PRISM: Prior Relational Information for Self-supervised Modeling to Enhance Solubility OOD Generalization

Xinyi Chen; Jiahuan Pang; Titus Chima; Paul Weng; Wendong Wang

cs.LGOct 19, 2026

PRISM: Prior Relational Information for Self-supervised Modeling to Enhance Solubility OOD Generalization

Authors: Xinyi Chen, Jiahuan Pang, Titus Chima, Paul Weng, Wendong Wang

Organizations: Global College, Shanghai Jiao Tong University, Shanghai, China. · Digital Innovation Research Center, Duke Kunshan University, Kunshan, Jiangsu, China. · Zu Chongzhi Center, Duke Kunshan University, Kunshan, Jiangsu, China. · National Key Laboratory of Advanced Micro and Nano Manufacture Technology, Shanghai Jiao Tong University, Shanghai, China.

Abstract

Solubility depends on intermolecular interactions between solutes and solvents, and is central to drug discovery, chemical and materials process engineering. Its prediction requires out-of-distribution (OOD) generalization to unseen solutes, solvents, and solvent mixtures, where supervised methods suffer from data scarcity, and existing self-supervised methods do not explicitly learn chemically meaningful relations. Learning chemically meaningful relational information without labels can alleviate data scarcity and improve OOD generalization, but remains challenging. We introduce Prior Relational Information for Self-supervised Modeling (PRISM) and apply it to solubility OOD generalization. PRISM is a label-free pretraining framework that converts expert-defined chemical priors into relational teachers. For solubility prediction, it trains four encoders to preserve the population-level relational information from priors capturing hydrophobic, electrostatic, polarizability, and substructural effects, using Kullback-Leibler (KL) divergence to match distance-based neighborhood distributions during pretraining. Across scaffold, solute, and solvent OOD settings, PRISM matches or surpasses supervised and self-supervised baselines. Under mixed-solvent OOD, freezing the four PRISM encoders and training a lightweight fusion-and-composition head outperforms strong baselines and substantially reduces run-to-run variation. Ablations and control studies confirm that gains stem from chemically meaningful relational structures baked into the encoders by PRISM. We expect this strategy of turning relational priors into self-supervision signals to extend beyond solubility prediction to domains where chemically or biologically meaningful relational priors are available.

Figures & tables

Figure 1: PRISM overview. (a) Prior-guided alignment pretrains an encoder per prior space. (b) Weighted fusion produces a fused molecular embedding.

Relational object	Objective	Discrepancy metric	Related instances
Pairwise distance matrix	Pointwise metric matching	Distance regression	Talibart et al. [ 21 ]
Neighbor ordering	Rank preservation	Rank / ListMLE loss	PH-TDL [ 22 ]
Top- $n$ prior-space kNN graph	Neighborhood-graph alignment	InfoNCE over graph positives	Moleco [ 23 ]
Pair-wise distance-based distribution	Distribution matching	KL divergence	SNE-style [ 24 ] / GraphMSL [ 25 ]

Table 1: Relational objects and alignment objectives in PRISM with related instances.

Figure 2: Task-specific prediction heads. (a) Single-molecule prediction. (b) Pure-solvent prediction combines solute, solvent, and temperature embeddings. (c) Mixed-solvent prediction freezes encoders, trains fusion, and compositionally pools solvent embeddings.

Objective	Alignment metric $\downarrow$			ESOL RMSE $\downarrow$
Objective	C1	C2	C3	C1	C2	C3
$\ell_{2}$ distance	0.968	0.933	0.851	0.956	0.865	0.987
Rank	0.180	0.109	0.025	1.023	1.027	1.022
Neighborhood-graph alignment	2.53	2.02	1.34	2.011	1.241	1.083
Distribution matching	0.813	0.736	0.723	0.844	0.776	0.772

Table 2: Alignment objective selection on ESOL. C1–C3 denote fixed early, intermediate, and late checkpoints from one uninterrupted pretraining run for each objective.

Model	ESOL $\downarrow$	FreeSolv $\downarrow$	Lipo $\downarrow$
XGBoost	$0.925\pm 0.00$	$3.398\pm 0.00$	$0.741\pm 0.00$
D-MPNN [ 20 ]	$1.050\pm 0.01$	$\mathbf{1.673\pm 0.08}$	$0.683\pm 0.02$
MolCLR [ 10 ]	$1.113\pm 0.02$	$2.301\pm 0.25$	$0.789\pm 0.01$
MoAMa [ 29 ]	$1.394\pm 0.12$	$2.700\pm 0.11$	$0.772\pm 0.03$
PRISM	$\mathbf{0.772\pm 0.002}$	$1.770\pm 0.09$	$\mathbf{0.538\pm 0.02}$

Table 3: MoleculeNet structural OOD on solubility-related tasks under scaffold splits. RMSE (

\downarrow

). Results averaged over three seeds with independent splits.

Model	RMSE $\downarrow$		$\%\|\Delta\log S\|\leq 1$ $\uparrow$
	Leeds	SolProp	Leeds	SolProp
Vermeire [ 27 ]	2.16	1.43	41.2	66.9
MolFormer [ 27 ]	1.07	0.98	64.1	70.7
ChemBERTa [ 27 ]	1.26	1.01	57.0	72.4
Chemprop [ 27 ]	0.99	0.83	70.9	76.1
Fastprop [ 27 ]	0.95	0.83	73.6	78.1

Table 4: Pure-solvent external transfer from BigSolDB to Leeds and SolProp. Published baseline values are from prior reported protocols; XGBoost and PRISM are mean

\pm

std over three seeds.

