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
Many researchers investigated neural networks with some of their weights fixed to values randomly drawn from a given distribution, e.g., N(0,I). Our proposed HalfNet draws random weights from N(0,Σ), where Σ, which defines the geometry of the distribution, has a low-rank factorization that we learn from data. Experiments on MNIST and CIFAR-10 demonstrate that HalfNet can match the performance of fully trained multilayer perceptrons while using substantially fewer parameters. Spectral analysis indicates that much of the predictive power of neural networks lies in the geometry of their weight space rather than in the precise values of individual parameters, and we observe that accuracy scales smoothly with rank. HalfNet is not a neural architecture trick for low-rank structure; it implements a data-dependent random embedding that can also be interpreted through supervised metric learning, or random-feature and kernel perspectives.
Random initialization of convolutional filters does not use the training images. Previous work has shown that image patches can be copied into the first layer, and that k-means or principal components of patches can serve as filters. This paper compares four initializations of the first layer of a small convolutional network, with every other factor held fixed: He initialization, random mean-centered patches, principal components of those patches, and k-means centroids. Pre-Warm, our proposed methodology, is the rule-based use of both dictionaries: the patch count follows the filter count and a foreground density, both dictionaries are built from a single minibatch, and whichever of principal components or k-means better reconstructs those patches is written into the first half of the filter bank, rather than chosen by a validation search. The remaining filters stay random. On five datasets, principal components improve CIFAR-10 and CIFAR-100 relative to He initialization, and k-means improves SVHN and MNIST, and is the stronger of the two on Fashion-MNIST; copying raw patches does not reproduce those color-set gains. Use principal components on photographic patches and k-means on stroke-like patches; the first-batch reconstruction check recovers that split.
Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance g2 and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical gc for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.
Tommaso Fioratti, Riccardo Marcaccioli, Francesco Casola