# A Simultaneous Perturbation Weak Derivative Estimator for Stochastic Neural Networks

## TL;DR

This paper introduces a novel gradient estimation method for stochastic neural networks, specifically the Little model, using measure-valued differentiation and simultaneous perturbation, enabling training without explicit stationary distribution solutions.

## Contribution

It presents a new derivative estimation technique applicable to general stochastic neural networks, extending previous methods limited to specific network structures.

## Key findings

- Effective gradient estimation for the Little model.
- Applicable to networks with complex, nonlinear stochastic units.
- Extends previous algorithms to more general network architectures.

## Abstract

In this paper we study gradient estimation for a network of nonlinear stochastic units known as the Little model. Many machine learning systems can be described as networks of homogeneous units, and the Little model is of a particularly general form, which includes as special cases several popular machine learning architectures. However, since a closed form solution for the stationary distribution is not known, gradient methods which work for similar models such as the Boltzmann machine or sigmoid belief network cannot be used. To address this we introduce a method to calculate derivatives for this system based on measure-valued differentiation and simultaneous perturbation. This extends previous works in which gradient estimation algorithms were presented for networks with restrictive features like symmetry or acyclic connectivity.