AssayRouter: Historical Utility Priors for Frozen Molecular Predictor Routing

• The practical problem is choosing which prediction channels to include when a new continuous endpoint has few measurements and source models are inaccessible.Source: §1 · p. 1
• AssayRouter scores each frozen source from its support-set behavior, selects a Top-4 set, and fits separate convex weights for the target.Source: §1 · p. 1
• Evaluation spans 24 external assays and six interface families, with matched interventions testing utility transfer, interface holdouts, and frozen ranking versus target-side subset search.Source: §1 · pp. 1–2
• Post-fit utility measures the incremental loss reduction from adding one frozen source to the local target predictor, providing transferable routing supervision.Source: §1 · pp. 1–2
• The approach replaces more than 20 million inner NNLS fits with zero counterfactual fits on the target.Source: §1 · p. 2
• Controlled interventions show that candidate-specific utility transfers across external assays and unseen predictor families, improving strict four-call routing over Support-CV@4.Source: §1 · p. 2

• Each support episode separates routing observations on Rt from fitting on disjoint Ct, and the confirmation set is reserved for final scoring.Source: §2 · p. 2
• The selector chooses four sources, then a normalized NNLS combiner fits the local target column and selected source outputs on Ct.Source: §2 · p. 2
• Because confirmation labels are sealed, the oracle action is unavailable at deployment; paired confirmation-loss differences equal paired differences in latent regret.Source: §2 · p. 2
• The study tests whether a policy learned from completed assays can reduce latent selection regret on a new label function under a frozen interface.Source: §2 · p. 2

3.1 LEARNING A POST-FIT UTILITY PRIOR

• AssayRouter measures each source’s post-fit utility as its incremental loss reduction under the same convex refit used at deployment.The historical utility label comes from held-out discovery loss after adding a candidate to the local target predictor.Source: §3.1 · pp. 2–4
• A shared HGB regressor predicts centered utility from candidate behavior and interface family, without source or assay identity.Its 11 primary coordinates capture residual alignment, source reliability, support size, and declared training size.Source: §3.1 · p. 3

3.2 ROUTING ONCE WITH THE FROZEN UTILITY PRIOR

• At deployment, the frozen prior selects four sources from routing support, then fits their simplex weights on separate combiner data before confirmation.The selected set is fixed before confirmation labels enter the final metric.Source: §3.2 · p. 4
• 20,445,696 Support-CV inner fits versus zero for AssayRouter before the shared final combiner; historical utility construction is paid once and reused across external assays.The count excludes frozen-source inference and the common final NNLS fit.Source: §3.2 · p. 5
• Strict scoring evaluates each constituent after exactly four source calls, whereas cross-fit scoring averages predictions across constituents and can use 5–21 unique sources.Strict scoring is the primary deployment estimand.Source: §3.2 · p. 5

4.1 ASSAYROUTER TRANSFERS POST-FIT UTILITY

• 0.1352 higher strict NLL under candidate-label permutation; the genuine candidate-to-utility mapping wins in 90.7% of paired cells.The intervention preserves feature rows, the utility multiset, model capacity, grouped folds, and external assignments; the effect is positive at every budget and across all six interfaces in the uncentered replication.Source: §4.1 · p. 6, Figure 2 · p. 6
• 0.0497 higher NLL after permuting transferred correspondence under leave-one-interface-out training; the effect is positive in all six held-out families.These unseen-interface routers also improve over Support-CV by 0.1116 NLL and win on all 24 targets.Source: §4.1 · p. 6, Figure 3 · p. 6

4.2 HISTORICAL UTILITY OUTPERFORMS SELECTION ON THE TARGET UNDER THE SAME ACTION

• 0.0409 lower strict NLL than Support-CV: AssayRouter-C has the best overall NLL, MAE, and RMSE among access-matched methods, with its advantage largest at 16 labels.The strict comparison scores each four-call constituent independently.Source: §4.2 · pp. 6–7, Table 1 · p. 7
• AssayRouter scores each source once and reuses its frozen ranking, avoiding Support-CV’s repeated target-side subset fits before the shared final combiner.Support-CV requires 20, 280, and 364 inner NNLS fits per direction on Biogen, ExpansionRx, and TDC, respectively.Source: Figure 4 · p. 7, §4.2 · p. 7

