CARTOGRAPH-A: A-Optimal Experiment Selector

• CARTOGRAPH-A is an A-optimal rule that selects experiments by reducing the posterior covariance trace over the unresolved subspace, enhancing model discrimination.
• It incorporates anisotropic covariance awareness, refining simpler disagreement metrics and showing improved performance in high-dimensional settings.
• Embedded in a three-phase select–resolve–refuse loop, it ensures targeted ambiguity reduction while safeguarding against premature scientific identification.

CARTOGRAPH-A is an experiment-selection rule within the broader CARTOGRAPH framework for autonomous scientific discovery. In that framework, an AI scientist is organized as a three-decision loop—select, resolve, and refuse—operating over a shared mechanism basis $\Phi=\{\phi_1,\dots,\phi_p\}$, a model library $\mathcal M=\{M_1,\dots,M_L\}$, and the controversial subspace on which library members disagree. CARTOGRAPH-A is the framework’s exact unresolved A-optimal acquisition rule: under a local linear-Gaussian bridge, it scores candidate experiments by the reduction they induce in posterior covariance trace restricted to the unresolved subspace, thereby refining simpler disagreement or projection heuristics into a covariance-aware experimental design criterion (Shah et al., 26 May 2026).

1. Conceptual setting and scientific objective

CARTOGRAPH is designed for the case in which an autonomous agent must identify scientifically relevant mechanisms from experimental behavior rather than by reading symbolic model coefficients directly. The paper formulates the true law as

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$

with the library $\mathcal M=\{M_1,\dots,M_L\}$ retaining different subsets of the shared mechanism basis. The decisive object is the part on which library members disagree, termed the controversial subspace $C$, with parameters $a_C^\star$ (Shah et al., 26 May 2026).

Within this formulation, the central task is not generic exploration, but targeted elimination of unresolved scientific ambiguity. CARTOGRAPH therefore decomposes autonomous discovery into three distinct decisions. Select chooses the next experiment that best reduces the remaining ambiguity. Resolve decides when ambiguity has been closed enough to stop experimentation. Refuse determines when the current model library is structurally inadequate and should not be trusted (Shah et al., 26 May 2026).

A key theoretical distinction is that symbolic access is treated as a coverage problem, whereas behavioral access is treated as a rank problem. This suggests that experimental design should be driven by the geometry of unresolved disagreement, not merely by coverage of possible mechanisms. CARTOGRAPH-A is the paper’s most exact formulation of that design principle (Shah et al., 26 May 2026).

2. Unresolved subspace and behavioral inverse problem

In the behavioral setting, experiments produce disagreement matrices rather than direct access to mechanism coefficients. The paper writes the inverse problem as

$y = H a_C^\star + \varepsilon,$

where $H\in \mathbb R^{n\times p_C}$ is the accumulated disagreement matrix. The current ambiguity is encoded by the unresolved subspace

$$U_\tau = \operatorname{span}\{v_j:\sigma_j\le \tau\},$$

where $v_j$ are right singular vectors of the current disagreement matrix $\mathcal M=\{M_1,\dots,M_L\}$0 with singular values $\mathcal M=\{M_1,\dots,M_L\}$1. In the exact case, $\mathcal M=\{M_1,\dots,M_L\}$2 and

$\mathcal M=\{M_1,\dots,M_L\}$3

This makes $\mathcal M=\{M_1,\dots,M_L\}$4 the subspace of directions that the present experimental record still cannot determine (Shah et al., 26 May 2026).

For a candidate experiment $\mathcal M=\{M_1,\dots,M_L\}$5, CARTOGRAPH locally linearizes the predicted observables of each library member: $\mathcal M=\{M_1,\dots,M_L\}$6 From these Jacobians it constructs pairwise disagreement blocks

$\mathcal M=\{M_1,\dots,M_L\}$7

and stacks them into the experiment’s disagreement design

$\mathcal M=\{M_1,\dots,M_L\}$8

The scientific meaning of $\mathcal M=\{M_1,\dots,M_L\}$9 is local but precise: it measures how strongly experiment $T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$0 probes the currently unresolved directions of model disagreement (Shah et al., 26 May 2026).

