Language models can predict numeric values as strings.
problem Regression tasks with numeric predictions.
method Causal sequence decoding models trained for next-token prediction.
result Decoder-based heads perform as well as standard heads in numeric regression tasks.
Paper introduces NumLLM for better financial text understanding with numeric variables.
problem Poor performance of existing financial large language models in numeric financial text.
method Constructed financial corpus, fine-tuned with LoRA modules, merged into foundation model.
result NumLLM achieves best performance on financial question-answering benchmark, especially with numeric questions.
This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), contr…
Recognizing written domain numeric utterances (e.g. I need $1.25.) can be challenging for ASR systems, particularly when numeric sequences are not seen during training. This out-of-vocabulary (OOV) issue is addressed in conventional ASR systems by training part of the model on spoken domain utterances (e.g. I need one …
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation …
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
LogEI improves Bayesian optimization by simplifying numerical computation of EI and related functions.
problem Numerical pathologies in optimizing EI and related acquisition functions.
method Proposes LogEI, a family of acquisition functions that simplify numerical optimization.
result LogEI members improve optimization performance and match or exceed state-of-the-art methods.
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
Study uses neural networks to solve complex equations efficiently.
problem Solving parametric partial differential equations.
method Machine learning and deep neural networks.
result Performance of the model is independent of parameter space dimension.
New method improves stability of Gaussian process approximations.
problem Numerical instability in Gaussian process computations.
method Cover tree modification for inducing points, alternative sparse approximation.
result Improved stability and predictive performance in spatial tasks.
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
New metrics reveal oversmoothing in GNNs more accurately than traditional methods.
problem Oversmoothing in graph neural networks reduces model performance.
method Rank-based metrics to measure oversmoothing in GNNs.
result Rank-based metrics consistently capture oversmoothing, while energy-based metrics often fail.
The paper compares numerical schemes for nonholonomic systems using retraction maps.
problem Optimal control of nonholonomic systems with numerical approximations.
method Retraction maps used as seed for geometric integrators of Hamilton equations.
result Performance comparison of symplectic and non-symplectic integrators.
Efficient method for vertex embedding and community detection.
problem Vertex embedding and community detection.
method Normalized one-hot graph encoder and rank-based cluster size measure.
result Excellent numerical performance of graph encoder ensemble algorithm.
Study evaluates neural networks based on random graph structures and finds key performance indicators.
problem Understanding and optimizing neural network architectures using graph theory.
method Evaluation of neural networks with random graph structures, focusing on structural and numerical properties.
result A new numerical graph characteristic selects a set of quasi-1-dimensional graphs that perform well.
This paper tackles ranking-based performance normalization for optimization algorithms.
problem Ranking optimization algorithms across diverse numerical scales disrupts performance comparisons.
method Introduces absolute ranking and a sampling-based computational method to address numerical scale variation.
result Provides a more robust framework for assessing performance across multiple algorithms and problems.
Probabilistic numerics expands numerical tasks with black box methods.
problem Difficult conditioning of random variables in numerical tasks.
method Construct probabilistic numerical methods based on final outputs, extrapolating limiting quantities.
result Higher orders of convergence achieved in various numerical tasks.
Study identifies numerical signs of blow-up in hydrodynamic equations.
problem Determining if numerical results of blow-up are genuine or artifacts.
method Geometrically consistent spatiotemporal discretization of complexified Euler equations.
result Identification of a signature based on supremum norm growth rates of vorticity.
A new PCA method using Tℓ1-norm outperforms existing methods.
problem Outliers and noise sensitivity in classical PCA.
method PCA based on Tℓ1-norm maximization. result The method outperforms PCA-ℓp, ℓpSPCA, and PCA in numerical experiments. Improved hypothesis testing and change-point detection using diffusion-based methods.
problem Limited power of score-based hypothesis tests and change-point detection.
method Extending score-based Fisher divergence to diffusion-divergence by multiplying score functions with a matrix-valued function or weight matrix.
result Theoretical quantification and demonstration of optimal performance of diffusion-based algorithms.
