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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,878 papers · 148 categories

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126253379505 · Jun 202019922001200920172026
48 results for adaptive solutions

Adaptive method improves numerical solution of Cox-Ingersoll-Ross model.

problem Approximating solutions to the Cox-Ingersoll-Ross model efficiently.
method Path-bounded timestepping with hybrid approach, including a backstop method.
result The adaptive method is strongly convergent, with strong error control.

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…

2009-11-10abs ↗pdf ↗

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drasti…

2017-05-23abs ↗pdf ↗

Adaptive learning of SPDE solutions using score-based diffusion models.

problem Model errors and reduced accuracy in SPDE solutions due to incomplete physical knowledge and environmental variability.
method Score-based diffusion models with recursive Bayesian inference, incorporating simulation data and observational information.
result Accuracy and robustness of the proposed method demonstrated on benchmark SPDEs.

Enhances physics-informed neural networks with adaptive sampling and weighting.

problem Challenges in training physics-informed neural networks on complex problems.
method Hybrid adaptive sampling and weighting method.
result Consistently improves prediction accuracy and training efficiency.

Improved iterative hard thresholding for faster, sparser solutions.

problem Finding sparser solutions without sacrificing runtime.
method Adaptive regularization framework applied to iterative hard thresholding.
result Returns solutions with sparsity O(sκ)O(sκ), improving over existing methods.

This paper explores adaptive methods in over-parameterized linear regression.

problem Understanding why neural networks generalize well in over-parameterized settings.
method Characterizes two sub-classes of adaptive methods and their generalization performance.
result Adaptive methods in over-parameterized linear regression converge to the minimum norm solution.

This work includes a number of novel contributions for the multiple-source adaptation problem. We present new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new guarantees that hold in the case where the conditional probabilities for the sour…

2018-05-20abs ↗pdf ↗

CoLoRA models predict PDE solutions quickly and accurately with minimal data.

problem Efficiently modeling PDE solutions with limited data.
method Continuous low-rank adaptation of neural networks trained on offline data.
result Predictions are orders of magnitude faster and more accurate than classical methods.

Local adaptive methods in FL can accelerate convergence but introduce bias, which is corrected.

problem The effect of using adaptive optimization methods for local updates in federated learning.
method Proposed correction techniques to overcome the bias introduced by local adaptive methods.
result Correction techniques can achieve faster convergence and higher test accuracy than baseline methods.

Proposes MEDM to balance entropy minimization and diversity maximization for better domain adaptation.

problem Trivial solutions in entropy minimization for unsupervised domain adaptation.
method Introduces diversity maximization to balance with entropy minimization, controlled by deep embedded validation.
result MEDM outperforms state-of-the-art methods on four domain adaptation datasets.

Study on generalization in gradient-based meta-learning, showing flatter solutions and coherence between adaptation trajectories.

problem Understanding generalization in gradient-based meta-learning.
method Analysis of objective landscapes, experimental demonstration of solution properties, and empirical evidence on coherence between adaptation trajectories.
result Meta-test solutions become flatter, lower in loss, and further away from the meta-train solution as meta-training progresses, even as generalization starts to degrade.

A new adaptive splitting method improves accuracy for Cox-Ingersoll-Ross model.

problem Improving numerical solution accuracy for Cox-Ingersoll-Ross model.
method Adaptive splitting method over deterministic and random meshes, with uniform moment bound and strong error results.
result Uniform moment bound and strong error results of order 1/4 in L1 and L2 for κθ>σ^2, and order 1 for large noise.

Adaptive SAA solves large-scale stochastic linear programs efficiently.

problem Solving large-scale two-stage stochastic linear programs.
method Iterative algorithm with adaptive sample size and warm starts.
result The algorithm converges to the true solution set with a probabilistic guarantee.

