arXiv research

Improved time complexity for parallel stochastic optimization in heterogeneous systems.

Let $P$ be a parabolic subgroup of a connected simply connected complex semisimple Lie group $G$. Given a compact Kähler manifold $X$, the dimensional reduction of $G$-equivariant holomorphic vector bundles over $X\times G/P$ was carried out by the first and third authors. This raises the question of dimensional reduct…

Efficiently reduces rank of non-negative matrices with quadratic time complexity.

WeldNet reduces complex dynamics to simpler, manageable segments.

Balanced Neural ODEs combine VAEs and Neural ODEs for efficient time series modeling.

Paper identifies reductive MDPs, solving them in polynomial time.

The study finds invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.

CLCNet improves noise reduction in hearing aids with deep learning.

The BC(n) Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups o…

The paper simplifies complex mechanical systems with external forces.

This work simplifies Gaussian process regression for multiple outputs.

Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By appl…

The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for machine learning by reductions: we develop reductions that take a method develo…

New algorithm reduces optimization complexity in adaptive mirror descent.

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent submodules we establish simple conditions under which an invariant metric f-structure (f,…

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In both cases the scalar manifold of the reduced theory is described as an eight-di…

The abstract discusses conditions for hyperkähler manifolds and Kähler reduction.

Study $G_2$-flows reducing to complex geometry flows, focusing on $G_2$-anomaly and $G_2$-Laplacian coflow.

We study reduction of generalized complex structures. More precisely, we investigate the following question. Let $J$ be a generalized complex structure on a manifold $M$, which admits an action of a Lie group $G$ preserving $J$. Assume that $M_0$ is a $G$-invariant smooth submanifold and the $G$-action on $M_0$ is prop…

Let $M$ be a compact connected complex manifold and $G$ a connected reductive complex affine algebraic group. Let $E_G$ be a holomorphic principal $G$--bundle over $M$ and $T\, \subset\, G$ a torus containing the connected component of the center of $G$. Let $N$ (respectively, $C$) be the normalizer (respectively, cent…

Despite their successes in the field of self-learning AI, Convolutional Neural Networks (CNNs) suffer from having too many trainable parameters, impacting computational performance. Several approaches have been proposed to reduce the number of parameters in the visual domain, the Inception architecture [Szegedy et al.,…

A complex vector space $V$ is a prehomogeneous $G$-module if $G$ acts rationally on $V$ with a Zariski-open orbit. The module is called etale if $\dim V=\dim G$. We study etale modules for reductive algebraic groups $G$ with one-dimensional center. For such $G$, even though every etale module is a regular prehomogeneou…

We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define \emph{extended…

Develops an efficient method for real-time data analysis and visualization.

In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We analyse the complexity of the proposed approach both in the case of fixed and in…

Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $H\subset G$ be a complex reductive subgroup which is not necessarily connected, and let $E_H\subset E_G$ be a holomorphic reduction of s…

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a general…

The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.

Consider an effective Hamiltonian torus action $T\times M \to M$ on a topologically twisted,generalized complex manifold $M$ of dimension $2n$. We prove that the $rank(T) \leq n-2$ and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying $rank(T) =…

Paper compares Lagrangian reduction methods for rigid body systems.

Improved sample complexity for actor-critic algorithms in MDPs.

Automates PDE model reduction with time-scale separation.

We consider dimension reduction for solutions of the Kähler-Ricci flow with nonegative bisectional curvature. When the complex dimension $n=2$, we prove an optimal dimension reduction theorem for complete translating Kähler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reducti…

Novel technique reduces Bayesian network complexity while preserving inference accuracy.

Study on $p$-Kähler structures on fibrations and Lie groups.

A new algorithm reduces time complexity for binary time series classification.

Real-time pruning during training reduces network size and training time.

We consider timelike and spacelike reductions of 4D, N = 2 Minkowskian and Euclidean vector multiplets coupled to supergravity and the maps induced on the scalar geometry. In particular, we investigate (i) the (standard) spatial c-map, (ii) the temporal c-map, which corresponds to the reduction of the Minkowskian theor…

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the Kähler geometry of a finite dimensional complex projective spaces.

Improved diffusion models for generative tasks without dimensionality constraints.

Modern techniques simplify complex high-dimensional data.

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we ca…

Asynchronous Q-learning achieves optimal Q-function estimation with reduced sample complexity.

Abstract: Generalized reduction methods for symmetries in graded geometry.

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure…

Reduces complexity of financial contagion dynamics on networks.

Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity, both statistically and computationally, of making such models satisfy the rigor…

Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.