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Calibration Study — Pre-Registration

Status: pre-registered, not yet run Date: 2026-06-01 Unblocks: adaptive agents study (arms 1–3) See also: graph-structural detector study — a separate pre-reg in the same series, evaluating topology-based coordination detection against threshold detectors. Pilot result: calibration pilot findings (rubric v1, n=82) — three-judge Ollama ensemble at rubric v1 fires the escalation rule on the middle p-bins; drove the rubric v2 / v3 work. Pilot re-run (rubric v2): calibration pilot findings — rubric v2 (n=82) — apples-to-apples re-run with rubric v2; headline α 0.87 → 0.94, four of five bins now strong or usable, mistral↔qwen ρ jumped 0.66 → 0.95. Pilot re-run (rubric v3): calibration pilot findings — rubric v3 — v3 replaces v2's caps with targets ("a target is the score, not a ceiling"); cross-scenario check on mixed confirmed over-fit on obfuscation (the middle bin α regressed on the other scenario), so v3 ships with the documented limitation.

Motivation

The adaptive agents study cannot distinguish three causes of a toxicity drop without an external signal:

  1. Agents improved quality. (governance worked)
  2. Agents rejected more. (filtering)
  3. Agents gamed the proxy — v̂ rises while true quality stays flat. (governance defeated)

The framework also rests on the implicit assumption that the proxy-derived p = sigmoid(v̂) is well-calibrated against SoftInteraction.ground_truth (the realized v ∈ {+1, -1} label). That has never been measured. Until both things are anchored, every downstream result is interpretable only at the level of p — which is exactly what a strategic agent will defeat.

Central goal

Produce a triangulated quality signal that adaptive-agent results can be interpreted against:

  • a measured proxy-fidelity baseline (p vs ground_truth),
  • an external judge anchor (LLM-judge scores on accepted interactions),
  • inter-rater agreement across judges (so "the judge is also gameable" is bounded, not waved away).

The deliverable is a CSV of accepted interactions with {v_hat, p, ground_truth, judge_score_claude, judge_score_gpt4o_mini, judge_score_llama, agreement_metrics} that downstream studies can join against by run-id.

Arms

Arm A — Proxy fidelity

Measure how well p = sigmoid(v̂) from ProxyComputer tracks the realized ground_truth label.

  • Procedure: generate interactions with a known latent generator probability drawn from a controlled grid (e.g. {0.05, 0.2, 0.4, 0.6, 0.8, 0.95}, ≥500 interactions per bin) and sample ground_truth ∈ {+1, -1} from it. Run ProxyComputer to compute (v_hat, p) per interaction. Bin p, compute the empirical frequency of ground_truth = +1 per bin (reliability diagram).
  • Metrics: expected calibration error (ECE), maximum calibration error (MCE), Brier score, reliability-diagram bins.
  • Sweep: the sigmoid k parameter; report fidelity vs k. Identify the k that minimizes ECE.
  • Output: runs/<ts>_calibration_fidelity/ with per-bin CSV and reliability plot.

Arm B — External judge anchor

Build the un-gameable quality signal the adaptive study needs.

  • Procedure: sample a held-out set of accepted interactions from static-baseline runs (≥1000 interactions, stratified across scenarios and p bins). For each interaction, present its content artifact (text/output, not the proxy observables) to an LLM judge with a fixed rubric. Judge returns a score on [0, 1].
  • Prompt discipline: the judge prompt MUST NOT include the ProxyObservables fields ProxyComputer reads — concretely: task_progress_delta, rework_count, verifier_rejections, tool_misuse_flags, counterparty_engagement_delta. The judge rates on content quality dimensions orthogonal to those signals. This is what makes the signal un-gameable from an adaptive agent's perspective — the agent can shift observables without shifting what the judge sees.
  • Judges: Claude, GPT-4o-mini, Llama 3.x (matches existing Table 9 setup).
  • Output: runs/<ts>_calibration_judge/judge_scores.csv with one row per interaction × judge.

Arm C — Inter-rater agreement

Bound the "the judge is also gameable" concern.

  • Procedure: on Arm B's sample, compute pairwise agreement across the three judge models.
  • Metrics: Krippendorff's α (continuous), Spearman ρ between judge pairs, intra-class correlation (ICC). Report disagreement-by-bin so we see whether judges disagree more at the tails.
  • Decision rule: if α < 0.5, the judge ensemble is too noisy to anchor the adaptive study — escalate (add a 4th judge, switch to a stronger model, or fall back to human spot-checks on a smaller subsample). Pre-register the α threshold so we don't drift it post-hoc.

Critical confound

The judge is also a model. A sophisticated adaptive agent could, in principle, learn to game the judge rather than the proxy. Three defenses:

  1. The judge prompt rubric is fixed and orthogonal to ProxyComputer's observables, so the gaming channel is not the same one.
  2. Inter-rater agreement (Arm C) bounds the size of model-specific exploits — an attack that fools Claude but not GPT-4o-mini and Llama will surface in α.
  3. We pre-register an external-quality threshold before the adaptive runs and never tune it afterward. The adaptive study reports judge-rated quality as a held-out signal, not as a target.

These do not eliminate the recursion — they bound it. State the bound explicitly in any downstream finding.

