The Bergman measure converges to the Zhang measure on a hybrid space.
problem Proving convergence of Bergman measures to Zhang measure.
method Analyzing convergence on a hybrid space and metrized curve complex.
result Bergman measure converges to Zhang measure on a hybrid space.
Researchers compute limits of Kähler-Einstein forms on degenerating manifolds.
problem Understanding limits of Kähler-Einstein forms on degenerating manifolds.
method Hybrid convergence of Kähler-Einstein measures using algebro-geometric limits.
result Limit measure is a weighted sum of Dirac masses at divisorial valuations.
A new hybrid Newton algorithm improves convergence in logistic regression.
problem Solving large-scale binary classification problems efficiently.
method Proposes a hybrid stochastic Newton algorithm with two weighted components in the Hessian matrix estimation.
result Proves almost sure convergence to the true parameter of logistic regression.
We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in th…
Mathematical analysis of Riemann surfaces and their moduli spaces using hybrid Laplacians.
problem Analyzing the asymptotics of Arakelov Green functions on Riemann surfaces near boundary of moduli spaces.
method Introducing hybrid Laplacian, solving hybrid Poisson equation, and defining hybrid Green functions.
result Layered description of asymptotics of Arakelov Green functions on Riemann surfaces near boundary of their moduli spaces.
Predicting firm's failure is one of the most interesting subjects for investors and decision makers. In this paper, a bankruptcy prediction model is proposed based on Artificial Neural networks (ANN). Taking into consideration that the choice of variables to discriminate between bankrupt and non-bankrupt firms influenc…
This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups (G,⋆) which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant subma…
Lecture notes on using non-Archimedean geometry for complex variety degenerations.
problem Complex algebraic variety degenerations with non-Archimedean Berkovich spaces.
method Hybrid spaces and non-Archimedean pluripotential theory.
result Relation between convergence of psh metrics and Monge-Ampere measures in hybrid spaces.
Hybrid deep architectures with reasoning layers show promising convergence and generalization properties.
problem Understanding the theoretical foundations of hybrid deep architectures with reasoning layers.
method Analyzing the interplay between algorithm layers and neural components in deep architectures.
result Properties of algorithm layers are closely related to the approximation and generalization abilities of end-to-end models.
This paper improves inverse problem solving with weakly convex regularisers and proves convergence.
problem Improving solution methods for inverse problems.
method Generalised formulation of convergent regularisation using weakly convex regularisers, and proof of convergence for primal-dual hybrid gradient method.
result Proves convergence of primal-dual hybrid gradient method for variational problems and shows improved performance with IWCNNs.
Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum. These methods can make great progress initially, but often…
Study shows how volume forms on degenerating varieties converge to a non-Archimedean measure.
problem Convergence of volume forms on degenerating log-Calabi-Yau varieties.
method Extending a result of Boucksom and Jonsson, the study uses a hybrid space filled with Berkovich analytification.
result Measures induced by meromorphic volume forms on fibers converge to a measure on the Berkovich analytification as the puncture is approached.
Paper improves a method for fast global and local convergence in optimization.
problem Slow global convergence in optimization methods with noisy Hessian estimates.
method Stochastic Newton Proximal Extragradient method using HPE framework.
result Faster global linear rate and superlinear convergence in fewer iterations.
Improved hybrid acoustic model using interleaved self-attention and convolution.
problem Limited application of transformer in hybrid acoustic models.
method Proposed a model structure with interleaved self-attention and 1D convolution.
result Competitive recognition results on Librispeech dataset.
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite programs and hence can be readily applied to a variety of machine learning problems. We…
We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent financial literature thanks to their ability to reproduce a rough volatility beha…
Paper develops MMOT framework for financial applications with neural acceleration.
problem Financial optimization and calibration under multi-period martingale constraints.
method Theoretical analysis, incremental updates, adaptive sparse grids, hybrid neural-projection solver.
result Neural solver achieves 1597x speedup for real-time applications.
A new method for optimizing functions without gradients, improving efficiency and convergence.
problem Optimizing functions without gradient information in machine learning.
method Hybrid Gradient Descent (HGE) using random and coordinate-wise gradient estimates.
result The proposed method achieves optimal convergence rates in convex cases and generalizes to non-convex cases.
A new autoencoder combines deep learning with SVD to reduce model complexity.
problem Overcoming the Kolmogorov barrier in high-dimensional systems.
method Learnable weighted hybrid autoencoder combining SVD and deep learning.
result Empirically, the model exhibits a sharpness thousands of times smaller than other models.
Noise-resilient optimization on noisy quantum computers.
problem Noise's impact on hybrid quantum-classical optimization.
method Iterative quantum circuit with noise consideration, using Quantum Fisher Information bound.
result Algorithm robustness against different noise strengths.
Unified reinforcement learning methods using hybrid inference.
problem Combining model-based and model-free reinforcement learning approaches.
method Control as Hybrid Inference (CHI) framework.
result CHI algorithm balances model-based and model-free learning.
