AssayRouter: Historical Utility Priors for Frozen Molecular Predictor Routing

Dong Xu; Zhangfan Yang; Jiantao Wu; Shipeng Zhang; Zexuan Zhu; Jiangqiang Li; Jun Zhang; Junkai Ji

cs.AISep 29, 2026

AssayRouter: Historical Utility Priors for Frozen Molecular Predictor Routing

Authors: Dong Xu, Zhangfan Yang, Jiantao Wu, Shipeng Zhang, Zexuan Zhu, Jiangqiang Li, Jun Zhang, Junkai Ji

Organizations: School of Artificial Intelligence, Shenzhen University · EasternDawn · School of Computer Science, University of Nottingham Ningbo

Abstract

Laboratories often face a new molecular assay with 16-64 labels and a bank of predictors whose training data and parameters are unavailable. The practical question is which frozen outputs to include in a small local model. AssayRouter treats completed assays as pseudo-targets and labels each candidate by its post-fit utility: the reduction in held-out discovery loss when the candidate is added to the local target predictor. A shared regressor learns to predict this utility from candidate behavior on the support set, without source identity; on a new assay, one frozen ranking selects four sources and separate labels fit a convex combiner. We train only on completed ChEMBL-MT assays and evaluate 24 external regression assays across six frozen interface families. AssayRouter-C lowers strict four-call negative log-likelihood (NLL) by 0.0409 relative to Support-CV@4. Frozen candidate-label permutations confirm that candidate-utility correspondence carries the transferred information, and leave-one-interface-out training shows that the mapping generalizes to unseen predictor families. Completed assays therefore provide transferable supervision for scarce-label routing through frozen prediction interfaces.

Figures & tables

Figure 1: Completed assays supervise frozen predictor routing. (1) A historical pseudo-target measures the reduction in discovery loss from adding one candidate. (2) A shared AssayRouter prior maps candidate behavior to utility without source identity. (3) On a new assay, the frozen prior scores the bank once, selects four sources, and fits simplex weights for the target before confirmation.

	NLL by target labels			Overall
Method	16	32	64	NLL $\downarrow$	MAE $\downarrow$	RMSE $\downarrow$	Pred. $\rho\uparrow$
AR-Marginal	2.2711	2.1052	1.9886	2.1216	23.8597	35.3358	0.3191
Support-CV	2.3287	2.1309	1.9938	2.1511	26.2446	38.0759	0.3033
Support-greedy	2.3806	2.1695	2.0410	2.1970	28.6550	40.3969	0.2949
Source-quality	2.4467	2.2451	2.0806	2.2575	29.3549	41.0480	0.3111
Residual	2.5339	2.2696	2.0806	2.2947	32.3550	44.8218	0.3053

Table 1: Strict four-call deployment. C,

\Delta

, and Z denote centered, uncentered, and standardized standalone utility; Marginal denotes marginal-over-states utility. Every row uses one-shot constituent scoring; bold and underline mark the two best point estimates.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Selector	History	Full-bank query	Query-local
AssayRouter	Utility	No	No
Support-CV	None	No	No
Frozen-DES	None	Yes	Yes
MINE-WS ( Moura et al., 2021 )	Competence	Yes	Yes
All-source	None	Yes	No

Appendix

Table 2: Information available to the principal selectors. Query-local methods may change the selected set across confirmation molecules.

Alternative explanation	Matched test	Changed axis
No value from bank reuse	Target-only	Bank reuse
Generic source strength suffices	Source-quality	Utility supervision
Metadata/support statistics suffice	Size / SNR	Ranking signal
Profile compatibility suffices	Residual (strict)	Ranking signal
Candidate–label pairing is arbitrary	Frozen permutations	Ranking signal
Target-side search suffices	Support-CV@4	Access/timing

Appendix

Table 3: Coverage of alternative explanations relevant to the decision across five contract axes. Each control changes one scientific axis while preserving the frozen prediction contract wherever that axis permits.

Test	NLL effect	Positive breadth
Candidate-label intervention	0.1352	90.7% of cells
Unseen-interface intervention	0.0497	6/6 held-out families
Support-CV@4 vs. C	0.0409	77.8% of target–interface units
Residual compatibility vs. C	0.1844	83.3% of targets

Appendix

Table 4: Evidence-chain index. Effects favor AssayRouter-C; the final column reports the scientific unit appropriate to each test.

