相关论文: Geometric and Spectral Alignment for Deep Neural N…

This paper introduces new tests of fundamental physics by means of the analysis of disturbances on the GNSS signal propagation. We show how the GNSS signals are sensitive to a space variation of the fine structure constant $\alpha$ in a…

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input…

Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine…

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…

Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

Many wireless vision applications, such as autonomous driving, require preservation of global structural information rather than only per-pixel fidelity. However, existing Deep joint source-channel coding (DeepJSCC) schemes mainly optimize…

Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…

We study the deterministic skeleton of the renormalized stochastic Allen--Cahn equation in spatial dimension $2$. For all sufficiently small regularization parameters $\delta>0$, we construct monotone traveling wave front solutions…

Modern neural network architectures often generalize well despite containing many more parameters than the size of the training dataset. This paper explores the generalization capabilities of neural networks trained via gradient descent. We…

Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…

State-space models (SSMs) have become a cornerstone for unraveling brain dynamics, revealing how latent neural states evolve over time and give rise to observed signals. By combining the flexibility of deep learning with the principled…

The interplay between quantum geometry and electron correlation has emerged as a compelling paradigm in quantum many-body physics. Recent studies have highlighted the diagnostic utility of quantum geometry in identifying magnetic…

We present a detailed numerical study of the electronic properties of single-layer graphene with resonant ("hydrogen") impurities and vacancies within a framework of noninteracting tight-binding model on a honeycomb lattice. The algorithms…

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network.…

Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is…

We present a pipeline for geomorphological analysis that uses structure from motion (SfM) and deep learning on close-range aerial imagery to estimate spatial distributions of rock traits (size, roundness, and orientation) along a tectonic…

Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…

Graph structural information such as topologies or connectivities provides valuable guidance for graph convolutional networks (GCNs) to learn nodes' representations. Existing GCN models that capture nodes' structural information weight in-…

Recent Graph Neural Networks (GNNs) combine spectral-spatial architectures for enhanced representation learning. However, limited attention has been paid to certified robustness, particularly regarding training strategies and underlying…