K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles

K-Models doesn't just add interpretability as a reporting layer; it bakes ordinal relationships into the loss function itself, meaning the clustering objective actively penalizes violations of domain structure rather than discovering structure after the fact. This is a design choice with real optimization consequences, not a visualization trick.

This connects directly to the broader pattern in recent work around specification-driven ML. Like XFP's quality-targeted quantization (which accepts user targets and auto-determines compression ratios) and GPart's geometric preservation in fine-tuning, K-Models inverts the typical workflow: instead of fitting a generic model then retrofitting constraints, it asks what structure the domain already knows and makes that structure part of the learning signal. The shift from post-hoc explainability to constraint-embedded architecture is becoming a template across multiple subfields.

If K-Models shows measurable improvement in cluster stability or downstream task performance on held-out biomolecular datasets compared to standard k-means plus post-hoc ordinal reranking, that validates the core claim that embedding structure improves generalization, not just interpretability. If adoption remains confined to specialized sensor applications, the method is domain-specific; if practitioners in other regulated domains (medical imaging, finance) begin adopting the ordinal-embedding pattern, it signals a broader methodological shift.