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Quantum-Inspired Unitary Pooling for Multispectral Satellite Image Classification

Georgios Maragkopoulos, Aikaterini Mandilara, Ralntion Komini, Dimitris Syvridis

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.

Quantum-Inspired Unitary Pooling for Multispectral Satellite Image Classification

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.
Paper Structure (8 sections, 8 equations, 2 figures, 1 table)

This paper contains 8 sections, 8 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. $\mathrm{SU}(d)$ Unitary Pooling Layer
  4. Quotient Geometry and Dimensionality Reduction
  5. Optimization Dynamics and Jacobian Rank Deficiency
  6. Experiments
  7. Discussion
  8. Conclusion

Figures (2)

  • Figure 1: Architecture of the quantum-inspired pooling CNN. The pipeline begins with a standard CNN backbone extracting spatial features from the satellite imagery (left). These features are flattened and projected into the Lie algebra dimension ($d^2-1$) via a fully connected (FC) layer. The quantum-inspired pooling layer then maps these values to the special unitary group $SU(d)$, applies the unitary action to a reference state, and outputs a normalized vector of size $2d$. Finally, standard FC layers classify the representation into the target classes.
  • Figure 2: Convergence Efficiency vs. Peak Performance. The number of epochs required to reach 80% and 90% test accuracy milestones, alongside the epoch of peak performance. The Deep Hybrid model (red circle, Model 5) demonstrates superior convergence velocity, reaching 90% accuracy in approximately 10 epochs—twice as fast as the strongest classical baseline (Model 4). Lower values on the y-axis indicate faster learning.