4.3 POST-FIT SUPERVISION SURVIVES SHORTCUT AND STABILITY TESTS

• 0.1844 strict NLL improvement over residual compatibility, the closest support-profile shortcut under the same four-source contract.The advantage appears in all six interfaces and at least 79% of targets at every budget; residual correlation tracks local-model errors, whereas post-fit utility measures value after competing channels enter the combiner.Source: §4.3 · p. 8
• Better utility-prediction MSE does not necessarily improve external routing: deployment changes only when Top-4 membership changes and the refitted combination changes.This separates proxy regression quality from deployed decision quality.Source: §4.3 · p. 8
• Every leave-one-target, leave-one-interface, and leave-one-collection estimate preserves the direction of the candidate-label, unseen-interface, and strict Support-CV effects.The deletions cover 24 targets, six interfaces, and three collections; no single assay, predictor family, or external collection drives the conclusions.Source: §4.3 · pp. 8–9

Molecular adaptation and representation

• Adaptation and representation methods train, fine-tune, or condition predictors; AssayRouter keeps source contracts frozen and learns which outputs complement a local model.The related approaches include few-shot conditioning, set representations, pretrained representations, and learned task transfer.Source: §5 · p. 9

Source and task selection

• AssayRouter supervises source selection with value measured after the local predictor and source output are fitted together, unlike signals based on pre-combination relatedness or competence.Earlier approaches include prediction-profile methods such as pQSAR and task- or auxiliary-evidence methods such as GATE (Lee et al., 2024) and AssayMatch (Fan & Barzilay, 2026).Source: §5 · p. 9

Model portfolios and learned routing

• Model portfolios rank validation libraries or pretrained models, while AssayRouter selects a fixed-size frozen subset and fits convex weights afterward.Matched comparators preserve the bank, routing roles, fan-in, and final NNLS; alternative actions and information budgets provide positioning precedents.Source: §5 · p. 9

6 DISCUSSION AND CONCLUSION

• Historical supervision transfers across three external collections and six frozen interfaces, with the advantage strongest at 16 labels and narrowing as target evidence grows.Candidate-label and identity holdouts support transfer beyond memorized assays or predictor families.Source: §6 · p. 9
• Router evaluation should test the deployed decision under its exact information and call budget, because a better proxy matters only when it changes consequential membership near the Top-4 boundary.The refitted combiner must assign consequential weight to the changed membership.Source: §6 · p. 9
• The demonstrated scope is continuous regression with homogeneous interface banks, a fixed four-source action, and 20 historical pseudo-targets.Learning target-dependent fan-in would extend the action space; a larger historical panel would test scaling with assay diversity, and learned interface representations could cover contracts without historical counterparts.Source: §6 · pp. 9–10
• AssayRouter can complement few-shot adaptation by selecting the frozen channel set before an adaptive method operates within it.The present evidence establishes the selection step.Source: §6 · p. 10

A.1.1 HISTORICAL MATRIX

• Training uses 20 continuous ChEMBL-MT pseudo-targets crossed with six interfaces, three support budgets, and four episodes, producing 27,360 candidate contexts and 355,680 state-expanded rows.The primary label is discovery-loss reduction from adding a candidate; grouped cross-validation by target selects the histogram gradient-boosting regressor.Source: §A.1.1 · p. 13

A.1.2 FROZEN FITTING CONFIGURATION

• Ridge regression on molecular fingerprints supplies the local target column, while NNLS fits the local and selected source columns and normalizes weights to the simplex.The local model uses four shuffled out-of-fold folds on R and a fit on all C rows for query predictions; five target-grouped folds select the HGB configuration by target-averaged MAE.Source: §A.1.2 · p. 13
• Source-quality is a capacity-matched selector that preserves the 11 candidate coordinates, HGB search, Top-4 action, external assignments, and final NNLS, changing only the historical supervision label.The appendix maps central claims to matched controls and identifies the evidence chain, but the supplied passages do not report table cell values.Source: §A.1.2 · p. 13, Table 3 · p. 13, Table 4 · p. 14

