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When Should an AI Scientist Stop? Verifiable Experiment Steering and Refusal for Autonomous Discovery

Neel Tushar Shah, Manglam Kartik

arXiv:2606.07576v1cs.LGcs.ETcs.MA

TL;DR

Autonomous scientific systems need a way to choose informative experiments, recognize when ambiguity is resolved, and stop identifying models when their library is inadequate. CARTOGRAPH combines unresolved-subspace steering and resolution checks with a residual-based refusal guard. Its evaluations include strong high-dimensional selection gains and revocation of out-of-library PK identifications, while the authors emphasize that its guarantees and audits have bounded scope.

  • Problem

    Existing BOED and model-discrimination approaches assume the truth is in the prior support or that a rival is correct, leaving refusal of an inadequate library without a first-class output.

    Source: §1 · p. 1

  • Method

    CARTOGRAPH steers experiments using unresolved-subspace geometry, certifies ambiguity closure, and uses residuals to refuse or revoke identifications.

    Source: §1 · p. 2, §3.3 · p. 3, §3.4 · p. 3

  • Results

    On three out-of-library PK mechanisms, CARTOGRAPH tentatively identifies library members in rounds 0–1, then revokes those identifications in rounds 2–5 as residuals exceed δ=0.25.

    Source: §5.6 · p. 7

  • Takeaways & Limitations

    CARTOGRAPH-A gives statistically strong high-dimensional selection gains, while PK and A-Lab audits illustrate why an explicit refuse signal belongs beside acquisition in AI-scientist workflows.

    Source: §7 · p. 8

    The BOED bridge is local linear-Gaussian, PK and EPA are low-dimensional feasibility checks, and the A-Lab audit is a small retrospective cohort.

    Source: §6 · p. 8

Abstract

from arXiv · show

We present CARTOGRAPH, a verification layer for AI scientists that couples unresolved-subspace experiment steering (select), explicit ambiguity closure (resolve), and residual-based library inadequacy detection (refuse). Under a local linear-Gaussian bridge, raw unresolved projection is the isotropic unresolved Fisher-information trace, while CARTOGRAPH-A is the exact unresolved A-optimal rule; closed-form EIG and Box-Hill arise as local comparators rather than global equivalents. Across five testbeds, CARTOGRAPH-A beats raw projection 129W/0T/15L at d = 8 (p < 10^-21) in a replicated structured cascade. More distinctively, the framework tentatively identifies three out-of-library pharmacokinetic mechanisms and then revokes those identifications as residuals expose structural misfit, while one perturbed in-library control stays identified throughout. In low-dimensional pharmacokinetic and filtered EPA settings, near-ties against disagreement are predicted by theory and observed. Finally, in a retrospective audit of 40 positive claims from the published A-Lab autonomous materials system, the refuse guard flags all 4 claims later marked inconclusive under manual reanalysis while passing 32/36 confirmed claims. Code is available at https://github.com/ai4science-boed/cartograph.git

1. Introduction

As AI systems enter closed scientific discovery loops, the central challenge is not just proposing experiments but deciding what to test, when ambiguity is resolved, and when a model library is inadequate. CARTOGRAPH links those decisions and is distinguished empirically by revoking tentative identifications when later evidence exposes structural misfit.

1. Introduction

  • In closed discovery loops, the bottleneck is deciding which experiment is informative, when the question is resolved, and when to stop making claims because the library is structurally wrong.The introduction contrasts this need with systems that can already generate more candidate experiments than a laboratory can run.Source: §1 · p. 1
  • CARTOGRAPH frames the verification-and-steering problem as selecting informative experiments, resolving ambiguity, and refusing identification when the library is inadequate.Its contributions include a distinction between symbolic and behavioral access, a local BOED bridge, scaling theory, and evaluations across five testbeds.Source: §1 · pp. 1–2
  • Existing BOED and model-discrimination methods address experiment selection and some resolution, but assume the truth lies within the prior support or that at least one rival is correct.The paper identifies refusal as missing from these approaches, a gap it says matters in high-stakes discovery.Source: §1 · p. 1
  • The authors identify revocation as the distinctive empirical finding: three out-of-library mechanisms are tentatively identified, then those claims are withdrawn as evidence exposes structural misfit.A perturbed in-library control stays identified; the authors frame this as an auditable stop-and-escalate signal, not a universal selection gain.Source: §1 · p. 2

2. Problem Setup

The problem is recovery of the controversial mechanisms on which candidate library members disagree. What can be recovered depends on whether the scientist can inspect symbolic coefficients or must infer them through experiments.

