5 papers
Fluctuations of Nonlinear Observables in Mean Field Neural Network Training
Arnaud Descours, Geoffrey Lacour
Mean field limits describe the training dynamics of wide neural networks through the evolution of the empirical distribution of their parameters. Although functional central limit…
Borel dimension growth and hyperfiniteness
Jan Grebík, Andrew S. Marks, Václav Rozhoň +1
We show that every increasing union of Borel graphs of pointwise volume growth at most is hyperfinite, where is the unique real root of $(1 - γ)^3…
Bolzano: Case Studies in LLM-Assisted Mathematical Research
Martin Balko, Jan Grebík, Pavel Hubáček +5
We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orc…
Convergence of spectra of digraph limits
Jan Grebík, Daniel Král', Xizhi Liu +2
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness…
Fractional Divisibility of Spheres with Partially Generic Sets of Rotations
Jan Grebík, Christian Ikenmeyer, Oleg Pikhurko
We say that an r-tuple of special orthogonal matrices fractionally divides the -dimensional sphere if there is a non-constant function in $L^…