Direct-prior control
	Random split			Solvent-pair-disjoint OOD
Model	RMSE $\downarrow$	$R^{2}$ $\uparrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$	RMSE $\downarrow$	$R^{2}$ $\uparrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$
XGBoost	$0.055\pm 0.011$	$\mathbf{0.998\pm 0.001}$	$\mathbf{100\pm 0.0}$	$0.459\pm 0.022$	$0.796\pm 0.086$	$96.0\pm 0.8$
End-to-end D-MPNN aggregation controls
D-MPNN + Concat	$0.103\pm 0.003$	$0.995\pm 0.000$	$99.9\pm 0.0$	$0.587\pm 0.093$	$0.703\pm 0.072$	$91.6\pm 3.8$
D-MPNN + Weighted Sum	$0.101\pm 0.005$	$0.995\pm 0.001$	$\mathbf{100\pm 0.0}$	$0.498\pm 0.161$	$0.766\pm 0.134$	$93.8\pm 4.5$

Table 5: Mixed-solvent solubility prediction under random and solvent-pair-disjoint splits. All results are mean

\pm

std over five independently resampled splits under the corresponding protocol.

	Leeds		SolProp		Mixed OOD
Model	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$
D-MPNN w. prior	$0.990\!\pm\!0.013$	$72.3\!\pm\!1.2$	$0.820\!\pm\!0.035$	$80.2\!\pm\!0.9$	$0.466\!\pm\!0.078$	$95.3\!\pm\!1.7$
D-MPNN (reconstruction)	$1.076\!\pm\!0.033$	$62.1\!\pm\!2.1$	$0.956\!\pm\!0.082$	$69.0\!\pm\!4.7$	$0.618\!\pm\!0.133$	$87.3\!\pm\!2.1$
D-MPNN (all spaces)	$0.930\!\pm\!0.004$	$73.9\!\pm\!1.6$	$0.860\!\pm\!0.017$	$77.2\!\pm\!0.8$	$0.580\!\pm\!0.107$	$92.5\!\pm\!2.1$
4 $\times$ D-MPNN (scratch)	$1.001\!\pm\!0.020$	$71.6\!\pm\!0.7$	$0.901\!\pm\!0.038$	$74.7\!\pm\!3.4$	$0.472\!\pm\!0.123$	$92.1\!\pm\!3.6$
PRISM-Distilled	$0.950\!\pm\!0.014$	$73.9\!\pm\!0.6$	$0.970\!\pm\!0.024$	$77.2\!\pm\!1.1$	$0.457\!\pm\!0.110$	$95.6\!\pm\!3.8$

Table 6: Effect of PRISM pretraining on solubility transfer. Controls use comparable downstream heads. Mixed OOD denotes the solvent-pair-disjoint split.

Dataset	$\rho_{\mathrm{VSA}}$	$\rho_{\mathrm{FP}}$	Gaussian prior trained PRISM	4 $\times$ D-MPNN scratch	D-MPNN	PRISM
ESOL	0.107	0.150	$1.24\pm 0.025$	$0.848\pm 0.025$	$1.050\pm 0.008$	$\mathbf{0.772\pm 0.002}$
FreeSolv	0.072	0.090	$2.79\pm 0.058$	$2.222\pm 0.054$	$\mathbf{1.673\pm 0.082}$	$1.770\pm 0.093$
Lipo	0.305	0.315	$1.07\pm 0.014$	$0.642\pm 0.014$	$0.683\pm 0.016$	$\mathbf{0.538\pm 0.018}$

Table 7: Prior–task alignment and Gaussian-prior control on solubility-related tasks. Lower

\rho_{s}

indicates smoother prior-induced label neighborhoods. All downstream columns report RMSE (

\downarrow

Figure 3: Interpretability diagnostics in pure-solvent solubility. (a) Prior-space profiles and temperature-dependent predictions for two representative solutes in a fixed solvent. PRISM preserves the correct solute ranking, whereas Fastprop reverses it. (b) Molecule-wise space attribution on ESOL in water, shown as fusion-weight deviation from a uniform baseline.

Appendix figures & tables41 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$x$	Molecular graph input
$y$	Downstream label
$\hat{y}$	Model prediction
$\mathcal{D}_{\mathrm{pre}}=\{x_{i}\}_{i=1}^{N}$	Unlabeled molecular graph dataset for pretraining
$\mathcal{B}$	Mini-batch of molecules
$\mathcal{S}=\{s_{1},\ldots,s_{K}\}$	Set of expert-defined prior spaces

Appendix

Table 8: Summary of notation. Symbols match the main text.

Dataset	Task	#Samples	Split	Metric
ZINC250k	pretraining	$\sim$ 250k	—	—
BBBP	classification	2,039	scaffold 8:1:1	ROC-AUC $\uparrow$
BACE	classification	1,513	scaffold 8:1:1	ROC-AUC $\uparrow$
HIV	classification	41,127	scaffold 8:1:1	ROC-AUC $\uparrow$
ESOL	regression	1,128	scaffold 8:1:1	RMSE $\downarrow$
FreeSolv	regression	642	scaffold 8:1:1	RMSE $\downarrow$

Appendix

Table 9: Summary of datasets used in this work.

Metric	Value
Total samples	26,730
Unique solutes	125
Unique solvents	44
Unique binary solvent pairs	110
Unique solute–binary-solvent systems	377
Temperature range (K)	252.55–368.15

Appendix

Table 10: Statistics of the processed mixed-solvent solubility dataset.

Figure 4: FreeSolv scaffold split visualization.

