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Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception
Announce Type: replace Abstract: Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potential process and increases its effective order through Kirchhoff-inspired cascade composition. A single Kirchhoff Neural Cell implements a stable first-order update,...
Chaos-Free Networks are Stable Recurrent Neural Networks
Announce Type: replace-cross Abstract: Gated Recurrent Neural Networks (RNNs) are widely used for nonlinear system identification due to their high accuracy, although they often exhibit complex, chaotic dynamics that are difficult to analyze. This paper investigates the system-theoretic properties of the Chaos-Free Network (CFN), an architecture originally proposed to eliminate the chaotic behavior found in standard gated RNNs. First, we formally prove that the CFN satisfies Input-to-State...
On the Evaluation of Spiking Neural Network Configurations for Network Intrusion Detection
Announce Type: new Abstract: Network intrusion detection is a core component of modern cybersecurity infrastructure, yet the deep learning models that dominate the field are computationally demanding, motivating interest in lightweight alternatives suited to edge and neuromorphic deployment. Spiking Neural Networks (SNNs) are therefore a natural candidate, but their design space, spanning the choice of neuron model and spike encoding scheme, remains poorly characterized for intrusion...
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
Announce Type: cross Abstract: We introduce Lie groupoid equivariant neural networks as a specialization of recently proposed topological category-equivariant neural networks to the differentiable setting. Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers, and we show how for suitable Lie groupoids they are equivalent to certain Lie algebroid-equivariant neural networks. We additionally describe groupoid invariant...
Introduction to Graph Neural Networks for Machine Learning Engineers
Announce Type: replace Abstract: Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on a broad range of tasks. This survey introduces graph neural networks through the encoder-decoder framework and provides examples of decoders for a range of graph analytic tasks.
Optimizing Energy-based Neural Network Training with Coherent Ising Machine
Announce Type: new Abstract: While Ising machines serve as advanced physical solvers for the Ising model,enabling applications in combinatorial optimization and neural network training,their scalability for large-scale neural networks remains constrained by hardware connectivity limitations and suboptimal training methodologies. In this work,we leverage a Coherent Ising Machine (CIM) to train an energy-based neural network using Equilibrium Propagation, achieving performance comparable to...
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....
Multigrade Neural Network Approximation
arXiv:2601.16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures remains challenging due to highly nonconvex and often ill-conditioned optimization landscapes. In contrast, for relatively shallow networks, most notably certain one-hidden-layer ReLU models, training...
Optimal Rates for Generalization of Gradient Descent Methods with Deep Neural Networks
Announce Type: cross Abstract: Recent progress has been made in understanding the statistical generalization performance of gradient descent methods for overparameterized neural networks within the neural tangent kernel (NTK) regime. However, most of the existing work on regression problems is limited to shallow network architectures, leaving a notable gap in the theory of deep neural networks.
Knockoffs-based False Discovery Rate Control and Simplification for Deep Neural Networks
arXiv:2606.04404v1 Announce Type: cross Abstract: The deep neural network is a widely used framework in machine learning that has been widely applied in various fields. However, deep neural networks often involve a large number of parameters and inputs, many of which may be irrelevant to the goal or true output. These parameters and \textcolor{black}{input variables} not only increase computational complexity, but also contribute to additional computational cost.