Tutorials

The Dimension of Change

Every domain has entities that transform over time — a patient’s language evolves, a market regime shifts, a molecule folds, an ML model drifts. Traditional vector databases store snapshots. ChronosVector stores trajectories and provides the mathematical tools to understand their shape.

The temporal dimension is not just “when” — it is the dimension of change, evolution, and transformation. CVX’s 17 analytical functions form a layered framework for understanding how entities move through embedding spaces:

Level	Question	CVX Functions	What It Reveals
1	Where has the entity been?	trajectory, search	The raw path through embedding space
2	How fast is it changing?	velocity, drift	Rate and direction of transformation
3	Is change persistent or erratic?	hurst_exponent	Long-range dependence: trending vs oscillating
4	When did regime transitions happen?	detect_changepoints	Structural breaks in behavior
5	How does the distribution transform?	region_trajectory, wasserstein_drift, fisher_rao_distance	Semantic migration between topics/clusters
6	What is the shape of the transformation?	path_signature, signature_distance	Universal nonlinear trajectory fingerprint
7	How does the topology evolve?	topological_features	Fragmentation, convergence, structural change

Each tutorial applies this framework to a different domain, demonstrating that the same mathematical tools reveal transformation across fundamentally different data.

---

Available Tutorials

Tutorial	Domain	Data	Key Insight	Status
Mental Health Explorer	Clinical NLP	eRisk (D=768)	13 CVX temporal features → F1=0.60 (AUC=0.64); early detection at 10% of posts	Available
Clinical Anchoring	Clinical NLP	eRisk (D=768)	DSM-5 anchor projection: F1=0.744 (AUC=0.886) on temporal split, early detection at 10%	Available
MAP-Elites Archive	Quality-Diversity	Synthetic (D=20)	HNSW replaces CVT with adaptive niches; archive topology reveals exploration structure	Available
MLOps Drift Detection	Production ML	Synthetic (D=64)	5 independent drift signals detect gradual and sudden distribution shifts	Available

Planned

Tutorial	Domain	Focus
Molecular Dynamics	Computational Chemistry	Conformational clustering via graph regions, trajectory comparison
Drug Discovery	Medicinal Chemistry	Campaign navigation through chemical space
Quantitative Finance	Trading	Market regime detection, path-dependent analysis

---

Running the Tutorials

Each tutorial is a self-contained Jupyter notebook in the notebooks/ directory.

# Setup
conda activate cvx
cd crates/cvx-python && maturin develop --release && cd ../..

# Launch
jupyter notebook notebooks/T_MAP_Elites.ipynb

The Mental Health tutorial requires the eRisk dataset (see Research Protocol 001). The MAP-Elites and MLOps tutorials generate synthetic data and require no external files.

---

From Examples to Tutorials

The Examples section provides a quick API reference for each of CVX’s 17 functions with concise code snippets. The tutorials below go deeper: each is a complete, executable analysis that follows the 7-level framework above, showing real outputs, interactive visualizations, and domain-specific interpretation.

Need	Go to
”How do I call path_signature()?”	Examples → API Reference
”How does path signature analysis work on real data?”	Tutorials
”What functions does CVX have for distributional analysis?”	Temporal Analytics Toolkit