A.1.3 SUPPORT-SCALE Qdisc UTILITY-LOSS SENSITIVITY

• Recomputing utility loss on frozen historical episodes preserves the candidate-specific advantage across direct, strict, unseen-interface, and matched-search comparisons.The sensitivity applies the same 24 targets, six interfaces, three budgets, and 12 support episodes as the parent experiment.Source: §A.1.3 · p. 14, Table 5 · p. 14

A.1.4 SOURCE-IDENTITY HOLDOUT

• Source-identity holdout preserves utility MAE and Top-4 overlap, while fine-grained Spearman correlation decreases by 0.0197 (95% interval [−0.0355, −0.0025]).The deployment candidate sources are disjoint from historical candidate-source identities; the reported ordering decrease is beyond the selection boundary.Source: §A.1.4 · p. 14

A.1.5 MATCHED POST-FIT LABEL CONTROLS

• Matched controls identify post-fit candidate value relative to its historical block as the transferable supervision: raw loss and rank are weaker, while centered and standardized utility remain matched to the primary router in overall strict NLL.The strict matched-control table scores each four-call constituent before aggregation.Source: §A.1.5 · p. 14, Table 6 · p. 15

A.1.6 DIRECT ASSAYROUTER-C CORRESPONDENCE INTERVENTION

• Candidate-label pairing remains decisive under the selected deployment variant, and four additional fixed mappings each have a positive clustered lower bound.The primary intervention permutes utility among candidates within blocks while preserving candidate features and the label multiset; the table caption defines effects as permuted minus genuine NLL.Source: §A.1.6 · p. 15, Table 7 · p. 15, §A.1.8 · p. 17

A.1.7 FEATURE INVENTORY

• The primary router uses 11 candidate coordinates, including residual alignment, source response and uncertainty, support size, and declared training size; 14 additional coordinates describe selected-set state in the extension.All coordinates are available before confirmation labels are read, and interface indicators are appended separately.Source: §A.1.7 · pp. 15–16

A.1.9 EXTERNAL REPLAY

• External replay scores strict constituents separately, averages support repetitions before comparison, and uses a target–interface bootstrap with 10,000 resamples for aggregate uncertainty.Each sparse constituent selects four sources and uses the same no-prior simplex NNLS on C.Source: §A.1.9 · p. 17, §A.1.10 · p. 17

A.1.11 SMALL-CLUSTER SENSITIVITY

• The candidate-label intervention, leave-one-interface-out transfer, and strict Support-CV comparison remain positive after deleting any one target, interface, or collection; interface-level sign-flip tests give p = 0.03125 for all three.The sign-flip tests over 24 target effects also remain positive.Source: §A.1.11 · pp. 17–18

A.1.12 EVIDENCE DESIGN

• The study contrasts source-quality supervision, deterministic rankings, support-greedy selection, and a target-only learner; Support-CV@4 is the primary matched search comparator, while Frozen-DES@4 and MINE-WS@4 receive richer query access.The compound-overlap sensitivity measures exact-parent overlap; scaffold independence lies outside its scope.Source: §A.1.13 · p. 18, §A.1.14 · p. 19, §A.2.1 · p. 20

A.2.2 STRICT RESIDUAL COMPATIBILITY

• Residual compatibility scores candidates by signed correlation with the local predictor’s out-of-fold residuals, but its overall NLL is 2.2947.The NLL difference between Residual and AssayRouter-C is 0.1844 across 432 paired target–interface–budget cells, with interval [0.1138, 0.2609].Source: §A.2.2 · pp. 20–21
• Support-CV@4 uses 64 source calls and 5–21 unique sources per episode, so none of its episodes has a strict four-source union.The section distinguishes its selection-stage ensemble construction from accuracy evaluated under the strict four-call estimand.Source: §A.2.2 · p. 21
• 0.0409 is AssayRouter-C’s overall NLL difference in the matched comparison, with interval [0.0211, 0.0623]; lower NLL occurs in 77.8% of target–interface units.The effect is resolved at 16 and 32 labels and for ExpansionRx and TDC, but not at 64 labels or for Biogen.Source: §A.2.2 · p. 21

