Property elicitation for verifiable ML training

What it found

Quantile, expectile and Bregman scoring rules, a check that variance is not elicitable alone but is jointly, and a study of pricing benign-drift thresholds for replica verification.

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Proper scoring & elicitation

• How many bits does a probability report need?Finite-precision probability reports under proper scoring: optimal-grid regret law matched to 0.3%, uniform grids lose a ln N factor under log score, raw minifloat formats are ~13× worse than symmetrised.
• What do risk-averse verifiers report under proper scoring?Risk-averse verifiers under proper scoring: log score reports exactly odds^(1/(1+αb)), Brier reports solve logit p = logit r + k(2r−1) and can be debiased exactly, a mean-k aggregation correction is worse than none, and a binarised lottery rule is truthful for any utility at a 2.6–27% certainty-equivalent cost.
• What does a verifier's silence tell you?Selective reporting under proper scoring: abstention iff |p−α| < √c (Brier), silence is evidence unless the anchor is a symmetric prior, ignoring it costs 30× the log-loss at n=12, and a stale anchor makes silence point at the wrong state.
• How do you price the tail of benign drift?Jointly eliciting VaR and expected shortfall of benign drift with a scale-free Rockafellar–Uryasev score: ES alone is not elicitable, misreport cost is exactly ln r + 1/r − 1, quantile-only tolerances leave a/(a−1) of the Pareto tail uncovered, and auditing tail reports breaks down at index ≤ 2.
• Should you pay verifiers for their calibration?Paying verifiers for resolution, not calibration: raw Brier/log excess is exactly E[(r-p)²]/E[KL(p‖r)], Brier is bounded but log is not, log-score selection reverses for overconfident high-resolution verifiers (a ≥ 2.49), and n-sample recalibration costs tr(HI⁻¹)/2n (0.264/n).
• Should a verifier's continuous drift report be scored by CRPS or log score?CRPS vs log score for continuous drift reports: exact Gaussian closed forms, overconfidence capped at 0.234σ under CRPS (unbounded under log), 1-Lipschitz outcome sensitivity, plug-in cost 5σ/(8√π n), and finite score variance for tails ν>2 vs ν>4.

All 28 Proper scoring & elicitation projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.