Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data

TL;DR

This paper introduces Stochastic Latent Differential Inference (SLDI), a novel probabilistic framework combining SDEs with deep generative models to enhance uncertainty quantification in structured temporal data modeling.

Contribution

It presents a new variational autoencoder-based approach embedding neural SDEs in latent space, with a coupled forward-backward system and variance-reduced training methods, advancing stochastic deep learning.

Findings

Enables flexible, continuous-time uncertainty modeling for irregularly sampled data.

Provides a new theoretical framework unifying variational inference and stochastic control.

Improves training stability through variance reduction and pathwise regularization.

Abstract

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach, termed Stochastic Latent Differential Inference (SLDI), embeds an It\^o SDE in the latent space of a variational autoencoder, allowing for flexible, continuous-time modeling of uncertainty while preserving a principled mathematical foundation. The drift and diffusion terms of the SDE are parameterized by neural networks, enabling data-driven inference and generalizing classical time series models to handle irregular sampling and complex dynamic structure. A central theoretical contribution is the co-parameterization of the adjoint state with a dedicated neural network, forming a coupled forward-backward system that captures not only latent evolution but also gradient dynamics. I introduce a pathwise-regularized adjoint loss and analyze variance-reduced gradient flows through the lens of stochastic calculus, offering new tools for improving training stability in deep latent SDEs. My paper unifies and extends variational inference, continuous-time generative modeling, and control-theoretic optimization, providing a rigorous foundation for future developments in stochastic probabilistic machine learning.