用张量网络分析野火易发性，揭示类别可区分性的物理机制
Tensor Network Machine Learning for Wildfire Susceptibility Mapping: from Grokking Dynamics to Quantum Mixedness of Class Representations
- 基于矩阵乘积态构建量子启发的分类框架，融合地理空间嵌入
- 二分类中观察到明显的grokking现象，多分类中非邻近类别更易区分
- 通过约化密度矩阵诊断类别可区分性层级，模型兼具准确与可解释
本文提出一种受量子启发的张量网络框架，用于加尔加诺地区野火易发性分类，结合AlphaEarth嵌入与矩阵乘积态（MPS）模型。该方法将可扩展的地理空间表征与可解释的量子掩码相结合，实现二分类与多分类任务。除了预测性能外，研究在二分类中发现显著的grokking过渡，并对多分类中的类间混淆进行详细分析。通过基于约化密度矩阵的层次化混度诊断，表明MPS分类器自然编码了类别可区分性的层级结构，非相邻类别比相邻类别更具可分性。结果表明，张量网络模型不仅达到竞争性分类准确率，还为复杂环境数据集中的类别可区分性提供了物理基础量化与解释框架。
原文摘要 · Abstract (English)
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.
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