[2605.12580] CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks
[Submitted on 12 May 2026]
Title:CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks
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Abstract:Randomized neural networks (RdNNs) enable efficient, backpropagation-free training by freezing randomly initialized input-to-hidden weights, which permits a closed-form solution for the output layer. However, conventional random initialization is blind to inter-feature dependence, ignoring correlations, asymmetries, and tail dependence in the data, which degrades conditioning and predictive performance. To the best of our knowledge, this limitation remains unaddressed in the RdNN literature. To close this gap, we propose CAWI (Copula-Aligned Weight Initialization), a framework that draws input-to-hidden weights from a data-fitted copula that matches empirical dependence, ensuring the frozen projections respect inter-feature dependence without sacrificing the closed-form solution. CAWI (i) maps each feature to the unit interval using empirical CDFs, (ii) fits a multivariate copula that captures rank-based dependence among features, and (iii) samples each weight column w_j from the fitted copula and applies a fixed inverse marginal transform to set scale. The objective, solver, and "freeze-once" paradigm remain unchanged; only the sampling law for W becomes dependence-aware. For dependence modeling, we consider two copula families: elliptical (Gaussian, t) and Archimedean (Clayton, Frank, Gumbel). This enables CAWI to handle diverse dependence, including tail dependence. We evaluate CAWI across 83 diverse classification benchmarks (binary and multiclass) and two biomedical datasets, BreaKHis and the Schizophrenia dataset, using standard shallow and deep RdNN architectures. CAWI consistently delivers significant improvements in predictive performance over conventional random initialization. Code is available at: this https URL
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2605.12580 [cs.LG]
(or arXiv:2605.12580v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.12580
arXiv-issued DOI via DataCite
Journal reference: Proceedings of the 29th International Conference on Artificial Intelligence and Statistics (AISTATS) 2026
Submission history
From: M Tanveer PhD [view email] [v1] Tue, 12 May 2026 15:46:23 UTC (2,007 KB)
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