activity
20172021
most citedExtracting Global Dynamics of Loss Landscape in Deep Learning Models

1 citations · 1 across the 2 of their papers we have counts for

collaborators

5 papers

math.DS20211 cited

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…

math.DS2021

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…

math.DS2019

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…

nlin.AO2019

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…

math.DS2017

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…