Randomized Neural Networks
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HalfNet: Randomized Neural Networks with Learned Subspace Geometry
arXiv:2606.04583v1 Announce Type: new Abstract: 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 $N(0, \Sigma)$, where $\Sigma$, 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...
Robust class-gated single-pixel diffractive optical neural network with random-aberration-aware training
Announce Type: new Abstract: Optical computing offers the theoretical potential for high-speed, energy-efficient inference, yet its practical deployment remains constrained by fundamental input-output bottlenecks, particularly the reliance on electronic sensors with limited frame rates and stringent alignment requirements between optical components. Here, we demonstrate an image-class-gated single-pixel DONN that overcomes these limitations by converting spatial complexity into a temporal...
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
Announce Type: new Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional input, it employs $d$ independent subnetworks -- each acting on a single coordinate -- and constructs basis functions via element-wise multiplication of their outputs....
Pruning Deep Neural Networks via the Marchenko--Pastur Distribution
Announce Type: new Abstract: We study a Marchenko--Pastur (MP) random-matrix approach to pruning deep neural networks with very small post-pruning fine-tuning budgets. The main practical contribution is accuracy retention under short calibration and fine-tuning schedules, rather than a long post-pruning reoptimization pipeline. The theory gives deterministic data-path certificates: if the removed component $R$ has small propagated logit effect $L_s \| R \psi_1(s) \|_\infty$, pruning...
Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
Announce Type: replace Abstract: This paper introduces the Stochastic-Dimension Frozen Sampled Neural Network (SD-FSNN), a novel computational framework for solving high-dimensional Gross-Pitaevskii equation (GPE) on unbounded domain. The proposed method circumvents the curse-of-dimensionality that plagues traditional discretizations and the computational bottlenecks of gradient-based neural network solvers through a synergistic combination of techniques. First, a prescribed Gaussian...
Rank dependency of rescaled pruning in recurrent neural networks
Throughout development and maturity, neural circuits undergo massive synaptic pruning, yielding highly sparse connectivity while preserving robust population-level computations. These population dynamics are often low-dimensional, allowing task-related computations to be formalized as trajectories within latent subspaces. How such low-dimensional dynamics are preserved amid widespread network sparsification remains unclear.
Neural Networks Provably Learn Spectral Representations for Group Composition
arXiv:2606.02993v1 Announce Type: new Abstract: Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict $g_1 \star g_2$ for elements of a finite group $G$. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient...
Impact of Graph Structure on Membership-Inference Risk for Graph Neural Networks
arXiv:2601.17130v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are widely used for tasks such as node classification and link prediction, but their use in sensitive settings raises concerns about training-data leakage. Prior work on privacy leakage in GNNs largely borrows assumptions from non-graph domains, overlooking the role of graph structure. We argue for a graph-specific analysis of privacy risk and study how graph structure affects node-level membership inference.
Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs
Announce Type: new Abstract: Graph Neural Networks (GNNs) have emerged as a powerful tool for wireless resource allocation that leverages the underlying graph structure of communication networks. Their transferability property enables models trained on small-scale graphs to generalize to large-scale deployments with little performance deterioration, a desirable property for currently growing networks. Wireless networks are sparse regimes, where a single node is connected to a small number of...
Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process
Announce Type: new Abstract: Uncertainty quantification in neural networks prediction is a main issue for usual applications. Our approach seeks at reducing computation costs by directly evaluating uncertainty using PDE's information on the asymptotic variance, rather than the deep ensemble method which may be seen as a Monte Carlo estimation of the prediction, requiring the training of multiple networks. We thus study the law of the limiting process describing the random fluctuations around...