Figure 5: Diagnostics for the solvent-pair-disjoint mixed-solvent split.

Setting	Comparison type	Baseline group	Selection rationale	Protocol	Source
Single-molecule prediction	Supervised control	Supervised GNNs	Tests whether relational pretraining improves over direct supervised learning from molecular graphs.	One molecular graph as input; the full model is trained on the task-specific split.	Reported
Single-molecule prediction	Generic molecular SSL	2D and geometry-aware pretrained models	Compares scientific relational supervision with established molecular pretraining paradigms.	Respective pretrained encoders with task-specific downstream training.	Reported
Single-molecule prediction	Direct-prior control	Traditional ML with fingerprints and VSA priors	Tests whether gains can be explained by directly supplying the informative prior features.	Concatenated raw prior features; no relational pretraining.	Reproduced
External pure-solvent transfer	Protocol-matched supervised	Fastprop, Chemprop, Vermeire	Compares PRISM with established supervised solute–solvent predictors under external transfer.	Trained on cleaned BigSolDB and tested directly on Leeds and SolProp.	Reported
External pure-solvent transfer	Large-scale pretrained	MolFormer, ChemBERTa	Tests whether generic large-scale pretraining alone explains transfer performance.	Pretrained molecular encoders are fine-tuned on BigSolDB and evaluated unchanged on Leeds and SolProp.	Reported
External pure-solvent transfer	Direct-prior control	XGBoost	Tests whether relational pretraining adds transfer value beyond direct access to the same priors.	Raw prior features for solute and solvent together with temperature; trained on BigSolDB and tested on Leeds and SolProp.	Reproduced

Appendix

Table 11: Baseline selection and comparison protocols. “Reported” denotes values taken from prior studies under compatible published protocols, while “Reproduced” denotes baselines evaluated in our experiments.

Level	Feature group	RDKit field	Dim.
Atom	Atomic number	GetAtomicNum() shifted by $-1$	$101$
Atom	Total degree	GetTotalDegree()	$7$
Atom	Formal charge	GetFormalCharge()	$6$
Atom	Chiral tag	GetChiralTag()	$5$
Atom	Total #H	GetTotalNumHs()	$6$
Atom	Hybridization	GetHybridization()	$6$

Appendix

Table 12: Atom and bond features used in our D-MPNN featurization. All features are 2D RDKit-derived.

Parameter	Value
Pretraining corpus	ZINC250k
Prior branches	SMR_VSA, SlogP_VSA, PEOE_VSA, Morgan FP
Backbone	D-MPNN
Encoder hidden dimension	512
Projection head	2-layer MLP, 512–64, ReLU
Batch size	512

Appendix

Table 13: Reference hyperparameters for PRISM pretraining.

	ESOL	FreeSolv	Lipo	BBBP	BACE	HIV
Pretrain $\tau$	0.1	0.3	0.1	0.1	0.2	0.1
Pretrain $\gamma_{s}$	0.75	0.75	0.25	0.25	0.75	0.25
Fusion mode	Adaptive	Adaptive	Adaptive	Static	Static	Static
Dropout	0.3	0.3	0.3	0.1	0.1	0.1
Batch size	64	64	64	64	16	16
Weight decay	$10^{-5}$	0	0	0	$10^{-5}$	$10^{-5}$

Appendix

Table 14: Reference hyperparameters for single-molecule fine-tuning.

Parameter	Value
Pretrain $\tau$	0.1
Pretrain $\gamma_{s}$	0.25
Fusion mode	Static
Embedding dimension $D$	512
Temperature embedding $d_{T}$	32
Batch size	64

Appendix

Table 15: Reference hyperparameters for pure-solvent solubility fine-tuning.

Parameter	Value
Embedding dimension $D$	512
Temperature embedding $d_{T}$	32
Fusion mode	Static weighted fusion
encoders	Original PRISM-pretrained branches, frozen
Fusion module	Initialized from pure-solvent checkpoint and trainable
Mixed head	Linear composition-weighted MLP

Appendix

Table 16: Reference hyperparameters for mixed-solvent solubility fine-tuning.

$\tau$	$\gamma_{s}$	BBBP	BACE
0.1	0.25	0.9459	0.8389
0.1	0.50	0.8997	0.8548
0.1	0.75	0.9006	0.8227
0.2	0.25	0.9017	0.8510
0.2	0.50	0.9071	0.8480
0.2	0.75	0.9085	0.8946

Appendix

Table 17: Hyperparameter sensitivity on classification tasks. Test ROC-AUC (

\uparrow

) under different pre-training settings of embedding temperature

\tau

and locality scale

\gamma_{s}

. HIV is omitted due to its much larger scale.

$\tau$	$\gamma_{s}$	ESOL	FreeSolv	Lipo
0.1	0.25	0.874	1.835	0.538
0.1	0.50	0.878	1.831	0.673
0.1	0.75	0.772	1.812	0.678
0.2	0.25	0.863	1.820	0.681
0.2	0.50	0.925	2.067	0.656
0.2	0.75	0.848	1.828	0.679

Appendix

Table 18: Hyperparameter sensitivity on regression tasks. Test RMSE (

\downarrow

) under different pre-training settings of

\tau

and

\gamma_{s}

$\tau$	$\gamma_{s}$	best val RMSE $\downarrow$	Leeds RMSE $\downarrow$	Leeds $\%logS\pm 1$ $\uparrow$	SolProp RMSE $\downarrow$	SolProp $\%logS\pm 1$ $\uparrow$
0.1	0.50	0.1414	0.9340	73.65	0.7940	80.71
0.1	0.25	0.1398	0.9099	75.66	0.7719	82.29
0.2	0.25	0.1393	0.9352	74.81	0.7853	81.72
0.2	0.75	0.1429	0.9179	74.65	0.7739	82.87
0.3	0.25	0.1438	0.9331	74.03	0.7563	82.73

Appendix

Table 19: Hyperparameter sensitivity on pure-solvent pairwise solubility. We report best validation RMSE, and test RMSE /

\%logS\pm 1

(

\uparrow

) on Leeds and SolProp.

