CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks

Mushir Akhtar, M. Tanveer, Mohd. Arshad
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3781-3789, 2026.

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 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. Codes are provided at \url{https://github.com/mtanveer1/CAWI}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-akhtar26a, title = { CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks }, author = {Akhtar, Mushir and Tanveer, M. and Arshad, Mohd.}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3781--3789}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/akhtar26a/akhtar26a.pdf}, url = {https://proceedings.mlr.press/v300/akhtar26a.html}, 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 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. Codes are provided at \url{https://github.com/mtanveer1/CAWI}. } }
Endnote
%0 Conference Paper %T CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks %A Mushir Akhtar %A M. Tanveer %A Mohd. Arshad %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-akhtar26a %I PMLR %P 3781--3789 %U https://proceedings.mlr.press/v300/akhtar26a.html %V 300 %X 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 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. Codes are provided at \url{https://github.com/mtanveer1/CAWI}.
APA
Akhtar, M., Tanveer, M. & Arshad, M.. (2026). CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3781-3789 Available from https://proceedings.mlr.press/v300/akhtar26a.html.

Related Material