Quantum-Inspired Unitary Pooling for Multispectral Satellite Image Classification

TL;DR

This paper introduces a quantum-inspired pooling method for multispectral satellite image classification that leverages geometric structures to improve model stability, convergence speed, and reduce variance, all within classical deep learning frameworks.

Contribution

It presents a novel classical pooling mechanism inspired by quantum unitary actions, capturing geometric symmetries to enhance deep learning performance on spectral data.

Findings

Improved optimization stability and convergence speed.

Significant reduction in model variance.

Benefits of quantum-inspired structures are replicable classically.

Abstract

Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability, accelerates convergence, and substantially reduces variance compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.