Energy Descent Certificates (EDC)

Critical thinking, for critical systems. — Polished Snow

An energy-based reasoner answers by optimizing a learned energy E(h_x, z) over a latent — it descends to an answer. This project asks a question nobody has answered:

Is the geometry of that descent a calibrated signal of whether the answer is right — and can we turn it into a distribution-free guarantee?

We run the inference-time optimization from K stochastic restarts and read off the shape of the landscape it lands in:

• basin agreement — do independent restarts converge to the same answer?
• curvature — is the optimum a sharp spike or a wide, flat basin? (Hessian eigenvalues of the energy over the latent, per input, via Hessian-vector products)
• descent dynamics — how fast, how monotonically, how far did it settle?

Wrapped in distribution-free risk control, these features give a certificate:

• Selective prediction / abstention — answer only when a guaranteed error rate holds among answered inputs; otherwise abstain and route to a human/verifier (Learn-then-Test).
• Adaptive halting — stop "thinking" as soon as a guaranteed error budget is met (Conformal Risk Control).

The scientific claim — and the thing this repo is built to falsify — is that landscape geometry beats the scalar energy (the signal Energy-Based Transformers already use) as a predictor of correctness. See docs/RESEARCH_PLAN.md.

Why this is new

Energy-Based Transformers (arXiv 2507.02092) already use scalar energy as confidence and think longer on hard inputs — but with no restarts, no curvature/basin geometry, and no calibration guarantee. Curvature↔calibration work studies curvature of the loss over weights; ours is curvature of the energy over the latent, per input. No prior work turns inference-time landscape geometry into a distribution-free selective certificate for an EBM reasoner. Full positioning in docs/RELATED_WORK.md.

Quickstart

uv sync --python 3.12 --extra dev     # pinned CPU env, no GPU needed

make test        # offline, CPU-only test suite
make smoke       # end-to-end base reasoner on CPU (<60s); appends a ledger row

Run the reasoner directly:

PYTHONPATH=src python -m edc.cli smoke --config configs/smoke.toml

Layout

src/edc/
  energy/       encoder → E_θ(h_x, z) → decoder            (JAX/Flax)
  inference/    K-restart Langevin descent + trajectory logging
  geometry/     basin · curvature (HVP) · energy stats · dynamics   ✓
  conformal/    Learn-then-Test (abstention) · Conformal Risk Control (halting)  [Phase 3]
  halting/      adaptive compute policy                    [Phase 3]
  tasks/        synthetic reasoning families (+ OOD splits)
  train/        IREM/IRED-style energy training
  eval/         AURC · risk–coverage · ECE · compute-vs-accuracy     [Phase 3]
configs/  experiments/  analysis/  results/ledger.jsonl  tests/  docs/  paper/

Status (v0.0.1)

The full method and its distribution-free certificate machinery are implemented and tested (offline, CPU): base reasoner (Phase 1), 14-feature landscape geometry (Phase 2), the conformal layer — split-conformal, Learn-then-Test selective prediction/abstention, and Conformal Risk Control adaptive halting (Phase 3, 4b) — a multi-seed experiment/sweep/table harness, and the figure set F2–F6 + S1, all regenerable from results/ledger.jsonl.

Findings so far (honest).

• Geometry beats the EBT scalar energy as a nonconformity score on two structurally distinct tasks — arithmetic (E1) and graph shortest-path (E2) — with the paired-bootstrap ΔAURC CI excluding 0 on 5/5 seeds each. This is the project's specific falsification target (invariant 8).
• The restart geometry is the mechanism: the lift grows monotonically with K (S1 ablation); K=1 (≈ EBT, no basin geometry) barely separates.
• Both guarantees hold in-distribution (F2/F3 abstention validity, F4 halting saves ~58% compute at a guaranteed error budget) and break under distribution shift (F6) — the argument for abstention in critical systems.
• Key caveat (Phase 4e): geometry does not beat a standard softmax-confidence baseline (MSP / temperature-scaled / entropy) — it ties on arithmetic and loses on graph. So the current contribution is the certificate machinery + beating the EBT scalar-energy signal specifically, not a universal win over all confidence signals. The likely lever — a fully-learned IRED-style landscape (vs the current supervised basin-center reasoner) — is the priority next experiment.

Experiments and figures/tables: docs/EXPERIMENTS.md. Rolling state and next steps: docs/SESSION_HANDOFF.md. Decisions: docs/DECISIONS.md.

License

Unreleased research code. All rights reserved until a license is added.