The paper also gives a one-step gap-closure result,

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$1

which implies that only the projected action of an experiment on the unresolved subspace matters for ambiguity reduction. This relation is the immediate precursor to both the raw unresolved projection score and CARTOGRAPH-A’s A-optimal refinement (Shah et al., 26 May 2026).

3. Mathematical definition of CARTOGRAPH-A

The simplest CARTOGRAPH selector is the isotropic unresolved-projection norm

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$2

The paper emphasizes that this is the isotropic special case. It measures how much a candidate experiment “hits” the unresolved subspace, but it does not account for anisotropic covariance or non-isotropic observation noise (Shah et al., 26 May 2026).

CARTOGRAPH-A introduces that missing covariance structure. Under the local linear-Gaussian bridge, it defines

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$3

and scores a candidate experiment by

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$4

This is the framework’s CARTOGRAPH-A rule (Shah et al., 26 May 2026).

The corresponding local model assumes unresolved coordinates $T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$5 obey

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$6

Posterior precision then satisfies

$T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$7

The criterion is therefore exactly the reduction in posterior covariance trace on the unresolved coordinates (Shah et al., 26 May 2026).

This is why the paper calls CARTOGRAPH-A the exact unresolved A-optimal rule. Classical A-optimality minimizes posterior covariance trace; CARTOGRAPH-A applies that principle only on $T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$8, the subspace that remains scientifically unresolved. A plausible implication is that the method separates “what is still uncertain” from “what matters for experimental discrimination,” rather than optimizing over the full parameter space indiscriminately.

4. Relation to raw projection, EIG, and Box–Hill

Under isotropic observation noise, $T(x)=\sum_{j=1}^{p} a_j^\star \phi_j(x),$9, the paper shows that

$\mathcal M=\{M_1,\dots,M_L\}$0

Thus raw unresolved projection becomes exactly the Fisher-information trace on the unresolved subspace. In this limit, raw CARTOGRAPH is not an ad hoc heuristic but the isotropic Fisher-trace special case of the same local design logic (Shah et al., 26 May 2026).

The paper also derives a closed-form local expression for expected information gain: $\mathcal M=\{M_1,\dots,M_L\}$1 For small information gain,

$\mathcal M=\{M_1,\dots,M_L\}$2

Accordingly, EIG is described as first-order aligned with CARTOGRAPH-A, but not identical to it: EIG is a log-det criterion, whereas CARTOGRAPH-A is a trace-reduction criterion (Shah et al., 26 May 2026).

For Box–Hill, the paper gives

$\mathcal M=\{M_1,\dots,M_L\}$3

with $\mathcal M=\{M_1,\dots,M_L\}$4. Under shared isotropic noise and equal predictive covariances $\mathcal M=\{M_1,\dots,M_L\}$5, this collapses to

$\mathcal M=\{M_1,\dots,M_L\}$6

plus a constant. The contrast is therefore structural: Box–Hill remains a pairwise model-discrimination criterion, while CARTOGRAPH-A is an unresolved-subspace A-optimal design over the library’s disagreement geometry as a whole (Shah et al., 26 May 2026).

The paper’s broader theoretical message is that EIG and Box–Hill appear as local comparators rather than global equivalents. This suggests that CARTOGRAPH-A occupies an intermediate position: more principled than raw disagreement magnitude, but more specialized than global Bayesian design objectives because it explicitly restricts attention to unresolved coordinates (Shah et al., 26 May 2026).

5. Algorithmic role in the select–resolve–refuse loop

CARTOGRAPH iterates through a fixed decision procedure. First, it computes $\mathcal M=\{M_1,\dots,M_L\}$7 from the accumulated disagreement matrix. If $\mathcal M=\{M_1,\dots,M_L\}$8, it resolves: ambiguity is closed. Otherwise, it chooses the next experiment $\mathcal M=\{M_1,\dots,M_L\}$9 by maximizing either the raw score $C$0 or the CARTOGRAPH-A trace-reduction objective. After the experiment is executed, the disagreement matrix is updated and the system evaluates refusal diagnostics (Shah et al., 26 May 2026).

The refusal step is based on two quantities: $C$1 Identification is permitted only if

$C$2

If $C$3, the system refuses and revokes any tentative identification (Shah et al., 26 May 2026).