Comparison	Effect	Value
Direct intervention	Permuted $-$ genuine NLL	$+0.0463$
Strict intervention	Permuted $-$ genuine NLL	$+0.0816$
Unseen interface	Permuted $-$ genuine NLL	$+0.0299$
Unseen interfaces	Positive held-out families	$5/6$
Strict search	Support-CV $-$ genuine NLL	$+0.0439$

Appendix

Table 5: Support-scale

Q_{\mathrm{disc}}

sensitivity. Values are paired point effects; all five prespecified criteria are met.

Method	NLL $\downarrow$	MAE $\downarrow$	RMSE $\downarrow$	Spearman $\uparrow$
AssayRouter- $\Delta$	2.1142	23.5806	35.3864	0.2961
AssayRouter-C	2.1102	23.3872	35.0709	0.3011
AssayRouter-Z	2.1181	23.6652	35.3589	0.3124
Post-fit loss	2.1684	25.9818	37.2848	0.3002
Post-fit rank	2.1515	24.9610	36.3301	0.3228

Appendix

Table 6: Strict matched post-fit controls. Point estimates are averaged after each four-call constituent is scored.

Estimand	NLL effect	95% interval	Cell win rate
Cross-fit	0.0814	$[0.0427,0.1246]$	0.7222
Strict	0.1352	$[0.0852,0.1915]$	0.9074

Appendix

Table 7: Direct AssayRouter-C candidate-label intervention. NLL effects are permuted minus genuine; win rate is the fraction of 432 target–interface–budget cells favoring the genuine mapping. Intervals use target–interface clustered resampling.

Role	Collection	Targets	Interfaces
Historical supervision	ChEMBL-MT ( Adrian et al., 2025 )	20	6
Temporal holdout	ExpansionRx ( OpenADMET Consortium, 2026 )	9	6
Sparse-panel holdout	Biogen ( Fang et al., 2023 )	6	6
Scaffold holdout	TDC regression ( Huang et al., 2021 )	9	6

Appendix

Table 8: Training and frozen external evaluation. External target identities and confirmation labels are absent from router training and model selection.

Molecular representation	Source predictor	Reuse mode
Morgan FP ( Rogers and Hahn, 2010 )	Ridge	Contract
RDKit2D ( Landrum and RDKit Contributors, n.d. )	LightGBM ( Ke et al., 2017 )	Contract
CheMeleon emb. ( Burns et al., 2025 )	Ridge	Frozen repr.
ChemBERTa2 emb. ( Ahmad et al., 2022 )	LightGBM ( Ke et al., 2017 )	Frozen repr.
Molecular graph	GIN ( Xu et al., 2019 )	Per-source
CheMeleon repr. ( Burns et al., 2025 )	Prediction head	Fine-tuned

Appendix

Table 9: The six formal interfaces to frozen predictors. Abbreviations keep each cell on one line: FP, emb., repr., and GIN denote fingerprint, embedding, representation, and graph-isomorphism network. A bank contains independently trained source-assay predictors from one interface family.

Scope	Mean difference
Overall	$-0.0038$
16 labels	$-0.0067$
32 labels	$-0.0002$
64 labels	$-0.0043$
Biogen	$-0.0035$
ExpansionRx	0.0008

Appendix

Table 10: Matched supervision refinements. Differences are marginal-over-states utility NLL minus standalone-utility NLL; positive values favor the primary utility prior.

Router	Historical target	State features	External NLL
AssayRouter (standalone-utility prior)	$\Delta(s\mid\varnothing)$	No	2.0418
Marginal-over-states utility	$\mathbb{E}_{A}\Delta(s\mid A)$	No	2.0380
State-conditioned extension	$\Delta(s\mid A)$	Yes	2.0392

Appendix

Table 11: Prediction refinement and external decision quality. Historical out-of-fold (OOF) mean-squared error (MSE) is defined only for the shared marginal-over-states label; lower is better.