2.1. Model Library With a Shared Mechanism Basis

  • The shared mechanism basis defines the true law, while library members retain different subsets of its mechanisms and possibly different retained coefficients.The scientific task is to recover the coefficients on which library members disagree.Source: §2.1 · p. 2

2.2. Two Access Models

  • With symbolic access and omission-only retention, the controversial coefficients are uniquely recoverable exactly when every mechanism appears in at least one library member.This is a coverage condition.Source: §2.2 · p. 2
  • With behavioral access, experiments yield numerical disagreement features rather than coefficient vectors, and recovery becomes a rank property of the resulting design matrix.The paper focuses on this regime, which it says matches systems querying simulators, lab robots, or tool endpoints.Source: §2.2 · p. 2

3. The CARTOGRAPH Framework

CARTOGRAPH uses the subspace left unresolved by prior experiments to steer selection and certify resolution, while a separate residual guard can refuse or revoke identification when the library fits poorly. Its loop uses interpretable thresholds and estimates its scores from quantities available in a typical AI-scientist workflow.

3.1. Unresolved Subspace

  • The unresolved subspace Uτ contains directions in controversial-coefficient space on which accumulated experiments carry little or no information.Candidate experiment blocks are built by linearizing predicted observables and stacking pairwise model differences.Source: §3.1 · pp. 2–3

3.2. Select

  • Selection scores candidate experiments by their action on unresolved directions, using a noise-aware information matrix and an exact A-optimal score based on current posterior covariance.The raw projected score is the isotropic special case; the default acquisition rule is A-optimal.Source: §3.2 · p. 3

3.3. Resolve

  • Resolution is declared when Uτ is empty exactly, or when the smallest singular value of the accumulated disagreement matrix exceeds τ approximately.This certifies closure of library-relative ambiguity, not correctness of the best-fit library member.Source: §3.3 · p. 3, §3.4 · p. 3

3.5. Algorithm

  • Algorithm 1 repeats selection, resolution checks, and residual monitoring, with τ, δ, and µmin as its three physically interpretable hyperparameters.They respectively threshold unresolved singular values, flag structural inadequacy, and set the identification gap requirement.Source: §3.4 · p. 3, §3.5 · p. 3

3.4. Refuse

  • Identification requires both a normalized residual ρ ≤ δ and a top-model BIC gap µ ≥ µmin, allowing later residuals to revoke a tentative identification.When the residual exceeds δ, the system flags library inadequacy and refuses or revokes the identification.Source: §3.4 · p. 3

3.6. Estimating Λcur and Σe

  • The A-optimal score uses current unresolved posterior covariance Λcur and candidate-noise covariance Σe, estimated from warm-start residuals and empirical Bayes updates.The prior scale is matched to controversial-coefficient magnitudes, and cascade and PK results are reported as insensitive to it within a factor of 10.Source: §3.6 · pp. 3–4

3.7. Calibration Protocol for (τ, δ, µmin)

  • The thresholds are calibrated on a fixed warm-start protocol within each benchmark family and then held fixed across that family’s reported truths and seeds.τ uses a singular-value elbow, δ the 95th percentile of in-library residuals, and µmin a BIC evidence threshold.Source: §3.7 · p. 4

3.8. Complexity Scaling

  • Per-round computation uses a truncated SVD and candidate projected norms, with an optional A-optimal update, and is independent of posterior sample count.The paper characterizes this as millisecond-cheap compared with Monte-Carlo EIG.Source: §3.8 · p. 4

4. Theoretical Guarantees

The theory separates recovery conditions by access model, characterizes how experiments close unresolved directions, and predicts when unresolved-subspace selection outperforms disagreement. A local linear-Gaussian bridge relates CARTOGRAPH to Fisher information, posterior variance, EIG, and Box–Hill, without claiming global nonlinear equivalence.

