Geometric observables for financial regime detection

QCML, an unsupervised ML framework, uses Hilbert space geometry to uncover intrinsic structure in data, rather than relying on labels. It learns manifold curvature and topological invariants from Hamiltonian ground state eigenfunctions. This is a three-paper series; Paper 1 focuses on four geometric observables (Berry Phase Rate, Spectral Entropy, Reduced State Purity, Hamiltonian Sensitivity) and their walk-forward evaluation.

Key results (Paper 1)

• 46 detectors compared on 17 historical crises (2000-2024).
• Walk-forward Berry Phase Rate: Cohen's d ≈ 0.72 under nested HPO with 30% fewer false alarms than Random Forest (2.5 vs 3.6/yr).
• Offline: Reduced Purity d = 0.83 (rank 1/46), Absorption Ratio d = 0.80 (classical benchmark, rank 2), Berry Phase Rate d = 0.61 (rank 9).
• Friedman test on the big panel: χ² = 233.1, p < 10⁻¹⁶ (methods are not exchangeable).
• Geometry channels sit far from classical baselines in correlation space: mean |ρ| ≈ 0.13.
• Lead-time example: Berry Phase Rate ~90 days ahead of the RF benchmark on the median crisis (retrospective methodology; walk-forward median is 4 days).

Upcoming papers

• Paper 2: Full 19-channel geometric observatory with orthogonality analysis and per-crisis specialization.
• Paper 3: Adaptive fusion strategies (Regime-Adaptive fusion d ≈ 0.78 on holdout crises).

How it works

Spectral metric learning builds the embedding. The 46-method leaderboard adds classical baselines to 19 geometric detectors evaluated on the crisis panel; 17 of those geometric streams participate in fusion. Three are marked dead in code (near-zero d on all 17 crises) and excluded from ACTIVE_CHANNELS in qcml_geometry/fusion.py: QGT Phase Rigidity, Berry Velocity Coupling, Curvature Rate.

Fusion taxonomy (display names match OBSERVABLE_FAMILIES):

Family	Observables
Holonomy	Berry Phase Rate, Geometric Phase Rate
Metric	QFI Determinant, Hamiltonian Sensitivity
State Dynamics	Multi-Lag Fidelity, Reduced Purity, Quantum Relative Entropy
Kinematics	Geodesic Velocity, Speed Limit Ratio
Spectral	Spectral Entropy, Spectral Complexity, Effective State Dim, Level Spacing Ratio
Curvature	Sectional Curvature Sign, Geodesic Curvature
Topology	QCML Chern, Dimensionality Collapse

Implementations and HPO keys live in qcml_geometry/observables.py; paper tables are authoritative for headline d values.

Project Structure (Paper 1 Scope)

qcml_geometry/              Core library (pure math, no I/O)
  core.py                   QCMLGeometry: Hamiltonian, ground state, Berry curvature, metric tensor
  observables.py            Geometric regime detectors (4 headline + 15 extended)
  fusion.py                 Channel taxonomy + fusion methods
  indicators.py             Spectral gap, energy, fidelity indicators
  topology.py               Topological regime detectors
  info_geometry.py          Information-geometric utilities

experiments/                Paper 1 experiment scripts
  regime_comparison.py      Main 46-method x 17-crisis pipeline
  data_loader.py            yfinance + feature engineering (17 crises)
  baselines.py              RF, GARCH, HMM, CUSUM, BOCPD, IF, EWMA, ...
  evaluation.py             Cohen's d, Friedman test, bootstrap CI
  generate_paper_figures.py Narrative panels (2008 GFC, 2020 COVID, 2022 rates)
  lead_time_analysis.py     Lead time measurement
  backtest/                 Walk-forward backtest suite
  config.yaml               Experiment configuration

paper/                      LaTeX paper (~25 pages, 3 theorems, 1 proposition, ~44 refs)
tests/                      pytest suite
scripts/                    Verification utilities (make verify, make pre-submit)
demo/                       Interactive Streamlit app

paper2_staging/             Deferred work (Papers 2/3: observatory, fusion)
archive/                    Dead experiments, old code
qcml_course.html            Interactive course (open in browser)

Quick Start

pip install -r requirements.txt

# Run the full 46-method comparison (quick mode, ~10 min)
python experiments/regime_comparison.py --causal

# Run tests
pytest tests/ -x -q

# Interactive demo
python demo/cache_data.py
streamlit run demo/app.py

Reproducibility

Paper claims tied to numbers are checked with make verify (see memory/results_registry.yaml). Three canonical JSON runs are tracked in git under experiments/outputs/ (see experiments/outputs/README.md); everything else there is ignored. Clone → install → make verify should pass without rerunning the full pipeline.

Video assets under media/ are generated (e.g. make video); that directory is gitignored.

Makefile Targets

make test              # Run all unit tests
make rebuild           # Incremental experiments + tables + compile paper
make paper             # Compile LaTeX paper
make paper-full        # Regenerate tables from JSON + compile
make review            # Deploy multi-agent paper review
make verify            # Check paper numbers vs source data
make pre-submit        # Full pre-submission gate check
make clean             # Remove build artifacts

Paper

Paper 1: ~25 pages, 3 theorems, 1 proposition, ~44 references. Source: paper/qcml_geometric_sde.tex Full 19-channel version archived in paper2_staging/paper/qcml_geometric_sde_full.tex.

Citation

@article{hammond2026geometric,
  title   = {Geometric Observables for Financial Regime Detection},
  author  = {Hammond, Will},
  year    = {2026},
  note    = {Pitzer College}
}

Author

Will Hammond, Pitzer College, whammond@pitzer.edu