Zobrazeno 1 - 10
of 190
pro vyhledávání: '"58Z05"'
Large language models encode the correlational structure present in natural language by fitting segments of utterances (tokens) into a high dimensional ambient latent space upon which the models then operate. We assert that in order to develop a foun
Externí odkaz:
http://arxiv.org/abs/2410.08993
We consider families $A(t)$ of self-adjoint operators with symmetry that causes the spectral flow of the family to vanish. We study the secondary $\mathbb{Z}_2$-valued spectral flow of such families. We prove an analog of the Atiyah-Singer-Robbin-Sal
Externí odkaz:
http://arxiv.org/abs/2409.15534
Fr\'echet means of samples from a probability measure $\mu$ on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). The methods and results proceed by introducing and proving analytic
Externí odkaz:
http://arxiv.org/abs/2311.09455
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field and lays t
Externí odkaz:
http://arxiv.org/abs/2311.09454
Any measure $\mu$ on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fr\'echet mean $\bar\mu$ yields a continuous "tangential collapse" from the tangent cone of M at $\bar\mu$ to a vector spa
Externí odkaz:
http://arxiv.org/abs/2311.09453
We review how diffeologies complete the settings classically used from infinite dimensional geometry to partial differential equations, based on classical settings of functional analysis and with classical mapping spaces as key examples. As the class
Externí odkaz:
http://arxiv.org/abs/2302.07838
Autor:
Chen, Gui-Qiang G.
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of mixed typ
Externí odkaz:
http://arxiv.org/abs/2208.06769
Autor:
Braun, Mathias
For a Lorentzian space measured by $\mathfrak{m}$ in the sense of Kunzinger, S\"amann, Cavalletti, and Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds by $K\in\boldsymbol{\mathrm{R}}$ and upper dimension bou
Externí odkaz:
http://arxiv.org/abs/2206.13005
Autor:
Braun, Mathias
Let $(M,\mathsf{d},\mathfrak{m},\ll,\leq,\tau)$ be a causally closed, $\mathscr{K}$-globally hyperbolic, regular measured Lorentzian geodesic space satisfying the weak timelike curvature-dimension condition $\smash{\mathrm{wTCD}_p^e(K,N)}$ in the sen
Externí odkaz:
http://arxiv.org/abs/2205.06950
Publikováno v:
Eur. Phys. J. Plus 138, 339 (2023)
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the lit
Externí odkaz:
http://arxiv.org/abs/2204.00954