Scope	Marginal utility MSE	State-conditioned MSE	Relative reduction
Overall	0.02064	0.01949	5.58%
16 labels	0.02584	0.02419	6.41%
32 labels	0.02061	0.01923	6.72%
64 labels	0.01546	0.01504	2.66%

Appendix

Table 12: Nested post-fit utility-prediction audit. Both columns use frozen target-grouped out-of-fold predictions for the same marginal labels.

Frozen mapping	Mean NLL effect	Cell win rate
1	0.0494	73.38%
2	0.0477	70.83%
3	0.0146	60.65%
4	0.0339	72.69%
5	0.0454	71.53%

Appendix

Table 13: Independent candidate-label interventions under the cross-fit prediction-average estimand. Each row uses a distinct frozen bijection; effects are permuted minus genuine NLL.

Alternative	Cross-fit	Strict
Target-only	0.2403	0.2197
Source-quality	0.0969	0.1433
Train-size	0.0912	0.1174
Source-SNR	0.0789	0.1304
Support-CV	0.0030	0.0369

Appendix

Table 14: Matched alternatives. Paired mean NLL differences; positive values favor AssayRouter-

\Delta

Matched refinements
Method	16 labels	32 labels	64 labels
AssayRouter (standalone-utility prior)	2.1606	2.0300	1.9348
Marginal-over-states utility	2.1539	2.0297	1.9305
State-conditioned extension	2.1589	2.0285	1.9301
Search and information-rich controls
Support-CV@4 ensemble	2.1806	2.0315	1.9223

Appendix

Table 15: Stability-focused cross-fit estimand. Absolute support-standardized robust NLL on 24 external targets excluded from router fitting and six prediction interfaces; lower is better. All sparse constituent models have four-source combiner fan-in, but their information permissions differ as described in the text.

Scope	Mean difference	Win rate
Overall	0.0494	73.38%
16 labels	0.0813	84.03%
32 labels	0.0415	72.22%
64 labels	0.0254	63.89%
Biogen	0.0030	50.00%
ExpansionRx	0.0865	85.19%

Appendix

Table 16: Direct standalone-utility permutation. Differences are permuted-router NLL minus genuine AssayRouter NLL; positive values favor genuine post-fit labels.

Metric	Mean effect
Robust NLL	0.0494
MAE	3.5805
RMSE	3.1850
Spearman correlation	0.0327

Appendix

Table 17: Secondary metrics for the direct standalone-utility permutation. NLL, MAE, and RMSE are permuted minus genuine; Spearman is genuine minus permuted.

Scope	Mean difference
Overall	0.0870
16 labels	0.1260
32 labels	0.0816
64 labels	0.0533
Biogen	0.0263
ExpansionRx	0.1081

Appendix

Table 18: Strict four-call standalone-utility intervention. Differences are permuted minus genuine NLL; positive values favor AssayRouter.

Metric	Mean effect
Robust NLL	0.0870
MAE	4.6262
RMSE	4.9810
Spearman correlation	0.0405

Appendix

Table 19: Overall secondary effects for the strict four-call intervention. Losses are permuted minus genuine; Spearman is genuine minus permuted.

Held-out scope	Permuted	Support-CV
Overall	0.0497	0.1116
16 labels	0.0697	0.1769
32 labels	0.0492	0.1029
64 labels	0.0301	0.0550
Biogen	$-0.0023$	0.0367
ExpansionRx	0.0770	0.1594

Appendix

Table 20: AssayRouter-C leave-one-interface-out evaluation. Differences are comparator minus genuine-router NLL after the named family is removed from historical supervision; positive values favor AssayRouter-C.

Router	Scope	Targets	Retention	Mean difference
Direct	Full	9	100.00%	0.0433
Direct	$H$ -clean	9	62.38%	0.0419
Direct	$S$ -clean	8	55.97%	0.0403
Direct	Union-clean	8	42.71%	0.0385
LOIO	Full	9	100.00%	0.0525
LOIO	$H$ -clean	9	62.38%	0.0512

Appendix

Table 21: TDC exact-parent nonoverlap sensitivity. Differences are permuted minus genuine NLL for the AssayRouter-

\Delta

replication; positive values favor historical candidate–utility correspondence. Retention is the mean confirmation fraction.

