Tensor Network Machine Learning for Wildfire Susceptibility Mapping: from Grokking Dynamics to Quantum Mixedness of Class Representations

2026-07-21

AI Summary

This study addresses wildfire susceptibility classification in the geographically complex Gargano region of Italy by proposing an interpretable modeling framework that integrates AlphaEarth geospatial embeddings with matrix product state (MPS) tensor networks. The approach innovatively incorporates a quantum-inspired masking mechanism to enhance discriminative power and, for the first time, employs the mixedness of reduced density matrices from tensor networks to analyze the hierarchical separability among multiple susceptibility classes. This diagnostic reveals that non-adjacent classes are more readily distinguishable and uncovers grokking dynamics during training. While maintaining high classification accuracy, the method quantifies and elucidates the intrinsic discriminative structure of wildfire susceptibility categories, offering a novel paradigm for environmental risk modeling that combines scalability, interpretability, and physical grounding.

Abstract

A quantum-inspired tensor network framework for wildfire susceptibility classification in the Gargano region is introduced, leveraging AlphaEarth embeddings and Matrix Product State models. The approach combines scalable geospatial representations with an interpretable quantum mask, enabling both binary and multiclass classification of wildfire susceptibility. Beyond predictive performance, the study reveals a pronounced grokking transition in the binary case and provides a detailed analysis of inter-class confusion in the multiclass setting. By introducing level-resolved mixedness diagnostics based on reduced density matrices, we show that the MPS classifier naturally encodes a hierarchy of class distinguishability, with non-adjacent categories becoming more separable than neighboring ones. These results demonstrate that tensor network models not only achieve competitive classification accuracy but also offer a physically grounded framework to quantify and interpret class separability in complex environmental datasets.

Problem

• wildfire susceptibility mapping
• tensor network
• class separability
• quantum mixedness
• geospatial classification

Innovation

• Tensor Network
• Matrix Product State
• Quantum Mixedness
• Grokking
• Wildfire Susceptibility Mapping