Related papers: Yet another delooping machine
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic integrator is a numerical method specifically designed for…
Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…
A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…
It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The…
This is a research announcement on what is best termed `nonlocal' methods in mathematics. (This is not to be confused with global analysis.) The nonlocal formulation of physics in \cite{principia} points to a fresh viewpoint in mathematics:…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
We prove the converse of the universal approximation theorem, i.e. a neural network (NN) encoding theorem which shows that for every stably converged NN of continuous activation functions, its weight matrix actually encodes a continuous…
The paper introduces a new differential-geometric system which originates from the theory of $m$-Hessian operators. The core of this system is a new notion of invariant differentiation on multidimensional surfaces. This novelty gives rise…
We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…
A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie…
We present a generalization of standard Turing machines based on allowing unusual tapes. We present a set of reasonable constraints on tape geometry and classify all tapes conforming to these constraints. Surprisingly, this generalization…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
This talk describes the work done in calculating leading logarithms in massive effective field theories. We discuss shortly leading logarithms in renormalizable theories and how they can be calculated using only one-loop calculations in…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural…
This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…
A major focus in designing methods for learning distributions defined on manifolds is to alleviate the need to implicitly learn the manifold so that learning can concentrate on the data distribution within the manifold. However,…