New algorithm solves nonconvex-convex minimax problems efficiently.
problem Solving nonconvex-convex minimax problems with nonsmooth, nonconvex, and nonlinearity.
method Hybrid variance-reduced SGD algorithm combining smoothing and biased techniques.
result Achieves O(T^(-2/3)) convergence rate and best oracle complexity.
We propose a hybrid approach aimed at improving the sample efficiency in goal-directed reinforcement learning. We do this via a two-step mechanism where firstly, we approximate a model from Model-Free reinforcement learning. Then, we leverage this approximate model along with a notion of reachability using Mean First P…
Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth …
PINN-FEM combines PINNs and FEM for accurate Dirichlet boundary condition enforcement.
problem Challenges in enforcing Dirichlet boundary conditions in PINNs.
method Hybrid approach combining PINNs and FEM for strong boundary condition enforcement.
result PINN-FEM outperforms standard PINN models in accuracy and robustness.
We present a hybrid continuum-atomistic scheme which combines molecular dynamics (MD) simulations with on-the-fly machine learning techniques for the accurate and efficient prediction of multiscale fluidic systems. By using a Gaussian process as a surrogate model for the computationally expensive MD simulations, we use…
A hybrid method clusters and characterizes cancer data efficiently.
problem Challenges in clustering high-dimensional biomedical data.
method Gaussian mixture with generalized factor analyzers for efficient estimation.
result Our approach outperforms existing methods with faster convergence and higher accuracy.
We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labordère [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost surely for a class …
A new hybrid-ordered SGD method reduces communication and complexity for non-convex optimization.
problem Balancing communication, computational complexity, and convergence rate in distributed non-convex optimization.
method Hybrid-ordered distributed SGD with pre-shared scalers and periodic vector communication.
result Order-wise faster convergence compared to existing methods.
A hybrid training method reduces SNN training time and complexity.
problem Training deep SNNs is computationally expensive and time-consuming.
method Hybrid training technique combining initialization from converted SNNs and incremental spike-timing dependent backpropagation (STDB).
result The method converges in less than 20 epochs, reducing training complexity and time.
Improves deep neural network training and accuracy with adaptive basis approach.
problem Gap between theoretical and practical performance of deep neural networks.
method Adaptive basis viewpoint, novel initializations, hybrid optimizer.
result Dramatic increases in accuracy and convergence rate for various DNN applications.
Study on PDEs in Heston model with unique solution and convergence proof.
problem Analyzing PDEs in the Heston model for financial applications.
method Regularity results, verification theorem, unique viscosity solution, convergence proof.
result Unique viscosity solution for wide initial and source data.
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker's approximation of Brownian motion to the f…
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
Defines non-parabolic curves in spatial hybrid space with applications.
problem Defining and analyzing non-parabolic spatial hybrid framed curves.
method Definition and proof of existence and uniqueness theorem for non-parabolic spatial hybrid framed curves.
result Existence and uniqueness theorem for non-parabolic spatial hybrid framed curves.
Paper improves SVaR estimation for stress testing under macro scenarios using a hybrid GPR-HS framework.
problem Numerical instability in traditional SVaR estimation under extreme shocks.
method Extends GPR-HS framework to forward-looking stress scenarios with SACS for stable covariance.
result Stable SVaR ranges from -2.1020% to -2.2231%, preserving coherence property.
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate O(n−2r/(2r+1)) for Sobolev space functions. Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods …
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional d…
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been recognized that solving this kind of problem is challenging since the closed-form…
Study on error rates for approximating rough volatility models.
problem Simulation of rough volatility models with fractional Brownian motion.
method Analysis of weak error rates for numerical schemes, focusing on fBm and cubic test functions.
result Convergence rates for approximations are (3H+21)∧1 for exact left-point discretization and H+21 for hybrid schemes. Discussing hybrid models in Bayesian networks.
problem Improving accuracy in network modeling.
method Hybrid semiparametric Bayesian approach.
result Enhanced model performance in complex networks.
Expert augmentation improves hybrid model generalization.
problem Limited generalization of hybrid models outside training distribution.
method Introducing expert augmentation to improve hybrid model performance.
result Expert augmentation improves generalization of hybrid models.
Optimizes hybrid insurance contracts for heavy-tailed losses.
problem Providing insurance against heavy-tailed losses with finite expected loss.
method Combines traditional and parametric insurance, using a Pareto-type criterion for optimization.
result The hybrid contract outperforms traditional contracts in simulations and real data.
A hybrid method combines data assimilation and machine learning to predict chaotic dynamics from sparse noisy data.
problem Predicting chaotic dynamics from sparse and noisy observations.
method Iterative application of ensemble Kalman filter for data assimilation and neural network for model emulation.
result The hybrid method successfully predicts chaotic dynamics up to two Lyapunov times, retrieves positive Lyapunov exponents, and more energetic frequencies.
Deploying deep learning (DL) models across multiple compute devices to train large and complex models continues to grow in importance because of the demand for faster and more frequent training. Data parallelism (DP) is the most widely used parallelization strategy, but as the number of devices in data parallel trainin…
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.