Pre-registered commitments

  • p grid, sample sizes, and k sweep range for Arm A are fixed before data collection.
  • Judge prompt rubric, judge model versions, and excluded observable features for Arm B will be version-locked at swarm/judges/rubric_v1.md before any Arm B data collection.
  • The Krippendorff α decision threshold for Arm C is set in advance.
  • The CSV schema downstream studies join against is frozen before the adaptive study begins.
  • All judge calls are logged in append-only JSONL alongside the run artifacts for full reproducibility.

Outcomes

  • p is well-calibrated AND judges agree (α ≥ 0.7): the strong result. Adaptive study unblocked with confidence; p can be reported as a calibrated proxy; judge serves as the un-gameable anchor.
  • p is poorly calibrated but judges agree: the framework still has a usable external anchor; we report the calibration gap honestly and re-tune k. Adaptive study still unblocked.
  • Judges disagree (α < 0.5): the anchor itself is too noisy. The adaptive study cannot rely on a single ensemble score. We either add judges, switch models, or fall back to a smaller human-rated subsample. This is itself a publishable result about LLM-judge reliability.
  • p well-calibrated AND judges agree with each other, but the proxy and the judge ensemble disagree: p and the external judge measure different things. Most interesting result — interpret carefully; this is where the proxy-gaming threat model lives.

Order of operations

  1. Arm A — proxy fidelity on existing static-baseline data (no new runs needed if logs are sufficient). Cheap, runs first.
  2. Arm B — build judge pipeline, freeze rubric, run on stratified sample.
  3. Arm C — compute agreement on Arm B's output.
  4. Freeze the joined CSV schema. Adaptive study (arms 1–3) is unblocked.

Arm A is independent and can begin immediately. Arms B and C share the judge pipeline and are run in sequence.

Post-registration addenda (append-only; not part of the registered design)

  • 2026-07-19 — Arm A findings & deviation analysis: calibration-arm-a-deviation-analysis.md. Registered readout k*=5.0, ECE 0.187, Brier 0.0906; outcome branch 2 ("report the gap honestly, re-tune k; adaptive study still unblocked") applies. Includes a labeled exploratory k-extension and the latent-p-unrecoverability root cause; the ECE<0.1 / Brier<0.05 numbers circulating in the tracker are the c89o scenario spec, not registered criteria of this document.

  • 2026-07-22 — c89o controlled-injection scenario: registered design and criteria (written and committed BEFORE the confirmatory run):

  • Design: scenarios/calibration_proxy_fidelity.yaml — six 2-agent clusters with v_hat_target ∈ {−1, −0.6, −0.2, +0.2, +0.6, +1}; observables solved in closed form so ProxyComputer.compute_v_hat lands on the target (max residual 2.2e-4, on the −1 penalty-floor target only); latent ground truth drawn per interaction from p_latent = compute_p(target) with the pipeline's default sigmoid_k = 2.0; governance fully disabled; single confirmatory run at seed 42, 10 epochs × 200 steps (measured throughput ≈1.6 interactions/step ⇒ expected ≥500 latent draws per cluster, matching arm A's registered per-bin minimum; the architect sketch's 10×20 was ~12× underpowered and is amended here, pre-run).
  • Criteria (confirmatory):
    1. ECE < 0.1 (10 equal-width bins, as arm A).
    2. Excess Brier < 0.02, where excess = Brier − Σ_c (n_c/N)·p_c(1−p_c) over realized cluster counts. The architect spec's raw Brier < 0.05 is unachievable by any estimator under honestly stochastic latent truth: the refinement (irreducible) term alone is ≈0.174 for these targets. The raw criterion was only satisfiable under old arm A's quasi-deterministic generator; registering it verbatim would preregister a guaranteed failure, so it is replaced pre-hoc by the calibration-referenced form.
    3. Reliability convergence: every occupied bin with n ≥ 100 has |accuracy − mean confidence| < 0.06 (≈2.7 binomial σ at n=500, p=0.5).
  • Analysis: python -m swarm run scenarios/calibration_proxy_fidelity.yaml --seed 42 --export-json <out> then python -m experiments.calibration_fidelity --from-run <out>.

  • Disclosure: development smoke runs before this registration used seeds 42 (2×10 steps), 7 (2×100), and 5 (1×30) to verify plumbing and measure throughput; they are excluded from the confirmatory analysis. No confirmatory-length run was executed before this addendum was committed.

  • 2026-07-22 — c89o confirmatory result: ALL THREE registered criteria pass. Run runs/20260723T011931Z_calibration_proxy_fidelity_seed42 (n=2458), analysis runs/20260723T011956Z_calibration_fidelity_scenario: ECE 0.0128 (< 0.1), excess Brier −0.0026 (Brier 0.1874 vs realized-count refinement floor 0.1900; < 0.02), max per-bin gap 0.0246 (< 0.06; all six occupied bins, including the two below the n≥100 scope, pass). Conclusion for the epic: ProxyComputer at the default k is well-calibrated when latent probability is recoverable — arm A's ECE 0.187 was a property of its outcome-leaking synthetic generator, not of the proxy (deviation analysis). Observed and disclosed: cluster volumes are imbalanced (negative-target clusters n=62/82 vs ≈560 — the ecosystem marginalizes low-p agents even with governance disabled), an emergent effect that does not affect the criteria; expected per-cluster n≥500 was met only for four of six clusters, and every bin still clears its convergence bound with margin.