A.3.1 SELECTION-WORK PROPOSITION

• AssayRouter ranks candidates once with a frozen score, whereas sequential greedy selection evaluates remaining candidates after each addition.The comparison concerns selection work after frozen predictions and candidate features are constructed.Source: §A.3.1 · p. 22

A.3.2 PROOF AND BOUNDARY

• 20,445,696 inner NNLS fits were performed by the screened selection procedure across the evaluation.For the formal comparator, the screen width is L = 8 and the subset size is K = 4; selection uses routing-support labels and predictions before confirmation scoring.Source: §A.3.2 · p. 22
• Selection fit counts measure subset construction on the target, while strict confirmation calls define the accuracy budget; neither count is total wall-clock latency.The workload includes a screen when the bank exceeds L and exhaustive scoring of surviving subsets of size K.Source: §A.3.2 · p. 22, Table 24 · p. 23

A.3.3 AUDITED FIT-COUNT CROSSOVER

• Support-CV@4’s repeated search reaches the primary standalone-label cost after 116.8 routing directions and the full historical-development cost after 2,885.8 directions.These crossover counts compare the shared NNLS primitive, not wall-clock time, and exclude feature construction, HGB execution, source prediction, and the final combiner.Source: §A.3.3 · p. 23

B.1.1 OFFICIAL FEW-SHOT CHECKPOINTS

• Across the three support budgets, AssayRouter–ProtoNet NLL differences are −0.0190, 0.2182, and 0.0125; target-bootstrap intervals cross zero at every budget.Positive differences favor ProtoNet, and ProtoNet is the strongest of the five official systems evaluated.Source: §B.1.1 · p. 24

B.1.2 PUBLISHED BIOGEN PREDICTORS

• On the Biogen endpoints, reproduced mean Pearson correlations are 0.6683 for Random Forest, 0.7069 for LightGBM, 0.6373 for GINE, and 0.7259 for SR-GINE.These full-training predictors are reported separately from support-budget-matched routing methods.Source: §B.1.2 · p. 24, Table 28 · p. 25

B.1.3 MINIMOL REPRODUCTION

• The MiniMol reproduction completed all 22 TDC ADMET tasks, with mean and maximum absolute deviations from released metrics of 0.0122 and 0.0830.The protocol fitted 550 heads above one frozen official checkpoint.Source: §B.1.3 · p. 25

B.1.4 CONTRASTIVE KERMT REPRODUCTION

• Contrastive KERMT reproduction reports endpoint-averaged MAE of 0.3515 on four Biogen endpoints and 0.2836 on all nine ExpansionRx endpoints.These public-checkpoint reproductions use full training and are separate from matched-support routing comparisons.Source: §B.1.4 · p. 25, Table 29 · p. 25

B.1.5 STATISTICAL AND REPRODUCIBILITY DETAILS

• Robust NLL uses a Student-t loss with ν = 3 and residuals scaled by the episode-support median absolute deviation, with fallback scaling when it vanishes.The sample standard deviation is used as fallback, with a 10^-6 floor; aggregate bootstraps resample interfaces and target tasks independently across their crossed structure.Source: §B.1.5 · p. 25

C RETROSPECTIVE DEVELOPMENT BOUNDARY

• All 24 external targets are excluded from router fitting and grouped capacity selection; the paper identifies these model-held-out tests as carrying its conclusions.Earlier sourcewise studies informed the deployment contract, while the reported claim is scoped to transfer under that fixed contract.Source: C RETROSPECTIVE DEVELOPMENT BOUNDARY · p. 26