A central point in the paper is that refusal is not the same as predictive uncertainty. It is driven by library-relative residual misfit. This allows the system to behave dynamically: it may identify early, then retract the claim when further data reveal structural mismatch. The paper treats this revocation behavior as a governance property rather than a failure mode (Shah et al., 26 May 2026).

Within this loop, CARTOGRAPH-A has a sharply delimited function. It is a selector, not a stopping rule and not a refusal diagnostic. Resolve depends on closure of unresolved ambiguity; refuse depends on residual-based evidence of model-library inadequacy. The separation of these three decisions is one of the framework’s defining features (Shah et al., 26 May 2026).

6. Empirical performance and boundary cases

The paper’s main selection benchmark is a structured nonlinear cascade. At $C$4, it reports the replicated result Cartograph-A vs raw Cartograph: 129W / 0T / 15L, with $C$5. At $C$6, it reports 120W / 0T / 24L, with $C$7. By contrast, at $C$8 all methods tie completely, and at $C$9 the behavior is transitional or mixed (Shah et al., 26 May 2026).

These results support the paper’s stated interpretation: in higher dimensions, raw projection leaves information unused, whereas CARTOGRAPH-A exploits anisotropy in unresolved covariance. In low dimensions, there may be little room to improve on simpler unresolved-projection or disagreement-style heuristics. The paper also states that CARTOGRAPH-A tracks closed-form EIG very closely in this benchmark while being much cheaper than Monte Carlo BOED (Shah et al., 26 May 2026).

The low-dimensional pharmacokinetics benchmark is presented as a boundary case. There, raw Cartograph is reported as $a_C^\star$0 versus disagreement, and CARTOGRAPH-A is said to be identical to raw Cartograph on all seven truths; the one-sided sign test is not significant. In filtered EPA pharmacokinetics, the results are again near-tie or modest-gain: raw Cartograph versus disagreement is $a_C^\star$1, and local T-opt versus disagreement is $a_C^\star$2 (Shah et al., 26 May 2026).

The paper explicitly treats these outcomes as theoretically expected rather than anomalous. Its stated scaling law says that in random-candidate settings, the useful unresolved fraction scales like $a_C^\star$3, explaining when disagreement heuristics are sufficient and when CARTOGRAPH-A should outperform them. This suggests that CARTOGRAPH-A is most distinctive in high-dimensional and anisotropic unresolved settings, not as a universal dominance result (Shah et al., 26 May 2026).

7. Refusal behavior, retrospective audit, and significance

Although CARTOGRAPH-A is a selection rule, the paper’s broader significance depends on its embedding within the refuse mechanism. In an out-of-library pharmacokinetic benchmark, the framework tentatively identifies three mechanisms outside the library—time-varying clearance, saturable elimination, and enterohepatic recirculation—and then revokes those identifications when residuals cross the threshold $a_C^\star$4. A perturbed in-library control remains below threshold and stays identified (Shah et al., 26 May 2026).

The paper also reports a retrospective audit of 40 positive claims from the published A-Lab autonomous materials system. Among 36 confirmed claims, the refuse guard passes 32 and flags 4. Among 4 later-inconclusive claims, it flags 4 and passes 0. The paper contrasts this with an Rwp-only baseline that flags none of those inconclusive cases (Shah et al., 26 May 2026).

These findings matter for the interpretation of CARTOGRAPH-A because they situate it inside a broader doctrine of autonomous scientific conduct. The framework’s operative message is not only that experiment selection should reduce unresolved covariance efficiently, but also that an AI scientist should know when to stop and when to withhold belief. CARTOGRAPH-A supplies the exact unresolved-subspace A-optimal rule for the select decision, while the residual and BIC guards govern resolve and refuse at the system level (Shah et al., 26 May 2026).

In that sense, CARTOGRAPH-A is best understood not as a stand-alone acquisition function, but as the mathematically exact selector within a tripartite policy for autonomous discovery. Its contribution is strongest where unresolved disagreement is high-dimensional and structured; its restraint comes from the surrounding refusal machinery, which prevents efficient experiment selection from being mistaken for reliable scientific identification (Shah et al., 26 May 2026).