7 papers
Scale-Agnostic Kolmogorov-Arnold Geometry in Neural Networks
Mathew Vanherreweghe, Michael H. Freedman, Keith M. Adams
Recent work by Freedman and Mulligan demonstrated that shallow multilayer perceptrons spontaneously develop Kolmogorov-Arnold geometric (KAG) structure during training on synthetic…
Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
Bennett Chow, Michael H. Freedman, Henry Shin +1
This note corrects an error in the proof of Proposition 13 in arXiv:1903.09181 and simultaneously establishes a more general result. We prove that if is a compact connected or…
Kolmogorov--Arnold stability
Sviatoslav V. Dzhenzher, Michael H. Freedman
Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or <<expressing>> functions, we test its robustness by analyzing its stability t…
How Many Links Fit in a Box?
Michael H. Freedman
In an earlier note [arXiv:2301.00295] it was shown that there is an upper bound to the number of disjoint Hopf links (and certain related links) that can be embedded in the unit cu…
Enhanced Hantzsche Theorem
Michael H. Freedman
A closed 3-manifold may be described up to some indeterminacy by a Heegaard diagram . The question "Does smoothly embed in ?'' is equivalent to a…
Quantum Detection of Recurrent Dynamics
Michael H. Freedman
Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and syste…
Simplifying 3-manifolds in R^4
Ian Agol, Michael H. Freedman
We show that a smooth embedding of a closed 3-manifold in S^3 x R can be isotoped so that every generic level divides S^3 x t into two handlebodies (i.e., is Heegaard) provided the…