\%logS\pm 1

is shown in %. Only configurations available in our logs are listed.

Stage	Hardware	Time per run	Notes
PRISM pretraining per branch	RTX 3090	7–8 hours	Batch size 512; $\sim$ 75% peak GPU memory
Pure-solvent fine-tuning	RTX 3090	$\sim$ 6 hours	End-to-end
MoleculeNet fine-tuning	RTX 4070	$\leq$ 1 hour	Per task, per seed
Mixed-solvent training	RTX 4070 mobile	3 hours	Frozen encoders; trainable fusion and head

Appendix

Table 20: Computational cost and hardware. Reported times are wall-clock per run.

Objective	Lipo	FreeSolv	ESOL
Symmetric SNE	$0.592\pm 0.009$	$2.146\pm 0.079$	$0.803\pm 0.032$
PRISM conditional KL	$0.538\pm 0.018$	$1.770\pm 0.093$	$0.772\pm 0.002$

Appendix

Table 21: Comparison of conditional and symmetric SNE-style alignment under matched settings. Results are mean

\pm

std over three seeds. RMSE (

\downarrow

Objective	Lipo RMSE $\downarrow$	FreeSolv RMSE $\downarrow$	ESOL RMSE $\downarrow$
TDL-style alignment	$0.622\pm 0.011$	$2.221\pm 0.028$	$0.819\pm 0.003$
PRISM (conditional KL)	$\mathbf{0.538\pm 0.018}$	$\mathbf{1.770\pm 0.093}$	$\mathbf{0.772\pm 0.002}$

Appendix

Table 22: Controlled comparison of TDL-style and conditional KL alignment. Only the alignment objective is changed. Results are mean

\pm

standard deviation over three seeds. Lower RMSE is better.

Traditional ML (fingerprints + VSA)
	Classification (ROC-AUC %, $\uparrow$ )			Regression (RMSE, $\downarrow$ )
Dataset	BBBP	BACE	HIV	ESOL	FreeSolv	Lipo
# Molecules	2,039	1,513	41,127	1,128	642	4,200
MLP	85.1 $\pm$ 1.6	85.2 $\pm$ 0.8	70.0 $\pm$ 1.7	1.461 $\pm$ 0.060	4.942 $\pm$ 0.084	0.878 $\pm$ 0.016
XGBoost	84.7 $\pm$ 0.0	88.5 $\pm$ 0.0	74.7 $\pm$ 0.8	0.925 $\pm$ 0.000	3.398 $\pm$ 0.000	0.741 $\pm$ 0.000
Supervised GNNs (without pretraining)

Appendix

Table 23: Extended MoleculeNet comparison on classification tasks (ROC-AUC %,

\uparrow

) and regression tasks (RMSE,

\downarrow

). Bold indicates the best result among reported values in each column. PRISM uses only 2D molecular graphs; geometry-aware baselines are reported for completeness and grouped separately. Dashes indicate that a matched value under our protocol is not reported.

Dataset	Slice	$n$	Fastprop		PRISM		$\Delta$ (PRISM–Fastprop)
			RMSE $\downarrow$	pct-in-1 (%) $\uparrow$	RMSE $\downarrow$	pct-in-1 (%) $\uparrow$	RMSE	pct-in-1 (pp)
Leeds
All solutes are unseen; all solvents are seen; all temperatures are in-range.
Leeds	Overall	1,294	0.954	73.57	0.909	75.43	$-0.045$	$+1.85$
SolProp
SolProp	Overall	5,230	0.833	78.07	0.773	82.28	$-0.060$	$+4.21$

Appendix

Table 24: OOD slice analysis on unseen-solute tests. Slices are defined relative to the complete processed BigSolDB dataset using canonical isomeric SMILES. Temperature slices use the solvent-specific temperature range and apply only to seen solvents. For Leeds, the seen-solvent and temperature-in-range slices coincide with the overall set. Metrics are RMSE (

\downarrow

) and pct-in-1 (

\uparrow

), the percentage of predictions within one

\log S

unit of the measured value. Differences are PRISM minus Fastprop; differences in pct-in-1 are reported in percentage points (pp).

Figure 6: Pure-solvent external-test behavior and temperature-gradient analysis. Panels (a,b) show PRISM predictions on Leeds and SolProp, together with error distributions for seen/unseen solvent slices. Panels (c,d) show the corresponding Fastprop predictions. Panels (e,f) compare the empirical and model-induced finite-difference temperature-gradient distributions. PRISM achieves lower normalized EMD to the empirical $d\log S/dT$ distribution than Fastprop (0.01 vs. 0.02), despite not using an explicit temperature-gradient loss.

Model	Overall log-RMSE $\downarrow$	Overall $R^{2}$ $\uparrow$	Ternary log-RMSE $\downarrow$
UNIFAC–PLS	0.3061	0.9042	0.0921
PRISM–Ridge	0.2738	0.9217	0.1954
UNIFAC + PRISM	0.2502	0.9409	0.0904

Appendix

Table 25: Independent pure-, binary-, and ternary-solvent evaluation on the Cenci et al. dataset. The original calibration–validation split is retained. Lower log-RMSE and higher

R^{2}

indicate better performance.

