Evaluation-invariant measurement for multi-agent AI systems.
A measurement made inside a designed environment — a benchmark score, a cooperation rate, an alignment pass — is a fact about that environment; whether it holds anywhere else is a question the measurement itself cannot answer. The field has no established way to check a result from one setup against a result from another — do measurements of multi-agent AI systems mean anything beyond the setup that produced them? Emmy is built to answer that, one metric at a time: calibrate each against systems whose true value is known, test it against look-alike conditions — agents driven into step by a shared model or prompt, with nothing passing between them — and measure how it moves as the setup changes1, so a measurement arrives carrying how far it reaches and where it stops.
Status: Pre-experiment. The
program overview is the canonical reference.
Work so far, in phase0/: estimator calibrations with
printed noise floors, discriminant-validity phantoms, a negative control
on the conditioning rule, and a ground-truth demonstration of
cross-environment inversion — plus a smoke-test in demo/.
AI agents increasingly work in groups — language-model agents calling tools and coordinating with one another, reinforcement-learning agents acting in a shared environment — and these systems are moving into deployment. The tools for measuring them are single-model methods — evaluation, interpretability, AI control — which inspect one model at a time and reveal little about the group.
Collective metrics are starting to appear, and some are tested for robustness across models or environments. But a measure of a genuine group property should read the same when the setup changes in ways that shouldn't matter, and shift only when the property does — and that invariance is not yet something a measure must establish, nor are the measures calibrated against known ground truth. So whether a published measurement reflects the group or the setup stays unclear; such measurements rarely carry from one paper to the next, or from lab to deployment. And the reporting conventions downstream safety work will inherit are taking root now, before the practice under them is sound.
Emmy is a research program building measurement foundations for groups of AI agents. Much of the field starts from a human description of what agents are doing — cooperating, competing, deceiving — and constructs a proxy metric for it. Emmy starts from quantities measurable from behavior and asks what they reveal.
The battery under test is the field's own published metrics — fragility/antifragility, misalignment propensity, multi-agent evaluation suites, interaction-graph measures. For each, emmy characterizes two things: invariance — does it move under setup changes that should not move a genuine collective property — and construct validity — does it track a collective property that joint task-performance cannot separate. One question underneath: does the metric track the group, or the setup it ran in? Where a metric holds on both, claims become comparable across papers, and an external evaluator can inspect a deployed group directly — which single-model methods cannot.
Everything is computed from actions and observations, with no privileged access to the models. In multi-principal deployments — agents from different vendors or operators in one arena — no party has privileged access to every agent, and the behavioral record is the only evidence available to all. Every estimator is calibrated first on synthetic systems with known ground truth, so each result stands against a printed noise floor: below it, a difference is not a result. Controlled environments usually characterize systems, and control is their limitation; here they calibrate instruments, and control is the point — calibration needs known ground truth. Invariance is then the licensed exit from the lab: what must hold before a lab measurement says anything about a deployment.
This is pre-experiment work. It measures behavior, so a positive identifies a behavioral disposition of the group; latent intent is beyond its reach, and the reach tightens further against agents optimizing to fool the measurement. It is complementary to benchmark evaluation and interpretability.
Before any metric runs on real LLM-agent rollouts, its estimator is
calibrated against a synthetic source whose value is known in closed
form — bias and noise floor measured directly, at ~zero compute.
phase0/ calibrates all three battery metrics:
- coordination (conditional mutual information) — recovers the known value to ~0.001 bits at N=10,000; noise floor 0.025 bits;
- fragility / antifragility (response curvature) — recovers sign and magnitude; the floor sets the budget at which fragile-vs-antifragile is callable;
- misalignment propagation (contagion) — recovers the coefficient; the floor sets the budget at which faint contagion is detectable.
The coordination metric is also calibrated for specificity: it must not fire when a shared cause moves two agents together with no link between them. On a two-knob phantom, a pure common cause drives plain mutual information to 0.64 bits while the conditional metric stays at zero within its floor; genuine coupling still registers. This is the case that matters for real agents, where a shared base model or system prompt makes two agents behave alike with no influence passing between them.
The conditioning rule is calibrated from both sides: in a companion negative control (the collider case), two uncoupled agents jointly produce an environment state, and conditioning on that state manufactures up to a full bit of apparent coordination, while plain MI correctly reads zero. The rule this pair pins down: condition on the shared cause, never on the shared effect — and for deployed agents the shared effect is exactly the jointly-produced state an audit is most tempted to stratify by.
And the invariance move is exercised where the answer is provable: the same coupling planted in two structurally different environments yields raw values up to 5.6× apart — comparing raw bits compares the setups — while inverting each environment's own calibration curve recovers couplings that agree to within 0.002 across the sweep. The invariant object is the calibrated estimate of the coupling; on real systems the closed-form curve becomes a measured dose-response curve, and the logic is identical.
Each result is the estimator's resolution limit — the floor a later
finding of "this metric is setup-invariant" or "this one is not" must
clear.
Next: the same estimators on small LLM-agent teams, the invariance
sweep. See phase0/README.md.
demo/ is a runnable smoke-test on the one corner where
invariance is provable — reward rescaling leaves policies unchanged, so
behavioral observables must hold. Two tabular Q-learning agents in the
iterated prisoner's dilemma: coordination and action autocorrelation are
unchanged under rescaling while reward-based quantities shift. It claims
nothing more. See demo/README.md.
After Emmy Noether (1882–1935), whose work connecting symmetries to invariants underlies the framing of evaluation-invariant measurement.
Apache 2.0 — see LICENSE.
Footnotes
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A setup is everything fixed when the measurement is made: the environment (task, action and observation spaces, context distribution), the agents' configuration (backbone model, prompts, decoding), the collective's composition (team size, topology, roles), and the harness. The environment is one component; the opening's "designed environment" is a whole setup. ↩