Scope	Support-CV NLL	Difference
Overall	2.0448	0.0030
16 labels	2.1806	0.0200
32 labels	2.0315	0.0015
64 labels	1.9223	$-0.0125$

Appendix

Table 22: Matched Support-CV@4 cross-fit comparison. NLL is computed after averaging the same 16 directional prediction vectors. Differences are Support-CV minus AssayRouter-

\Delta

Scope	Mean difference
Overall	0.0409
16 labels	0.0736
32 labels	0.0413
64 labels	0.0078
Biogen	0.0005
ExpansionRx	0.0716

Appendix

Table 23: Strict four-call Support-CV@4 comparison. Differences are Support-CV NLL minus AssayRouter-C NLL; positive values favor the frozen historical prior.

Quantity	AssayRouter-C	Support-CV@4
Historical label NNLS fits	28,800	0
Selection NNLS fits per direction	0	246.5
Selection NNLS fits, full evaluation	0	20,445,696
Strict confirmation calls per constituent	4	4
Constituents per cross-fit episode	16	16

Appendix

Table 24: Comparison scopes. Selection fit counts measure subset construction on the target; strict confirmation calls define the accuracy budget. Counts exclude total wall-clock latency.

Comparator	Biogen	ExpansionRx	TDC
50 random four-source sets	$-0.0026$	0.0713	0.0275
Support-greedy selection ( Caruana et al., 2004 )	$-0.0047$	0.0547	0.0356
Frozen-DES@4	$-0.0055$	0.0013	$-0.0044$
MINE-WS@4 ( Moura et al., 2021 )	$-0.0010$	0.0421	0.0229
All-source convex	$-0.0019$	0.0440	$-0.0274$

Appendix

Table 25: Cross-fit greedy and information-rich diagnostics by collection. Comparator NLL minus AssayRouter-

\Delta

NLL, averaged over interfaces and support budgets; positive values favor the post-fit utility prior.

Interface	Random	Greedy ( Caruana et al., 2004 )	DES@4	All-source
Morgan / Ridge	0.0333	0.0292	$-0.0010$	0.0078
RDKit2D / LGBM	0.0445	0.0413	$-0.0005$	0.0140
CheMeleon / Ridge	0.0311	0.0304	$-0.0096$	$-0.0023$
ChemBERTa2 / LGBM	0.0474	0.0459	0.0070	0.0100
GIN	0.0367	0.0351	0.0026	0.0126
CheMeleon / FT	0.0254	0.0141	$-0.0138$	$-0.0078$

Appendix

Table 26: Cross-fit greedy and information-rich diagnostics by interface. Comparator NLL minus AssayRouter-

\Delta

NLL, averaged over external targets and budgets; positive values favor the post-fit utility prior.

Comparator and scope	Mean difference
State-conditioned extension, overall	0.0011
State-conditioned, 16 labels	0.0051
State-conditioned, 32 labels	$-0.0012$
State-conditioned, 64 labels	$-0.0004$
Marginal labels permuted, overall	0.0532
Marginal labels permuted, 16 labels	0.0824

Appendix

Table 27: Matched marginal-over-states mechanism tests. Differences are comparator NLL minus genuine marginal-over-states NLL; positive values favor the genuine labels.

Method	Runs	Macro Pearson $r$
Random Forest ( Breiman, 2001 )	6	0.6683
LightGBM ( Ke et al., 2017 )	6	0.7069
MolSetRep GINE ( Boulougouri et al., 2024 )	18	0.6373
MolSetRep SR-GINE ( Boulougouri et al., 2024 )	18	0.7259

Appendix

Table 28: Official full-training reproduction on all six public Biogen endpoints. Pearson

r

is macro-averaged across endpoints.

Protocol	Biogen (4)	ExpansionRx (9)
Author KERMT task-specific	0.3320	0.3750
Author best Contrastive KERMT	0.3210	0.3590
Official-checkpoint reproduction	0.3515	0.2836

Appendix

Table 29: Full-training KERMT comparison (macro MAE; lower is better). Author values are transcribed from the official manuscript source; reproductions use the released Contrastive KERMT checkpoint, five seeds, and the frozen public splits.

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