# LegoQ: Density-Matrix Representation Learning with Spectral-Spatial State Transitions for Hyperspectral Classification

arXiv: https://arxiv.org/abs/2607.28970 · HTML: https://mlsanity.com/paper/2607.28970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers](https://mlsanity.com/paper/2107.02988/) (2021)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [MambaHSI: Spatial-Spectral Mamba for Hyperspectral Image Classification](https://mlsanity.com/paper/2501.04944/) (2025)

## Abstract (arXiv)

Hyperspectral image classification is complicated by mixed pixels, spectral ambiguity, class imbalance, and limited annotations. Most current classifiers encode a pixel or patch as a deterministic vector and apply a linear or multilayer softmax head. Although effective for discrimination, this representation does not directly expose how mixed or uncertain a sample is. This paper presents method, a classical density-matrix representation learning framework for hyperspectral images. The spectral bands are divided into groups and each group is mapped to a positive semi-definite, Hermitian, trace-normalized matrix state. A composable stack of spectral, spatial, and inter-group transitions then updates the states while repeatedly projecting them back to the valid state set. Instead of flattening the final features, method aggregates the group states and compares them with learnable class-prototype density matrices through Uhlmann fidelity. The normalized eigenspectrum, von Neumann entropy, purity, and prototype fidelity provide sample-level diagnostics that are unavailable from a conventional vector head. On Indian Pines, ten runs yield an overall accuracy of 96.20±0.70%, an average accuracy of 95.57±1.29%, and a kappa coefficient of 95.66±0.80%. On WHU-Hi-LongKou, the best of ten runs reaches 97.52% overall accuracy. Classification maps and feature projections show that the transition stack produces compact and better separated class structures. The results support constrained matrix-state learning as a practical alternative to vector-only hyperspectral classification without requiring quantum hardware.