arXiv research

The study establishes bounds for Schrödinger operators on Riemannian manifolds.

Abstract notes on generative modeling techniques.

Paper introduces a new generative learning model using Schrödinger bridge diffusion in latent space.

Unified framework for robust, stable, and efficient density ratio estimation.

In this paper, we partially settle down the long standing open problem of the finite time blow-up property about the nonlinear Schr$\ddot{o}$dinger equations on some Riemannian manifolds like the standard 2-sphere $S^2$ and the hyperbolic 2-space $H^{2}(-1)$. Using the similar idea, we establish such blow-up results on…

Characterizes Schrödinger operator boundedness on weighted Riemannian manifolds.

We give a new lower bound for the first gap $λ_2 - λ_1$ of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain $Ω$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new bound is explicit and computable.

Suppose that $G=(V, E)$ is a finite graph with the vertex set $V$ and the edge set $E$. Let $Δ$ be the usual graph Laplacian. Consider the following nonlinear Schr$\ddot{o}$dinger type equation of the form $\left \{ \begin{array}{lcr} -Δu-αu=f(x,u),\\ u\in W^{1,2}(V),\\ \end{array} \right.$ on graph $G$, where $f(x…

Study shows observability for Schrödinger equations on product manifolds with specific conditions.

Generative model for time series using Schrödinger bridge.

For the spherical Laplacian on the sphere and for the Dirichlet Laplacian in the square}, Antonie Stern claimed in her PhD thesis (1924) the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with exactly two nodal domains. These results were given complete proofs …

We solved the Schr{ö}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / Λ is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice Λ. The lattice is not neces…

The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{ö}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result for the associated Riesz transform with potential d(delta+V) --1/2…

New inequalities for spectral zeta kernels on spheres and manifolds.

CMCD sampler connects transport and variational inference for efficient sampling.

In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By introducing the Killing equation for spinors of arbitrary weight, the result of A…

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.

Examines algorithmic modeling across three cultures.

Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that $UCB$, $M3$, $S$ or $Exp3$ algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on predi…

Meta-algorithm selection aims to choose the best algorithm selector for a given problem instance.

Proposes CLRS benchmark to evaluate algorithmic reasoning.

Combines multiple bandit algorithms to create a nearly optimal single algorithm.

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…

The exchange algorithm is studied for its convergence and asymptotic variance.

Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algori…

No algorithm outperforms uniform sampling in A/B testing.

Improves algorithm selection for thousands of candidates using dyadic features.

This review article surveys data augmentation MCMC algorithms.

Bayesian learning rule unifies and generalizes various machine learning algorithms.

Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the first method that can automatically discover a better algorithm. We approach th…

This review summarizes five Lasso optimization algorithms.

Neural networks mimic algorithms to solve complex problems.

Paper proposes a reinforcement learning framework for efficient hyper-parameter tuning of stochastic optimization algorithms.

In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…

Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key problem faced by practitioners is measuring the accuracy of an approximate infe…

New algorithms reduce bilevel optimization complexity to ε^(-1.5).

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in [4], its impr…

Researchers analyze how algorithmic and implementation choices affect RL performance.

Study on selecting between base algorithms in stochastic bandit problems.

New bounds derived for KG algorithm's performance in finite time.

Paper proves linear convergence of SCMS algorithm for directional data.

We resolve the fundamental problem of online decoding with general $n^{th}$ order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline algorithm even when latency is small. Our algorithms admit efficient implementation vi…

MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.

New algorithm speeds up learning of graphical models.

The goal of data-driven algorithm design is to obtain high-performing algorithms for specific application domains using machine learning and data. Across many fields in AI, science, and engineering, practitioners will often fix a family of parameterized algorithms and then optimize those parameters to obtain good perfo…

The paper examines how algorithmic classification affects behavior and proposes democratizing stakes to mitigate predatory practices.

Run2Survive uses survival analysis for algorithm selection, outperforming traditional methods.

IRT improves algorithm evaluation across datasets.