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

Deep residual architectures are modeled as products of near-identity Jacobians. This paper proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors, emphasizing a normalized top-radial…

Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically available only for balanced deep linear models. We propose an…

Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical…

Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each…

This paper studies large-scale dynamical networks where the current state of the system is a linear transformation of the previous state, contaminated by a multivariate Gaussian noise. Examples include stock markets, human brains and gene…

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…

Weight matrices in deep networks exhibit geometric continuity -- principal singular vectors of adjacent layers point in similar directions. While this property has been widely observed, its origin remains unexplained. Through experiments on…

The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…

Graph neural networks (GNNs) have been proposed for medical image segmentation, by predicting anatomical structures represented by graphs of vertices and edges. One such type of graph is predefined with fixed size and connectivity to…

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…

Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian. Prior work has identified critical initialization schemes…

We provide a novel new approach for aligning geometric models using a dual graph structure where local features are mapping probabilities. Alignment of non-rigid structures is one of the most challenging computer vision tasks due to the…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

We characterize which local matrix structures saturate Weyl's eigenvalue perturbation bound for graph Laplacians under geometrically constrained vertex displacements. Geometric graphs with heavy-tailed vertex noise arise across sensor…

Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms, where they emerge as effective descriptions of strongly correlated phases and engineered dynamics. We introduce a…

Network-based Global Navigation Satellite Systems (GNSS) underpin critical infrastructure and autonomous systems, yet typically rely on centralized processing hubs that limit scalability, resilience, and latency. Here we report a…

Using the non-equilibrium Keldysh Green's function formalism, we investigate the local, non-equilibrium charge transport in graphene nanoribbons (GNRs). In particular, we demonstrate that the spatial current patterns associated with…

This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…

This article proposes a generative neural network architecture for spatially consistent air-to-ground channel modeling. The approach considers the trajectories of uncrewed aerial vehicles along typical urban paths, capturing spatial…

The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units…