Enhances FM models for numerical features using function basis encoding.
problem Challenges in incorporating numerical features into FM variants.
method Encoding numerical features into a vector of function values for learning segmentized functions.
result Improves model accuracy by learning segmentized functions of numerical features.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
The paper analyzes and improves the learning rates of distributed kernel ridge regression.
problem Generalization performance and learning rates of distributed kernel ridge regression.
method The paper derives optimal learning rates for DKRR in expectation and probability, proposes a communication strategy to improve learning performance, and evaluates these through theory and experiments.
result The communication strategy significantly improves the learning performance of DKRR, as demonstrated by both theoretical assessments and numerical experiments.
New method smooths integrands for efficient option pricing.
problem Improving numerical performance of option pricing methods.
method Combining hierarchical adaptive sparse grids, quasi-Monte Carlo, and numerical smoothing.
result Improved efficiency of ASGQ and QMC methods for high-dimensional problems.
Agent Trading Arena trains LLMs in real-time financial markets to improve numerical reasoning.
problem Limited real-world training for LLMs in financial markets.
method Virtual zero-sum stock market with competitive multi-agent trading.
result LLMs perform better with chart-based visualizations and a reflection module.
Study validates Libor model for insurance benefits calculation.
problem Valuation of long-term insurance guarantees.
method Mean-field Libor market model, numerical ALM, aggregated life insurance data.
result Derives estimators for future discretionary benefits.
In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic function of the log-price given volatility level. In particular, we…
Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.
problem Improving the efficiency of numerical integration methods.
method Uses normalizing flows to approximate distributions and quasi-Monte Carlo for sampling.
result Demonstrates an estimator with significantly lower variance.
Space mapping speeds up shape optimization for PDEs.
problem Efficiently solving shape optimization problems constrained by PDEs.
method Combines fine and coarse model optimizations using Riemannian metrics.
result Space mapping methods are highly efficient for complex shape optimization problems.
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to…
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we …
A new scheme for FBSDEs simplifies computation without Monte Carlo.
problem Numerical solution for decoupled FBSDEs with reduced complexity.
method Recursive marginal quantization for fully quantization-based scheme.
result Effective numerical procedure for financial applications.
Novel method for estimating SIRD model parameters and forecasting COVID-19 deaths in Poland.
problem Estimating epidemiological parameters for SARS-CoV-2 spread in Poland.
method Modified SIRD model, GPU architecture for computation.
result Effectiveness of short-term forecasts (up to 2 weeks) and stability of the method.
We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price …
We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear t…
New approach improves computational efficiency of Bass Local Volatility model.
problem Eliminate interpolation and improve computational efficiency in local volatility models.
method Combines local quadratic estimation and lognormal mixture tails for state price densities; uses trapezoidal rule for numerical convolutions.
result Proposed method outperforms traditional numerical methods in option pricing and market case studies.
New methods improve deep learning for solving linear PDEs.
problem Efficiently solving high-dimensional linear PDEs using deep learning.
method Rigorous investigation of gradient estimators for SDE-based variational formulations.
result Novel methods provide substantial performance improvements.
We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers important challenges related to the computation of conditional default probabilities. I…
A new method learns Hamiltonian functions from noisy data.
problem Learning Hamiltonian functions from noisy observations.
method Structure-preserving kernel ridge regression method.
result The method yields excellent numerical performances.
New method preserves spectral clustering performance under aggressive sparsification and quantization.
problem Maintaining spectral clustering performance with sparse and quantized data.
method Random matrix theory applied to eigenspectrum changes under sparsification and quantization.
result Spectral clustering performance is preserved even with aggressive sparsification and quantization.
Some recent studies have suggested using GANs for numeric data generation such as to generate data for completing the imbalanced numeric data. Considering the significant difference between the dimensions of the numeric data and images, as well as the strong correlations between features of numeric data, the convention…
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…