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arXiv Machine Learning

Deep Neural Operator Learning for Probabilistic Models

The paper introduces a deep neural-operator framework for a broad class of probabilistic models, proving a universal approximation theorem under global Lipschitz conditions and explicit network-size bounds. It requires only integrability and general tail-probability conditions on the underlying stochastic processes, which are verified for European and American option-pricing problems within the forward-backward SDE framework. A numerical example with a basket of American options demonstrates that the learned model can generate optimal stopping boundaries for new strike prices without retraining.

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arXiv Statistics ML
Oct 28

QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions

The paper introduces QD-PINN, a physics-informed neural network framework for estimating optimal stopping boundaries in quickest detection problems involving high-dimensional diffusion processes. It establishes a theoretical equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, justifying the use of finite-dimensional neural networks. The authors demonstrate the method’s robustness by quantifying uncertainty with deep ensembles and Monte Carlo dropout, showing low variability and close agreement with reference numerical solutions.

By Hang Ye, Yi Liu, Haipeng Xing
diffusion
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arXiv Machine Learning
Oct 15

Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricing

The paper introduces BeTINN, a structured conditional neural network architecture that extends time‑induced modulation with multi‑directional time‑parameter conditioning and a joint residual pathway. BeTINN is evaluated on the Heston stochastic‑volatility PDE, showing improved accuracy for both option values and key sensitivity metrics compared to baseline models. Ablation studies highlight the contributions of each architectural component, and the authors observe that physics‑based validation loss does not fully capture derivative fidelity, underscoring the need for derivative‑aware evaluation when sensitivities are important.

By Jose Miguel Lara Rangel, Mixtli Vazquez Mendoza
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arXiv AI
Aug 25

Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks

The paper presents a theoretical framework for approximating ratio-type functionals that arise in conditional generative modeling, specifically when the target density is expressed as a ratio of two kernel-based marginal densities. It proves that deep neural networks using the SignReLU activation can approximate these ratios with established L^p(Omega) bounds and convergence rates under standard regularity assumptions. Applying the framework to Denoising Diffusion Probabilistic Models, the authors construct a SignReLU-based estimator for the reverse process and derive bounds on the excess Kullback–Leibler risk, decomposing it into approximation and estimation errors to provide generalization guarantees for finite-sample training.

By Luwei Sun, Dongrui Shen, Feng Chuanwen, Jianfe Li, Yulong Zhao, Han Feng
diffusion
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