Protocol	Leeds RMSE $\downarrow$	SolProp RMSE $\downarrow$	Leeds pct-in-1 (%) $\uparrow$	SolProp pct-in-1 (%) $\uparrow$
ZINC-only pretraining (100 epochs)	$0.910\pm 0.002$	$0.770\pm 0.030$	$75.7\pm 0.9$	$82.3\pm 0.8$
Target-only adaptation	$0.920\pm 0.002$	$0.740\pm 0.041$	$74.1\pm 0.7$	$82.5\pm 0.6$
Target anchors, joint neighbors (100 epochs)	$0.910\pm 0.002$	$0.775\pm 0.040$	$75.6\pm 0.6$	$82.4\pm 0.5$
Target anchors, joint neighbors (300 epochs)	$0.941\pm 0.002$	$0.796\pm 0.022$	$73.1\pm 0.6$	$79.1\pm 0.4$
Joint anchors and neighbors (100 epochs)	$0.908\pm 0.002$	$0.766\pm 0.030$	$75.7\pm 0.9$	$82.5\pm 0.6$

Appendix

Table 26: Unlabeled target-domain adaptation for pure-solvent external transfer. “Target” denotes

\mathcal{T}

and “joint” denotes

\mathcal{U}=\mathcal{Z}\cup\mathcal{T}

. Epoch counts, where shown, refer to the relational-pretraining stage. Results are mean

\pm

standard deviation over three seeds. The metric pct-in-1 is the percentage of predictions within one log-solubility unit of the experimental value.

	Classification (ROC-AUC %, $\uparrow$ )			Regression (RMSE, $\downarrow$ )
Init	BBBP	BACE	HIV	ESOL	FreeSolv	Lipo
PRISM random	$93.0\pm 0.6$	$87.8\pm 1.7$	$75.1\pm 0.5$	$0.848\pm 0.025$	$2.222\pm 0.054$	$0.642\pm 0.014$
PRISM	$\mathbf{94.6\pm 0.3}$	$\mathbf{89.4\pm 0.4}$	$\mathbf{77.7\pm 0.6}$	$\mathbf{0.772\pm 0.002}$	$\mathbf{1.770\pm 0.093}$	$\mathbf{0.538\pm 0.018}$
$\Delta$ (PRISM $-$ random)	$+1.6$	$+1.6$	$+2.6$	$-0.076$	$-0.452$	$-0.104$

Appendix

Table 27: Effect of PRISM pretraining on MoleculeNet. Same four-branch PRISM architecture with identical heads trained from random initialization (PRISM random ) versus PRISM-pretrained initialization (PRISM).

Dataset	Distilled encoder		Normal encoder
	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$
Leeds	$0.95\pm 0.0136$	$73.93\pm 0.62$	$0.91\pm 0.002$	$75.7\pm 0.9$
SolProp	$0.97\pm 0.0235$	$77.24\pm 1.11$	$0.77\pm 0.030$	$82.3\pm 0.8$

Appendix

Table 28: Pure-solvent external transfer with distilled vs. normal encoder. RMSE is lower better,

\%|\Delta\log S|\leq 1

is higher better.

Encoder setting	Split	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$
Frozen distilled encoder	Random	$0.123\pm 0.013$	$99.95\pm 0.02$
Frozen normal encoder	Random	$0.095\pm 0.008$	$100.0\pm 0.0$
Fine-tuned distilled encoder	Random	$0.1321\pm 0.015$	$99.96\pm 0.03$
Frozen distilled encoder	Pair-disjoint	$0.457\pm 0.110$	$95.59\pm 3.75$
Frozen normal encoder	Pair-disjoint	$0.440\pm 0.010$	$96.6\pm 0.9$
Fine-tuned distilled encoder	Pair-disjoint	$0.462\pm 0.026$	$96.41\pm 3.52$

Appendix

Table 29: Mixed-solvent prediction with distilled vs. normal encoder, under random and pair-disjoint splits. RMSE is lower better,

\%|\Delta\log S|\leq 1

is higher better.

Dataset	Metric	Distilled encoder	Normal encoder
ESOL	RMSE $\downarrow$	$0.9072\pm 0.012$	$0.772\pm 0.002$
FreeSolv	RMSE $\downarrow$	$3.987\pm 0.106$	$1.770\pm 0.09$
Lipo	RMSE $\downarrow$	$0.888\pm 0.035$	$0.538\pm 0.02$
BACE	ROC-AUC $\uparrow$	$75.08\pm 5.2$	$89.4\pm 0.4$
BBBP	ROC-AUC $\uparrow$	$85.80\pm 3.2$	$94.6\pm 0.3$

Appendix

Table 30: Single-molecule downstream results with distilled vs. normal encoder, both fine-tuned. RMSE is lower better for regression, ROC-AUC is higher better for classification.

Model	BBBP $\uparrow$	BACE $\uparrow$	ESOL $\downarrow$	FreeSolv $\downarrow$	Lipo $\downarrow$
Single shared encoder	$0.851\pm 0.032$	$0.860\pm 0.020$	$0.9209\pm 0.027$	$2.040\pm 0.197$	$0.740\pm 0.011$
PRISM	$\mathbf{0.946\pm 0.003}$	$\mathbf{0.894\pm 0.004}$	$\mathbf{0.772\pm 0.002}$	$\mathbf{1.770\pm 0.093}$	$\mathbf{0.538\pm 0.018}$

Appendix

Table 31: Single shared encoder versus multi-branch PRISM on MoleculeNet. The shared-encoder baseline uses one D-MPNN trained with the sum of all prior-alignment losses. Classification metrics are ROC-AUC, and regression metrics are RMSE.

