1 citations · 1 across the 2 of their papers we have counts for
5 papers
Extracting Global Dynamics of Loss Landscape in Deep Learning Models
Mohammed Eslami, Hamed Eramian, Marcio Gameiro +2
Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states…
Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities
William Duncan, Tomas Gedeon, Hiroshi Kokubu +2
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge…
Lattice Structures for Attractors III
William D. Kalies, Konstantin Mischaikow, Robert C. A. M. Vandervorst
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattice…
Topological portraits of multiscale coordination dynamics
Mengsen Zhang, William D. Kalies, J. A. Scott Kelso +1
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaning…
Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds
William D. Kalies, Shane Kepley, J. D. Mireles James
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The proc…