Probabilistic Approach to Neural Networks Computation Based on Quantum Probability Model Probabilistic Principal Subspace Analysis Example

TL;DR

This paper introduces a quantum-inspired probabilistic model for neural network learning, demonstrating its application to principal subspace analysis and potential improvements in convergence and robustness.

Contribution

It presents a novel probabilistic framework based on quantum physics concepts for modeling neural network learning algorithms, specifically applied to PSA.

Findings

Probabilistic model based on density matrix and Born rule suitable for neural networks.

Application to online PSA learning algorithms with hardware implementation potential.

Potential improvements in convergence speed and robustness of learning algorithms.

Abstract

In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics - a density matrix and the Born rule. As an example, we will show that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for PSA, which are preferably realized by a parallel hardware based on very simple computational units. Proposed concept (model) can be used in the context of improving algorithm convergence speed, learning factor choice, or input signal scale robustness. We are going to see how the Born rule and the Hebbian learning rule are connected