Spaces used	BBBP	BACE	HIV
all	$0.9456\pm 0.0031$	$0.8936\pm 0.0047$	$0.7768\pm 0.0092$
w/o FP	$0.9316\pm 0.0031$	$0.8846\pm 0.0019$	$0.7140\pm 0.0107$
w/o PEOE	$0.9380\pm 0.0052$	$0.8821\pm 0.0013$	$0.7249\pm 0.0079$
w/o SlogP	$0.9256\pm 0.0023$	$0.8839\pm 0.0019$	$0.7191\pm 0.0045$
w/o SMR	$0.9283\pm 0.0085$	$0.8768\pm 0.0096$	$0.7274\pm 0.0091$

Appendix

Table 32: Leave-one-prior-space-out ablations on MoleculeNet classification. AUC is reported in the standard

[0,1]

scale.

Spaces used	ESOL	FreeSolv	Lipo
all	$0.7722\pm 0.0275$	$1.7702\pm 0.0444$	$0.5380\pm 0.0156$
w/o FP	$0.8129\pm 0.0175$	$2.5011\pm 0.2005$	$0.5739\pm 0.0099$
w/o PEOE	$0.7826\pm 0.0274$	$2.2335\pm 0.1533$	$0.5563\pm 0.0082$
w/o SlogP	$0.8080\pm 0.0046$	$2.4074\pm 0.1035$	$0.5525\pm 0.0007$
w/o SMR	$0.7780\pm 0.0085$	$2.4312\pm 0.1630$	$0.5733\pm 0.0106$
SMR only	$0.8247\pm 0.0295$	$2.4812\pm 0.1673$	$0.5736\pm 0.0041$

Appendix

Table 33: Leave-one-prior-space-out and single-prior ablations on MoleculeNet regression. Metrics are RMSE (

\downarrow

	RMSE ( $\downarrow$ )			$\%\|\Delta\log S\|\leq 1$ (%, $\uparrow$ )
Spaces used	Leeds	SolProp	Mixed OOD	Leeds	SolProp	Mixed OOD
all	$0.910\pm 0.002$	$0.770\pm 0.030$	$0.440\pm 0.008$	$75.7\pm 0.8$	$82.3\pm 0.8$	$96.6\pm 0.9$
w/o SMR	$0.9660\pm 0.002$	$0.8040\pm 0.008$	$0.501\pm 0.009$	$73.2\pm 0.3$	$80.8\pm 0.5$	$89.4\pm 1.5$
w/o SlogP	$0.9586\pm 0.002$	$0.8120\pm 0.031$	$0.472\pm 0.010$	$73.2\pm 0.6$	$78.2\pm 2.1$	$90.6\pm 1.0$
w/o PEOE	$0.9580\pm 0.002$	$0.8065\pm 0.027$	$0.488\pm 0.007$	$73.2\pm 0.8$	$80.0\pm 0.1$	$91.7\pm 0.7$
w/o FP	$0.9720\pm 0.004$	$0.8203\pm 0.102$	$0.637\pm 0.024$	$72.5\pm 1.3$	$79.3\pm 0.9$	$87.1\pm 2.7$

Appendix

Table 34: Leave-one-prior-space-out ablations on solubility tasks. Metrics are RMSE (

\downarrow

) and

\%|\Delta\log S|\leq 1

(%,

\uparrow

). Pure-solvent results are evaluated on Leeds and SolProp. Mixed-solvent results are evaluated under the solvent-pair-disjoint OOD split using the same frozen-encoder linear-mixing protocol as the main text.

Setting	Task-specific weights	Instance-wise weights
BBBP (AUC)	$94.6\pm 0.3$	$72.28\pm 1.5$
BACE (AUC)	$87.9\pm 0.4$	$80.91\pm 0.4$
HIV (AUC)	$77.7\pm 0.6$	$73.2\pm 0.8$
ESOL (RMSE)	$0.929\pm 0.003$	$0.782\pm 0.002$
FreeSolv (RMSE)	$2.069\pm 0.007$	$1.770\pm 0.093$
Lipo (RMSE)	$0.664\pm 0.034$	$0.538\pm 0.018$

Appendix

Table 35: Task-specific versus instance-wise weighted fusion. Classification reports ROC-AUC (%,

\uparrow

); single-molecule regression reports RMSE (

\downarrow

); pure-solvent solubility reports

\%|\Delta\log S|\leq 1

(%,

\uparrow

) and RMSE (

\downarrow

). The pure-solvent RMSE values follow the same external-transfer protocol as the main pure-solvent table.

Head design	RMSE $\downarrow$	$\%\|\Delta\log S\|\leq 1$ $\uparrow$
Direct concat head	$0.550\pm 0.031$	$91.3\pm 2.8$
Attention interaction head	$0.445\pm 0.020$	$94.3\pm 0.8$
Linear weighted-sum head	$\mathbf{0.440\pm 0.008}$	$\mathbf{96.6\pm 0.9}$

Appendix

Table 36: Mixed-solvent head ablation under the solvent-pair-disjoint OOD split. All variants use the same frozen PRISM encoders and train the fusion module together with the mixed-solvent prediction head. The simple composition-weighted head performs best and has the lowest variance.

