arXiv research

The paper proves differentiability of evolution maps in Lie groups.

New map constructed from equivariant spectra for manifold study.

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the evolution map is $C^0$-continuous on its domain $\textit{iff}\hspace{1pt}$ the Lie gro…

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the asymptotic estimate context. Specifically, let $G$ be a Lie group with asymptotic estimate Lie algebra $\mathfrak{g}$, and denote its evolution map by $\mathrm{evol}\colon \mathrm{D}\equiv \mathrm{dom}[\mathrm{evol}]\rightarrow G$, i.e.…

A hermitian algebra is a unital associative ${\mathbb C}$-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ${\mathbb R}$. In the case of an algebra ${\mathcal A}$ endowed with a Mackey-complete, locally convex topology such that the set of invertible elements is open an…

In the dual $L_{Φ^*}$ of a $Δ_2$-Orlicz space $L_Φ$, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology $τ(L_{Φ^*},L_Φ)$ if and only if on each order interval $[-ζ,ζ]=\{ξ: -ζ\leq ξ\leqζ\}$ ($ζ\in L_{Φ^*}$), it is lowe…

RPNN-EOFs model improves time series forecasting accuracy.

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of $K\times K$ invariant polarizations on $T^{\ast}K$. The …

Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.

We define and study the Burnside quotient Green ring of a Mackey functor. Some refinements of Dress induction theory are presented, together with applications to computation results for $K$-theory and $L$-theory of finite and infinite groups.

Counterexample disproves completeness of model space forcing regularity in infinite-dimensional Lie groups.

Characterizes continuity of monotone functionals in mixed topology.

Study on diffeologies on locally convex spaces and smooth multiplication of distributions.

Functor connects Lie groupoid algebras to bornological structures.

We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structur…

Spatio-temporal RBF neural networks improve chaotic time series prediction.

Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Shor…

Combines Fourier methods and RNNs for efficient time series prediction.

This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein and Xu. Secondly, it is shown how this procedure is quantized by Rieffel induction…

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration proce…

We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.

ICA accurately estimates treatment effects even with confounders.

For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state tra…

ForGAN uses GANs for probabilistic forecasting of sensory data.

Enhances supervised learning speed with KT algorithm.

Extends particle classification to curved space-times using groupoids.

Improves probability distribution compression with KT algorithm.

Compress++ speeds up distribution compression to near-linear time.

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of s…

Global models outperform univariate benchmarks in complex time series forecasting.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

The paper studies continuous submodular functions and their optimization.

Bilevel Continual Learning improves continual learning by transferring knowledge effectively.

Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.

The study proves unique continuation for biharmonic maps.

Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.

CANDI solves the gap between continuous and discrete diffusion models for text generation.

Faster policy learning via continuous-time gradients.

Study on Hölder continuity of complex Monge-Ampère solutions on Stein spaces.

Classifies when homeomorphism groups of stable surfaces have automatic continuity.

EBMs improve continual learning without external memory or regularization.

Root's barrier is continuous and finite under certain conditions.

We solve the Dirichlet problem for the complex Monge-Ampère equation on a strictly pseudoconvex with the right hand side being a positive Borel measure which is dominated by the Monge-Ampère measure of a Hölder continuous plurisubharmonic function. If the boundary data is continuous, then the solution is continuous. If…

Study on existence and properties of continuous solutions to complex Hessian equations.

Continuous time framework for discrete data denoising models.

Study on continual learning with Twitter data, developing ConGraD algorithm.

Continuity of Kähler-Einstein potentials at singularities proven.