4.1. Recovery Under Different Access Models

  • Under omission-only symbolic access, recovery requires coverage of every mechanism; under behavioral access, noiseless recovery requires the design matrix H to have full column rank.These results distinguish library coverage from experimentally determined rank.Source: §4.1 · p. 4

4.2. One-Step Gap Closure

  • In the exact regime, a candidate experiment updates the unresolved space from U to U ∩ ker(He), so its projected action on U determines gap closure.This motivates projected-norm and Fisher-information-trace acquisition scores in the noisy setting.Source: §4.2 · p. 4

4.3. Scaling Law

  • As mechanism dimension grows, the unresolved-projection selector’s probability of differing from disagreement approaches 1 − 1/n; theory predicts PK near-ties and stronger cascade separation.For PK at d = 2 and k = 1, disagreement already captures half the useful signal.Source: §4.3 · p. 4

4.4. BOED Bridge

  • Under isotropic noise, raw CARTOGRAPH is the unresolved Fisher-information trace, and when dim(Uτ) = 1 its score exactly maximizes posterior-variance reduction.In the local linear-Gaussian regime, closed-form EIG is first-order aligned with the score under isotropic prior and noise, while Box–Hill reduces to disagreement magnitude under an isotropic limit.Source: §4.4 · p. 5
  • The BOED bridge is local and linear-Gaussian; the authors do not claim global optimality, nonlinear equivalence, or a full nonlinear BOED reduction.The empirical comparison uses full nonlinear baselines, while the bridge itself concerns local criteria.Source: §4.4 · p. 5

5. Experiments

Experiments test CARTOGRAPH’s selection, resolution, and refusal roles across synthetic and real-world settings. The cascade results favor A-optimal selection, while refusal experiments show residual-triggered revocation and low-dimensional checks show predicted near-ties.

5.1. Select: Structured Nonlinear Cascade (Headline)

  • At d=8, CARTOGRAPH-A selected oracle hidden-best in 65% versus 2% for raw CARTOGRAPH and disagreement, with regret 19.94 versus 0.01 (129–15, p < 10^-21).At d=4, hidden-best improved from 0.00 to 0.09, but mean regret worsened from 0.312 to 0.418, a metric-misalignment regime rather than a clean win.Source: §5.1 · pp. 5–6, Table 1 · p. 6
  • CARTOGRAPH-A tracks closed-form EIG within 2 percentage points at every d; both dominate raw projection and Box–Hill at d ∈ {8, 16}, with one SVD versus nMC posterior samples.Source: §5.1 · p. 6, Figure 2 · p. 6

5.2. Select: Pharmacokinetic Boundary Case

  • In the seven-scenario PK benchmark (k/d ≈ 1/2), raw CARTOGRAPH beats disagreement 1W/6T/0L and CARTOGRAPH-A matches raw, consistent with predicted near-ties.Source: §5.2 · p. 6

5.3. Select: Scaling Law Validation

  • Across 500 random-candidate instances per (d, k), empirical useful fraction tracks theoretical k/d; selector-disagreement rises from 54.8% at d=2 to 73.0% at d=15.Source: §5.3 · p. 6, Figure 3 · p. 7

5.4. Real-World Audit Checks: EPA and A-Lab

  • EPA checks were near-ties (raw CARTOGRAPH versus disagreement 1W/7T/0L); the A-Lab audit flagged all 4/4 later-inconclusive claims and passed 32/36 confirmed claims.Only 8/96 oral EPA series were fit-stable for the three-model PK library; the audit is a pass/flag log, not a re-adjudication.Source: §5.4 · pp. 6–7, Table 2 · p. 7

5.5. Resolve: Exact Duffing Calibration

  • On the symbolic Duffing benchmark, CARTOGRAPH reached target rank 3 in one experiment and recovered controversial coefficients exactly, with L2 error 0.00 × 100.Source: §5.5 · p. 7

5.6. Refuse: Out-of-Library PK Mechanisms (Headline Honesty Result)

  • For three out-of-library PK mechanisms, CARTOGRAPH tentatively identifies library members in rounds 0–1, then revokes them in rounds 2–5 as residuals exceed δ=0.25; the in-library control stays identified.The benchmark is small and feature-based, evidencing auditable revocation rather than fully calibrated out-of-library detection across domains.Source: §5.6 · p. 7, Figure 4 · p. 7
  • All three failure truths refuse at δ ∈ [0.20, 0.25], while saturable elimination leaks at 0.30 and all leak at 0.35; predictive variance stays below threshold in every scenario.Source: §5.6 · pp. 7–8, Figure 5 · p. 8

6. Discussion

CARTOGRAPH adds an auditable refuse output alongside experiment selection and ambiguity resolution, but its theory and empirical checks have bounded scope.