Solvent aggregation	Prior aggregation	Warm start	RMSE $\downarrow$	pct-in-1 (%) $\uparrow$
Weighted sum	Fusion head	Yes	$\mathbf{0.438\pm 0.030}$	$\mathbf{96.6\pm 0.9}$
Weighted sum	Fusion head	No	$0.442\pm 0.080$	$96.1\pm 1.4$
Weighted sum	Branch concatenation	No	$0.525\pm 0.255$	$93.7\pm 6.4$
Concatenation	Fusion head	Yes	$0.550\pm 0.051$	$91.3\pm 3.1$
Concatenation	Fusion head	No	$0.557\pm 0.183$	$91.2\pm 7.1$
Concatenation	Branch concatenation	No	$0.570\pm 0.311$	$91.7\pm 8.3$

Appendix

Table 37: Ablation of solvent aggregation, prior-branch fusion, and warm-start initialization under solvent-pair-disjoint OOD. All configurations use frozen PRISM-pretrained encoders. Warm start refers to initialization of the fusion module from the pure-solvent task. Results are mean

\pm

standard deviation across five splits. The first row is the default PRISM configuration. The metric pct-in-1 is the percentage of predictions with absolute error at most one log-solubility unit.

Dataset	Energy (Gaussian)	PRISM + Gaussian prior	D-MPNN w/o pretraining
BBBP	0.356	$83.07\pm 3.04$	$91.9\pm 3.0$
BACE	0.498	$71.17\pm 9.70$	$85.2\pm 0.6$
HIV	0.067	$72.29\pm 1.98$	$77.1\pm 0.5$
CYP2D6	0.025	$66.34\pm 0.75$	$72.7\pm 0.37$
KOR	0.406	$74.42\pm 0.22$	$82.0\pm 0.18$

Appendix

Table 38: Gaussian random prior control on classification and bioactivity tasks. Classification performance is reported as ROC-AUC (%,

\uparrow

). The random prior degrades performance relative to supervised D-MPNN but does not cause abrupt collapse.

Dataset	$\rho_{\mathrm{Pharm2D}}$	$\rho_{\mathrm{FP}}$	$\rho_{\mathrm{VSA}}$	Selected priors	PRISM with selected priors	PRISM with all priors	D-MPNN w/o pretraining
BBBP	0.166	0.096	0.109	Pharm2D + FP + VSA	$95.8\pm 0.6$	$95.8\pm 0.6$	$91.9\pm 3.0$
BACE	0.264	0.109	0.118	Pharm2D + FP + VSA	$89.3\pm 0.9$	$89.3\pm 0.9$	$85.2\pm 0.6$
HIV	0.73	2.87	2.63	Pharm2D	$78.66\pm 2.00$	$76.35\pm 1.90$	$77.1\pm 0.50$
CYP2D6	0.96	1.05	1.06	Pharm2D	$73.31\pm 1.02$	$42.08\pm 9.35$	$72.7\pm 0.37$
KOR	0.48	0.47	0.56	Pharm2D + FP + VSA	$88.91\pm 0.29$	$88.91\pm 0.29$	$82.0\pm 0.18$

Appendix

Table 39: Dynamic prior selection using label-energy ratio. A ratio below one indicates that the candidate prior is more label-smooth than a Gaussian random prior. Classification performance is reported as ROC-AUC (%,

\uparrow

Model	BBBP $\uparrow$	BACE $\uparrow$	ESOL $\downarrow$	FreeSolv $\downarrow$	Lipo $\downarrow$
Random SchNet	$0.830\pm 0.033$	$0.807\pm 0.022$	$0.716\pm 0.045$	$1.318\pm 0.361$	$0.775\pm 0.032$
PRISM + SchNet (FP prior)	$0.835\pm 0.048$	$\mathbf{0.830\pm 0.043}$	$\mathbf{0.643\pm 0.032}$	$\mathbf{1.062\pm 0.150}$	$\mathbf{0.686\pm 0.038}$
PRISM + SchNet (3D descriptor prior)	$\mathbf{0.844\pm 0.022}$	$0.807\pm 0.070$	$0.704\pm 0.079$	$1.756\pm 0.262$	$0.801\pm 0.010$

Appendix

Table 40: PRISM with a 3D SchNet backbone. Classification metrics are ROC-AUC, and regression metrics are RMSE. The 3D prior uses RDKit shape descriptors covering global shape, anisotropy, compactness, spatial extent, and principal-axis mass distribution.

Pretrain size	ESOL	FreeSolv	Lipo
25k	$1.011\pm 0.031$	$2.029\pm 0.113$	$0.698\pm 0.011$
50k	$0.933\pm 0.009$	$2.138\pm 0.025$	$0.664\pm 0.003$
250k	$\mathbf{0.772\pm 0.002}$	$\mathbf{1.770\pm 0.093}$	$\mathbf{0.538\pm 0.018}$

Appendix

Table 41: Effect of pretraining data size on regression tasks. Metrics are RMSE (

\downarrow

, mean

\pm

std).

Fusion setting	Faithfulness test	Result
Task-specific weights	Weight–LOSO importance rank agreement	Spearman $\rho=0.80$
Instance-wise, ESOL	Top-vs-bottom suppression probability	0.64
Instance-wise, FreeSolv	Top-vs-bottom suppression probability	0.76
Instance-wise, Lipo	Top-vs-bottom suppression probability	0.64

Appendix

Table 42: Faithfulness tests for PRISM fusion weights. Task-specific weights are evaluated by rank agreement with leave-one-space-out importance. Instance-wise weights are evaluated by top-weight versus bottom-weight suppression.

