Quantum-Grassmann-Plucker Token Mixing for Deep Learning-Based Post-Disaster Damage Assessment

Timely post-disaster building damage assessment from satellite imagery is a critical engineering decision support task, yet it remains constrained by class imbalance, ambiguous intermediate damage states, and limited cross-event transferability. This study presents, to our knowledge, the first application of Grassmann-Plucker (GP) token mixing to computer vision and introduces two extensions for image classification: the Quantum-inspired Grassmann-Plucker (QGP) head and the Hybrid Quantum Machine Learning Grassmann-Plucker (HQML-GP) head. The GP head represents multiscale relationships among image patch tokens by encoding subspaces formed by token pairs with Plucker coordinates; QGP enriches these coordinates with amplitude-derived probability features, whereas HQML-GP incorporates expectation values generated by a simulated quantum circuit into the geometric token representation. Paired pre- and post-event image patches from the xBD tornado dataset were processed using a frozen six-channel Vision Transformer base encoder with 16 x 16-pixel patches. The three GP-based heads were compared with multilayer perceptron and Transformer baselines under identical training, checkpoint selection, and evaluation protocols. Joplin and Moore tornado samples were used for model development and seen-event testing, while Tuscaloosa was reserved for unseen-event evaluation. QGP led both test sets in accuracy and macro-F1: 83.46% and 64.50% for the seen events, and 66.45% and 52.70% for the unseen event. Although HQML-GP obtained the highest validation macro-F1 of 65.63%, it did not surpass QGP on either test set and required substantially more training time per epoch. These results establish GP token mixing as a competitive attention-free alternative to conventional Transformer-based token mixing for paired satellite image damage classification.

Ask Self, Ask Others: Relation Is All You Need

Attention directly derives normalized information flow from pairwise scores. We introduce Relation, an alternative token-mixing primitive that first organizes pairwise evidence into explicit Self and Exchange relations and derives information flow afterward. This relational organization gives rise to Full Relation, FlashRelation, Linear Relation, Hybrid Relation, and a KV-style Relation Cache. Across matched decoder-only models at approximately 10M, 30M, and 100M parameters, Full Relation achieves lower final validation NLL than MHA at all three scales. In a fixed-context reference benchmark, FlashRelation is 3.60-4.41x faster than the materialized Full Relation implementation. Across scale-matched production workloads, it reaches 76.4-84.9% of PyTorch FlashAttention throughput while executing the Full Relation operator. Hybrid Relation uses 75% Linear Relation layers and achieves strong language-modeling quality. These results support a relation-first view of token mixing: ask Self, ask Others, then let Flow follow Relation.

An Integrable Token Mixing Layer from the Generalized Yang Baxter Equation

The YB Mixer is a sequence token mixing layer derived from free fermion and generalized Yang Baxter structures. It applies a core principle from integrable systems where a local algebraic constraint guarantees global computational stability. By using the Ising exchange algebra the mixer creates a free fermionic structure that acts as an exactly norm preserving orthogonal map. This algebra also produces commuting transfer matrices which allow inference to be order free and adaptable to any variable budget. To ensure the model can generalize to longer sequence lengths it uses a spectral circulant generator. This generator maintains the crucial orthogonal and commuting properties of the system. The result is a highly stable and mathematically grounded architecture for sequence processing.