6. Discussion

  • CARTOGRAPH’s refuse output is a library-relative residual guard, distinct from predictive uncertainty for a fixed model.The framework’s “verifiable” output logs residuals, thresholds, and revocations; it is not universal reliability certification.Source: §6 · p. 8
  • The BOED bridge is local linear-Gaussian, and the scaling law assumes isotropic random candidates.The BOED baselines are closed-form local criteria, not amortized nonlinear BOED.Source: §6 · p. 8
  • PK and EPA are low-dimensional feasibility checks, while the A-Lab audit is a small retrospective cohort.These settings bound the empirical scope described for the framework.Source: §6 · p. 8

7. Conclusion

CARTOGRAPH links experiment selection, resolution, and refusal through an unresolved subspace. The paper reports strong high-dimensional CARTOGRAPH-A gains and presents PK and A-Lab audits as evidence for an explicit refuse signal in AI-scientist workflows.

7. Conclusion

  • CARTOGRAPH-A gives statistically strong high-dimensional selection gains, while PK and A-Lab audits show why an explicit refuse signal belongs beside acquisition.The framework’s theory ties rank recovery, one-step gap closure, k/d scaling, and local BOED criteria to the same unresolved subspace.Source: §7 · p. 8
  • CARTOGRAPH lets an autonomous scientific loop select experiments, declare resolution, and refuse overconfident identification.It is presented as a verification layer for the loop.Source: §7 · p. 8

Impact Statement

The supplied material combines an impact statement with reproducibility details and proofs about recovery, unresolved directions, and local BOED criteria.

Impact Statement

  • The framework is designed for governance, with logged refuse and revoke events, while miscalibrated δ can cause visible over-identification or over-refusal.The authors argue scientific credit should attach to supported refusals as well as positive identifications.Source: Impact Statement · p. 8

A. LLM Use and Reproducibility Statement

  • The authors used LLMs only to polish manuscript wording, while claiming responsibility for the scientific ideas, methods, code, results, and claims.They provide scripts, frozen result files, and run instructions; retrospective audits use public data and fixed calibration protocols.Source: A. LLM Use and Reproducibility Statement · p. 11

B.1. Proof of Proposition 4.1

  • Under omission-only symbolic access, the true coefficients are recoverable exactly if and only if every basis term appears in at least one library member.If any term is absent from the aggregated known set, its coefficient is unobserved and recovery fails.Source: §B.1 · p. 11

B.2. Proof of Theorem 4.2; B.3. Proof of Theorem 4.3

  • Behavioral recovery is unique when the design has full column rank; a nonzero kernel leaves an affine family of coefficients consistent with the observations.The rank gained by restricting a new experiment’s design to unresolved directions is the rank of that restricted design.Source: §B.2 · p. 11, §B.3 · p. 11

B.4. Proof of Theorem 4.5; B.5. Proof of Theorem 4.6

  • For isotropic random candidates, disagreement’s selected unresolved-energy fraction concentrates toward zero as dimension grows, so its choice approaches the resolved-energy maximum.The disagreement selector and the unresolved-energy selector coincide with probability tending to one under the stated limit.Source: §B.4 · pp. 11–12, §B.5 · p. 12

B.6. Proof of Proposition 4.7; B.8. Proof of Corollary 4.9

  • In the local linear-Gaussian model, an experiment updates unresolved-coordinate covariance by adding information to prior precision; for one unresolved dimension, maximizing raw score exactly minimizes posterior variance.The scalar equivalence assumes isotropic noise.Source: §B.6 · p. 12, §B.8 · p. 12

B.9. Proof of Proposition 4.10

  • In the local Gaussian setting, expected information gain is 1/2 log det(Λ_cur Λ_e^-1), with its small-information expansion beginning with a trace term.The expansion is stated for information matrices with norm below 1.Source: §B.9 · p. 12

B.10. Proof of Proposition 4.11

In the isotropic equal-covariance limit, the linear-Gaussian Box–Hill criterion reduces to disagreement; the worked example constructs disagreement blocks from model-pair differences.

B.10. Proof of Proposition 4.11

  • With equal isotropic predictive covariances, linear-Gaussian Box–Hill reduces to disagreement, which captures a k/d fraction of unresolved information.The empirical Box–Hill baseline retains model-specific predictive covariances and therefore need not coincide with disagreement.Source: §B.10 · p. 13

C. Worked Example of the Disagreement Operator

  • In the worked example, each experiment’s block maps a controversial-coordinate perturbation to first-order pairwise predictive differences, and executed blocks are concatenated into H_cur.The three model pairs are formed by subtracting their local Jacobians.Source: C. Worked Example of the Disagreement… · p. 13

D. Closed-Form BOED Baseline Implementations

The section situates closed-form BOED criteria as local comparators, explains when CARTOGRAPH remains usable without predictive distributions, and reports benchmark details for the cascade and PK settings.

