Agentic Active Metrology

NANO is a loop, not a model. The model produces maps; the loop spends a budget. This page states the contract of each step — inputs, outputs, and the rule that turns uncertainty into a decision.

Implementation status

The loop described here is implemented in nano/, and the contract below is enforced by the test suite. The estimator is nano/model.py, the acquisition rule is nano/policy.py, and the loop is nano/agent.py. Where code and page disagree, that is a bug in one of them — see System Design for the file-by-file map.

No page on this site prints a benchmark number that has not been generated. Running the benchmark against WM-811K is what fills them in — see Reproduce.

The loop

1. 01

   Observe

   Read the sparse set of real measurements available so far, plus the simulation prior for every die.

2. 02

   Estimate

   Fit a spatial model of reality and produce three maps: prediction, uncertainty, and prior-vs-reality gap.

3. 03

   Select

   Score every unmeasured die with the acquisition function and pick the argmax as the next measurement.

4. 04

   Measure

   Reveal the hidden real value at that die, append it to the observation set, and spend one unit of budget.

↻ Repeat until the measurement budget is exhausted. Every iteration is logged, so the decision trace is auditable.

Interface contract

Input, per iteration

Field	Shape	Meaning
coords	(N, 2)	Die grid coordinates on the wafer
prior	(N,)	Simulation prediction for every die, available everywhere
observed_mask	(N,) bool	Which dies have been measured so far
observed_values	(M,)	Measured values for those dies, M = observed_mask.sum()
budget_remaining	int	Measurements left before the run stops

Output, per iteration

Field	Shape	Meaning
prediction	(N,)	Best current estimate of reality at every die
uncertainty	(N,)	Model uncertainty at every die, 0 at measured dies
reality_gap	(N,)	Signed disagreement, prediction − prior
next_index	int	Die selected for the next measurement
next_score	float	Acquisition score of that die, for the decision trace

The three maps are the reason the agent is auditable. A prediction alone cannot be argued with; a prediction plus an uncertainty map plus a gap map can be inspected before the tool is scheduled.

Estimating reality

The estimator has one job: reconcile a dense, biased prior with a sparse, trusted set of measurements, and stay honest about how far the reconciliation reaches.

1. Start from the prior. With zero measurements, the estimate is the simulation prior, and uncertainty is 1.0 everywhere.
2. Correct locally. Each measurement contributes a residual, measured value − prior, spread by a Gaussian kernel in die distance. The weighted mean of those residuals is added to the prior and the result is clipped to [0, 1]; at a measured die the prediction is the measured value exactly.
3. Return to the prior where nothing was measured. The weighted mean is shrunk by prior_weight, which counts the prior as that many measurements' worth of evidence for "no correction here". Without it the estimate would extrapolate a global offset into regions nothing has been measured in.
4. Report the reach. Uncertainty is 1 / (1 + total kernel weight), raised back towards 1 by disagreement between the measurements that do reach a die. The scale is absolute — 1.0 means nothing measured reaches here, 0.0 means measured — so two maps from one episode are comparable, and "uncertainty fell" is a falsifiable claim rather than a rescaling artifact.

The two hyper-parameters (length_scale, defaulting to a twelfth of the wafer span, and prior_weight) are fixed before the comparison, identical across every arm, and written into results/benchmark_summary.json under experiment.model.

Ground truth for unmeasured dies is never read by the estimator. It exists only in the evaluation harness. Hidden from agent

Selecting the next measurement

The intended acquisition score combines three terms:

acquisition(i) = uncertainty(i) × simulation_disagreement(i) × spatial_novelty(i)

Term	Reads as	Why it belongs
uncertainty(i)	"I do not know this die."	Spending budget where the estimate is already firm buys nothing.
simulation_disagreement(i)	"The prior is expected to be wrong here."	This is where the Sim2Real gap actually lives. Uncertainty alone will happily sample empty agreement.
spatial_novelty(i)	"I have not looked in this region."	Prevents the loop from clustering measurements around one interesting spot.

Each term is min-max scaled to [0, 1] over the wafer and floored at eps = 1e-3, because a product is zero if any factor is zero and all three terms are legitimately zero somewhere on every wafer. The floor ranks a candidate last on a term instead of vetoing it outright.

The disagreement term is not |prediction − prior|. That map necessarily decays to nothing beyond the reach of the measurements, so a rule built on it would call every unexplored region settled and never look there. The model emits a second map, expected_disagreement: the locally weighted magnitude of the residuals, shrunk towards the wafer-wide mean residual magnitude wherever local evidence is thin. It reads as "the prior is off by about this much here, and I have no evidence to the contrary". reality_gap remains an output, because the correction actually applied is what a reviewer needs to see.

The next measurement is argmax over unmeasured dies:

next_index = argmax { acquisition(i) : observed_mask[i] == False }

Keep the formula and the code in sync

If the implementation reduced to plain argmax(uncertainty), this section would have to say argmax(uncertainty). A three-term product in the documentation and a one-term rule in the code is the failure mode this project exists to argue against, so the rule that ran is written into every results file as experiment.acquisition_rule, nano/policy.py returns the per-term breakdown with every decision, and tests/test_policy.py asserts that the score of the selected die equals the product of the three terms in its own trace.

Stating a rule is not the same as showing it helps. python -m nano.benchmark --ablation re-runs the loop with terms dropped, and the benchmark page publishes what each term is worth — including where a reduced rule beats this one, which on the published WM-811K run is exactly what happens: uncertainty alone scores better than the product documented above. The rule here has not been changed on the strength of twelve wafers; Honest Scope says why, and what would change it.

Stopping and determinism

Stopping. The run ends when budget_remaining reaches zero. There is no early stop on a convergence criterion, because a budget is the constraint that actually binds in a fab: tool time is allocated, not discovered.

Determinism. Every stochastic choice is driven by an explicit seed. Seeds are combined with a stable hash of the wafer id and the strategy name, so a run reproduces across interpreter sessions:

• which wafers enter the evaluation set,
• how the initial sparse observation mask is drawn,
• the Random baseline's selections,
• any tie-breaking inside argmax.

Given the same seed, the same wafer and the same budget, a run reproduces exactly. Baselines are handed the same initial observations and the same budget as NANO, so the only thing that differs between arms is the selection rule.

What this is not

• Not wafer-map interpolation with extra steps. Interpolation answers "what is the value here?" NANO answers "where should the next measurement go?"
• Not a replacement for physical simulation. The prior is an input to be corrected, not an output to be replaced.
• Not a calibration claim. NANO reports uncertainty and uses it to rank locations; that its uncertainty is calibrated is a separate assertion, and one this project does not make. See Honest Scope.

Next: the data and the experimental design →