioning compared to iterative hyperpower methods.
- Iterative methods are shown to be more sensitive to the spectral properties of the matrix.
- Width-dependent conditioning is discussed through a random feature interpretation.
- Experiments on synthetic matrices and ELM benchmarks confirm that stability is fundamentally governed by the singular value structure.
The findings suggest that understanding the singular value structure is critical for ensuring the stability of pseudoinverse-based ELMs.