Compitum
How Tess Learns
Geometry meets pedagogy. Montessori meets machine learning.
Riemannian Geometry
Prompts and models live in a learned curved space (SPD Mahalanobis metric). Distance reflects semantic fit, not raw position.
Utility (free-energy) optimization
We balance quality, latency, cost, distance, and evidence in a single scalarized utility. See protocol.
Control of Error
Immediate, judge-free signals (feasibility, ambiguity, uncertainty) drive bounded updates. See Control of Error.
Boundary Detection
High entropy, low utility gap, high uncertainty → flag for deferral. See decision curves in cs.CL.
Constraint Satisfaction
Feasibility-first selection enforces region/policy/capability limits. Approximate shadow prices are diagnostic. See constraints.
Adaptive Learning
Trust-region (Lyapunov-inspired) caps step size for online metric updates. Stability indicators in cs.SY.
Teacher Intuition, Made Operational
Compitum treats skilled teaching as serious system-design knowledge.
Good teachers do not only mark answers right or wrong. They design environments where errors become visible, interpretable, and correctable.
Tess makes that intuition legible. Compitum turns it into routing mechanics: feasibility gates, uncertainty signals, bounded updates, and certificates.
Prepared Environments
Constraints and diagnostics reveal mismatch before a model is chosen.
Timing-Sensitive Feedback
Bounded updates and drift signals replace theatrical confidence with measured adaptation.
Certificates, Not Vibes
Every route should leave an auditable trace: feasible set, utility components, diagnostics, and testable invariants.
Built for Science
Rigorous. Reproducible. Open.
Tests & QA
Hypothesis derandomized profile; invariants; mutation testing; coverage target 100%. See CI and determinism.
One-Shot Reproducible
Run scripts/run_peer_review.bat to regenerate tables, CEI, KPIs, and a consolidated HTML report with a SHA-256 manifest.
Peer-Review Ready
Docs for cs.LG, cs.CL, cs.SY, stat.ML; CEI; decision curves; control KPIs; fixed-? summaries. See documentation.
For Reviewers
Direct links to audience-specific notes.
cs.LG
Problem setup, decision rule, evaluation protocol, significance of instantaneous feedback.
cs.CL
Per-task routing behavior, decision curves, deferral quality, calibration.
cs.SY
Closed loop, trust-region controller, stability indicators, control KPIs.
stat.ML
Paired bootstrap, calibration, KDE/shrinkage, robustness notes.
SRMF ≈ Lyapunov (Compitum)
Instantaneous feedback, bounded updates, falsifiable claims.
Statement
In Compitum, the Self-Regulating Mapping Function (SRMF) plays the role of a Lyapunov functional for the discrete update map: metric updates decrease a surrogate energy via line search; the controller’s integral decays under zero drift; stride separation isolates timescales.
See the brief: SRMF as a Lyapunov Functional.
Falsifiability (Tests)
Learning descent, zero-error decay, two-timescale isolation, and routing-level distance descent are tested under tests/invariants/.
Discipline Hubs
Repository: github.com/PaulTiffany/compitum
Core Science 0.1.1
Geometry • Stability • Coherence • Constraints • Determinism • Pedagogy
- Geometry: SPD bounds, triangle inequality, ray monotonicity, update descent
- Stability: Lyapunov decay/saturation/recovery; dV proxy sequences; combined boundedness
- Coherence: monotone outward, symmetry (±v), inward score direction, mixture discrimination
- Constraints: feasibility monotone; duals slack≈0, boundary=0; monotone/scale sanity
- Determinism: batch/repeated determinism; paraphrase flip budget + explainability
- Pedagogy: practice raises evidence/utility (β_s>0); prepared environment fixes constraints
