# CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks

arXiv: https://arxiv.org/abs/2605.12580 · HTML: https://mlsanity.com/paper/2605.12580/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 15 of 15)

- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Provable Benefit of Orthogonal Initialization in Optimizing Deep Linear Networks](https://mlsanity.com/paper/2001.05992/) (2020)
- [Characterizing Truthfulness in Large Language Model Generations with Local Intrinsic Dimension](https://mlsanity.com/paper/2402.18048/) (2024)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Random Vector Functional Link Neural Network based Ensemble Deep Learning](https://mlsanity.com/paper/1907.00350/) (2019)
- [Random Vector Functional Link Networks for Function Approximation on Manifolds](https://mlsanity.com/paper/2007.15776/) (2020)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [Intuitionistic Fuzzy Broad Learning System: Enhancing Robustness Against Noise and Outliers](https://mlsanity.com/paper/2307.08713/) (2023)
- [Old can be Gold: Better Gradient Flow can Make Vanilla-GCNs Great Again](https://mlsanity.com/paper/2210.08122/) (2022)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [GB-RVFL: Fusion of Randomized Neural Network and Granular Ball Computing](https://mlsanity.com/paper/2409.16735/) (2024)
- [Random orthogonal additive filters: a solution to the vanishing/exploding gradient of deep neural networks](https://mlsanity.com/paper/2210.01245/) (2022)
- [Ensemble Deep Random Vector Functional Link Neural Network Based on Fuzzy Inference System](https://mlsanity.com/paper/2406.00801/) (2024)

## Built on by (most cited first, 3 of 3)

- [Residual-Guided Randomized Neural Networks](https://mlsanity.com/paper/2608.28267/) (2026)
- [Robust Broad Learning System with Wave Loss for Classification under Data Uncertainty](https://mlsanity.com/paper/2608.29983/) (2026)
- [IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss](https://mlsanity.com/paper/2609.02422/) (2026)

## Abstract (arXiv)

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: https://github.com/mtanveer1/CAWI