Optimizes staggered treatment rollouts to minimize cost and error.

problem Efficiently scheduling treatment initiation times for staggered rollouts.
method Non-adaptive and adaptive experimental designs, including a near-optimal solution for non-adaptive cases and a new algorithm for adaptive cases.
result Reduces experiment cost by over 50% compared to static design benchmarks.

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinu…

2018-05-29abs ↗pdf ↗

Proposes a regularization method for unsupervised domain adaptation that aligns predictions with target data's top singular vectors.

problem Domain adaptation challenges in high joint error scenarios.
method Regularizes classifier to align with unsupervised target data guided by label alignment property (LAP).
result The method improves performance in MNIST-USPS domain adaptation and cross-lingual sentiment analysis.

Chameleon optimizes neural network compilation for faster execution and shorter time.

problem Faster execution and shorter compilation time for neural networks.
method Adaptive code optimization using reinforcement learning and adaptive sampling.
result 4.45x speed up in optimization time over AutoTVM, 5.6% improvement in inference time.

Paper develops methods for solving complex stochastic equations using Malliavin calculus.

problem Existence, uniqueness, and regularity of solutions to BSVIEs.
method Malliavin calculus for tackling diagonal processes and nonlinear dependence.
result Developed well-posedness results for BSVIEs, including probabilistic interpretation of PDEs and portfolio optimization.

Study adaptive clinical trial methods for identifying patient subpopulations with treatment benefit.

problem Adaptive identification of patient subpopulations with treatment benefit in clinical trials.
method Proposes AdaGGI and AdaGCPI meta-algorithms for subpopulation construction.
result Empirical investigation of AdaGGI and AdaGCPI performance across various simulation scenarios.

New method learns diverse solutions in reinforcement learning without gradient bias.

problem Lack of diverse solutions in reinforcement learning tasks.
method Maximizes state-action-based mutual information directly, using variational lower bound.
result Successfully learns an infinite set of diverse solutions.

Adaptive PINNs improve accuracy by adding points where solutions are uncertain.

problem Inadequate sampling in PINNs leads to inaccurate solutions, especially near singularities.
method FI-PINNs use failure probability to dynamically add points, improving numerical accuracy.
result FI-PINNs achieve better accuracy through adaptive sampling, as proven by rigorous error bounds.

This paper provides a theoretical analysis of domain adaptation based on the PAC-Bayesian theory. We propose an improvement of the previous domain adaptation bound obtained by Germain et al. in two ways. We first give another generalization bound tighter and easier to interpret. Moreover, we provide a new analysis of t…

2015-01-13abs ↗pdf ↗

The paper examines how sampling data affects the performance of submodular maximization.

problem Performance loss due to probability sampling in submodular maximization.
method Examines a simple probability sampling method where each data point is selected with probability at least r.
result The sampling gap is both upper and lower bounded by 1/r for policywise submodular utility functions.

CMA-ME combines CMA-ES and MAP-Elites for better quality and diversity in continuous domains.

problem Finding a diverse set of high-quality solutions in complex continuous domains.
method Combines CMA-ES self-adaptation with MAP-Elites archiving and mapping.
result CMA-ME outperforms MAP-Elites in both quality and diversity of solutions.

Online learners track optimal solutions with constant step-size.

problem Tracking optimal solutions in online learning settings.
method Established a link between steady-state performance and tracking performance using analogies with adaptive filters.
result Inferred tracking performance from steady-state expressions directly.

Adaptive multi-domain learning reduces parameter count for efficient deep learning.

problem Different domains have varying complexity, leading to inefficient model training.
method Proposes adaptive parameterization to reduce model complexity without sacrificing performance.
result Efficient multi-domain learning solutions with far fewer parameters.

AdaPTS adapts univariate FMs for multivariate time series forecasting.

problem Challenges in managing feature dependencies and uncertainty quantification in multivariate time series forecasting.
method Adapters that transform multivariate inputs into a latent space and apply univariate FMs independently to each dimension.
result AdaPTS enhances forecasting accuracy and uncertainty quantification compared to baseline methods.