D. Closed-Form BOED Baseline Implementations

  • EIG costs one k × k log-determinant per candidate.The EIG baseline is specified under Theorems 4.7 and 4.10.Source: D. Closed-Form BOED Baseline… · p. 13
  • In the isotropic shared-noise limit, Box–Hill reduces to disagreement magnitude, but the cascade’s full model-specific V_i criterion is not expected to collapse to disagreement.The closed-form baselines operate within the same local linear-Gaussian framework.Source: D. Closed-Form BOED Baseline… · p. 13
  • Local T-optimal design maximizes squared predictive differences between the two best-fit library members and coincides locally with their restricted Box–Hill criterion at a dominant pair.Source: D. Closed-Form BOED Baseline… · p. 13
  • CARTOGRAPH remains defined for simulator libraries without tractable predictive distributions, unlike EIG and Box–Hill, which require each member’s predictive distributions at every candidate.It uses the disagreement design H_e and unresolved basis U_τ.Source: D. Closed-Form BOED Baseline… · p. 14

E. Cascade Benchmark Details

  • The cascade is a scalable-dimension first-order ODE benchmark with kinetic and output-coupling mechanisms, tested across four dimensions with 144 trials per dimension.Trials use six truths, 24 noise seeds, three rounds, and eight forcing-profile candidates.Source: E. Cascade Benchmark Details · p. 14

F. PK Divergence Details

  • Raw CARTOGRAPH and CARTOGRAPH-A have identical rounds to identification on all seven PK truths, while both beat disagreement only on the absorption variant.Source: Table 6 · p. 14
  • Raw CARTOGRAPH, CARTOGRAPH-A, and disagreement select different seven-experiment sequences, and all structured methods outperform random selection.Source: F. PK Divergence Details · p. 14

H. EPA Real-Data Full Breakdown

The EPA and A-Lab analyses show near-ties in low-dimensional experiment selection alongside a residual-based audit that flags inconclusive A-Lab claims under a fixed calibration rule.

H. EPA Real-Data Full Breakdown

  • Among EPA series, raw CARTOGRAPH ties disagreement 7 times and wins once; it ties T-opt 7 times and loses once, while T-opt beats disagreement 2 times and ties 6.Source: H. EPA Real-Data Full Breakdown · p. 15
  • Of eight named EPA series, three have no unresolved dimensions at warm start; among the other five, raw CARTOGRAPH matches T-opt on four and trails on one.Source: H. EPA Real-Data Full Breakdown · p. 15
  • The EPA cohort had 96 oral series, but 88 failed to fit at least one library member and were skipped; the paper treats these failures as evidence of library inadequacy.Source: H. EPA Real-Data Full Breakdown · p. 15

I. A-Lab Retrospective Audit Details

  • The audit covers 40 originally positive A-Lab claims, with inconclusive labels based on corrected manual conclusions for structure or composition.Source: §I · p. 15
  • With k=1, the scaling experiment used 500 random-candidate instances per dimension; disagreement and projection nearly agree at low d, while projection’s pointwise-optimal behavior emerges at high d.Source: Table 7 · p. 15, Figure 7 · p. 16
  • The A-Lab residual threshold δ was set to 0.776 from the 95th percentile on confirmed Success rows and frozen before evaluating all positive claims.A deterministic bootstrap gives a broad calibration interval of [0.496, 1.088], reflecting the small public cohort.Source: §I · p. 16
  • All 4 inconclusive A-Lab claims were flagged, while 32/36 confirmed claims passed; an Rwp-only baseline flagged 0/4 inconclusive claims.The combined guard’s result is presented as an auditable pass/flag log, not an independent determination of crystallographic status.Source: §I · p. 16

K. Failure-Mode Catalog for CARTOGRAPH

The failure catalog identifies approximation, noise, calibration, and unresolved-subspace conditions that constrain CARTOGRAPH; the worked example assigns candidate generation to an LLM and experiment selection to CARTOGRAPH.

K. Failure-Mode Catalog for CARTOGRAPH

M. Worked LLM-in-the-Loop Example

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