Neural Networks Stability and Synchronization

Latest papers

• Circuit realization and hardware linearization of monotone operator equilibrium networks

  Thomas Chaffey · 23 June 2026

  It is shown that the port behavior of a resistor-diode network corresponds to the solution of a ReLU monotone operator equilibrium network (a neural network in the limit of infinite depth), giving a parsimonious construction of a neural network in analog hardware. We furthermore show that the gradie…

• Learning Multi-Agent Coordination via Sheaf-ADMM

  Jeffrey Seely, Bart{\l}omiej Cupia{\l}, Llion Jones · 1 June 2026

  We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multiplier…

• Learning Dynamic Stability Landscapes in Synchronization Networks

  Christian Nauck, Junyou Zhu, Michael Lindner, Frank Hellmann · 25 May 2026

  The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchron…

• Von Neumann Networks

  Shekhar S. Chandra · 8 May 2026

  In the mid-twentieth century, mathematician and polymath John von Neumann created a computational system on an array of cells as a simple model of the human brain, where each cell had one of a finite set of roles or states that he predicted would be modelled by a diffusion process. In this work, we …

• Quantization Robustness of Monotone Operator Equilibrium Networks

  James Li, Philip H. W. Leong, Thomas Chaffey · 12 March 2026

  Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence. When deployed on low-precision hardware, weights are quantized, potentially destroying these guarantees. We analyze wei…

• Uncertainty Propagation Networks for Neural Ordinary Differential Equations

  Hadi Jahanshahi, Zheng H. Zhu · 25 February 2026

  This paper introduces Uncertainty Propagation Network (UPN), a novel family of neural differential equations that naturally incorporate uncertainty quantification into continuous-time modeling. Unlike existing neural ODEs that predict only state trajectories, UPN simultaneously model both state evol…

• On finite-dimensional encoding/decoding theorems for neural operators

  Vin\'icius Luz Oliveira, Vladimir G. Pestov · 3 February 2026

  Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations, one employs finite-dimensional encoding/decoding theorems o…

• The Alexander-Hirschowitz theorem for neurovarieties

  A. Massarenti, M. Mella · 26 November 2025

  We study neurovarieties for polynomial neural networks and fully characterize when they attain the expected dimension in the single-output case. As consequences, we establish non-defectiveness and global identifiability for multi-output architectures.…