Figure 7: Training diagnostics for PRISM prior-space alignment. (a) Two-dimensional t-SNE visualizations comparing the prior-feature geometry and the PRISM embedding geometry for SMR_VSA, SlogP_VSA, and PEOE_VSA. Representative anchors are highlighted to illustrate local-neighborhood preservation. (b) Anchor-wise neighborhood distribution matching. For each anchor, we compare the distance-to-anchor distribution induced by the prior space and by the learned embedding. The small KL divergences indicate that PRISM pretraining preserves prior-induced stochastic neighborhoods. The KL values in panel (b) are absolute anchor-wise KL divergences, whereas Table 2 reports normalized KL ratios for checkpoint-level comparison.

Prior space	Probe error $\downarrow$
SMR_VSA (MSE)	0.476
SlogP_VSA (MSE)	0.767
PEOE_VSA (MSE)	1.450
FP ( $1-\mathrm{Tanimoto}$ )	0.377

Appendix

Table 43: Prior-recoverability probe on ZINC250k (8:1:1 scaffold split). We freeze the pre-trained encoder and train a two-layer MLP decoder to reconstruct prior features from embeddings. For VSA priors, we report MSE; for fingerprints, we report

1-\mathrm{Tanimoto}

(lower is better). Metrics are computed on the test split.

Asset	Role	License / access terms
RDKit	Molecular parsing, descriptors, fingerprints, and featurization	BSD-style open-source license
PyTorch	Neural-network implementation and training	BSD-style open-source license
MoleculeNet / DeepChem	Single-molecule property benchmarks and scaffold-split evaluation	Open-source benchmark resources; DeepChem/MoleculeNet code is released under the MIT license
BigSolDB	Training source for pure-solvent solubility transfer	Creative Commons Attribution 4.0 International (CC BY 4.0)
SolProp	External pure-solvent solubility test set	Creative Commons Attribution 4.0 International (CC BY 4.0)
Leeds	External pure-solvent solubility test set	Open Zenodo record; license marked as “Other (Open)”

Appendix

Table 44: External assets used in this work.

Molecular Property Prediction

Molecular property prediction estimates chemical, physical, and biological properties from molecular structure and context.

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DISSOLVR: An Interpretable and Fast Framework for Aqueous and Organic Solubility Prediction

High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce DISSOLVR, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that DISSOLVR approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance, derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.

Vansh Ramani, Har Ashish Arora, Dhairya Kuchhal +2

1Indian Institute of Technology, Delhi, India.

Molecular Property Prediction Interpretable ML

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EnSol: an environment-aware graph neural network for molecular solubility prediction

Molecular solubility directly affects key aspects of molecular development such as reaction feasibility, formulation performance, separation efficiency, and solvent selection. However, experimental measurement across solutes, solvents, and temperatures remains costly and sparsely sampled. Existing computational models often rely on fixed-solvent assumptions, deterministic formulations, or simplified representations of solute-solvent interactions, limiting their ability to capture complex molecular interactions, continuous temperature effects, and experimental uncertainty. Here, we introduce EnSol, an environment-aware probabilistic framework for molecular solubility prediction. EnSol represents the solute and solvent as molecular graphs and learns separate representations for each before bringing them together through cross-attention to capture solute-solvent interactions. Temperature is incorporated directly into the solvent environment through feature-wise modulation, and a mixture density network predicts full solubility distributions to capture both temperature-dependent behavior and experimental uncertainty. On the independent SolProp and Leeds benchmark datasets, EnSol achieved Spearman correlations of 0.876 and 0.601, respectively, outperforming state-of-the-art solubility prediction models across both benchmarks. Beyond computational benchmarking, experimental validation across chemically diverse solute-solvent pairs showed that EnSol maintained strong predictive performance and supported reliable solvent ranking, achieving a Spearman correlation of 0.715. These results show that EnSol can support reliable solubility prediction and solvent selection across diverse chemical systems while accounting for predictive uncertainty.

Thao Nguyen, Saman Shafaei, Zhengyi Zhang +2

Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA. · Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA. · NSF Molecule Maker Lab Institute, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA. +2

Molecular Property Prediction Graph Neural Networks Molecular Representation Learning

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An Additive MLP-GNN Framework for Characterizing Chemical and Structural Contributions to Aqueous Solubility

Aqueous solubility is a key property in early-stage drug discovery, but most predictive models merge physicochemical descriptors and molecular graph information into a single representation, obscuring whether a prediction is driven by global chemistry, molecular structure, or both. We present an additive deep-learning framework that keeps these two sources of information separate throughout training: physicochemical descriptors are encoded by a multilayer perceptron (the chemical branch) and molecular graph topology by a graph neural network (the structural branch), with the two outputs combined only at the prediction stage through an additive model with an optional multiplicative interaction. This design provides a direct decomposition of chemical and structural components that can be examined separately after training. Furthermore, pretraining on the larger AqSolDB dataset and fine-tuning on the smaller BigSolDB2 dataset substantially improve accuracy and reduce run-to-run variations, indicating generalizability of the learned features from the data-rich settings. We further interpret the fitted model using best linear projections of the branch outputs, molecule-level embedding summaries across solubility classes, and atom-level GNNExplainer masks aggregated over functional groups. These analyses show that the chemical branch aligns with familiar physicochemical descriptors, while the structural branch captures graph-topological and functional-group patterns associated with solubility. Across both datasets, the framework attains competitive predictive performance while making the distinct roles of chemical and structural information more transparent.

Sampreeti Bhattacharya, Arkaprava Roy

Molecular Property Prediction

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Molecular Property Prediction

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