# Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators

arXiv: https://arxiv.org/abs/2512.24106 · HTML: https://mlsanity.com/paper/2512.24106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 5 of 5)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Dropout Injection at Test Time for Post Hoc Uncertainty Quantification in Neural Networks](https://mlsanity.com/paper/2302.02924/) (2023)
- [Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networks](https://mlsanity.com/paper/2309.17032/) (2023)

## Built on by (most cited first, 1 of 1)

- [Kantorovich-Type Stochastic Neural Network Operators for the Mean-Square Approximation of Certain Second-Order Stochastic Processes](https://mlsanity.com/paper/2601.03634/) (2026)

## Abstract (arXiv)

In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well as path-wise within the space of second-order stochastic (random) processes ( L2(Omega, F,mathbbP) ). Additionally, we provide quantitative error estimates using the modulus of continuity of the processes. These results highlight the effectiveness of SINNOs for approximating stochastic processes with potential applications in COVID-19 case prediction.