WEECFP-SuRGE: A Position-Aware Substructure Encoding Method for Molecular Property Prediction

Robert Epps

cs.LGSep 4, 2026

WEECFP-SuRGE: A Position-Aware Substructure Encoding Method for Molecular Property Prediction

Authors: Robert Epps

Organizations: Eli Lilly and Company Lilly Corporate Center, Indianapolis, IN, United States of America

Abstract

Computational molecular property prediction requires representations that capture local chemistry, long-range interactions, and molecular topology. Conventional fingerprints provide efficient local substructure features, whereas learned graph and sequence models can represent broader context but often rely on pretraining or three-dimensional conformers. We introduce Wide Encoded Extended Connectivity Fingerprints (WEECFP) with Substructure Rotary Graph-distance Encoding (SuRGE), a tokenized hierarchical Morgan representation in which graph-distance-dependent rotations are applied at the input and within transformer self-attention. Across MoleculeNet and the Therapeutic Data Commons ADMET benchmarks, WEECFP-SuRGE is competitive with recent pretrained and geometry-aware methods without external pretraining or conformer generation. We also show that the rotated token representation remains structurally informative. A guided confirmed-handshake overlap procedure reconstructs the correct constitutional isomer for 92.6% of a 4,200-molecule self-library evaluation. Together, the predictive and reconstruction results indicate that WEECFP-SuRGE preserves local substructure identity while making relative topology available to the model.

Figures & tables

Figure 1: WEECFP-SuRGE implementation. (A) WEECFP encodes successive Morgan environments around each center atom as signed continuous substructure tokens. (B) Mean-distance and three-reference position schemes assign graph-derived positions to the same molecular graph. (C) Input SuRGE rotates token embeddings before the transformer, whereas Layer SuRGE rotates query and key projections within each self-attention block.

Figure 2: Molecule reconstruction illustration. Illustration of (A) substructure and position extraction from tokens, (B) substructure handshake matching, and (C) confirmed-handshake reconstruction.

Method	Regression (RMSE ↓)							Classification (ROC-AUC ↑)
	FreeSolv N=642	ESOL 1,128	Lipo 4,200	QM9 $\mu$ 133,885	QM9 gap 133,885	QM9 $\alpha$ 133,885	QM9 $C_{v}$ 133,885	ClinTox 1,478	BACE 1,513	BBBP 2,039	Tox21 7,831	HIV 41,127
WEECFP-SuRGE Ensemble	2.060 2 ± 0.171	1.038 1 ± 0.132	0.666 1 ± 0.009	0.765 1 ± 0.089	0.0107 1 ± 0.0008	1.521 ± 0.541	0.661 ± 0.199	0.828 3 ± 0.041	0.810 2 ± 0.052	0.919 2 ± 0.012	0.681 3 ± 0.063	0.820 2 ± 0.032
GotenNet	2.259 3 ± 0.092	1.309 3 ± 0.322	0.714 2 ± 0.031	0.771 2 ± 0.100	0.0131 ± 0.0018	0.930 2 ± 0.197	0.492 2 ± 0.078	0.688 ± 0.052	0.757 3 ± 0.022	0.859 ± 0.041	0.655 ± 0.047	0.785 3 ± 0.036
MolGraph- xLSTM	2.862 ± 0.613	1.320 ± 0.184	0.737 ± 0.028	0.774 3 ± 0.115	0.0118 2 ± 0.0010	0.904 1 ± 0.161	0.430 1 ± 0.048	0.880 1 ± 0.032	0.743 ± 0.050	0.924 1 ± 0.042	0.707 2 ± 0.074	0.654 ± 0.047
ViSNet	2.620 ± 0.313	1.433 ± 0.292	0.734 3 ± 0.033	0.786 ± 0.095	0.0129 3 ± 0.0019	0.989 3 ± 0.293	0.516 3 ± 0.096	0.715 ± 0.056	0.742 ± 0.033	0.851 ± 0.045	0.626 ± 0.050	0.731 ± 0.050
Best Base Model	1.690 1 ± 0.167	1.231 2 ± 0.136	0.802 ± 0.028	0.850 ± 0.098	0.0136 ± 0.0013	1.653 ± 0.286	0.824 ± 0.209	0.844 2 ± 0.046	0.824 1 ± 0.033	0.898 3 ± 0.019	0.732 1 ± 0.058	0.832 1 ± 0.020

Table 3

Method	Regression rank (n)	Classification rank (n)	Overall rank (n)	Uses pretraining?
MapLight + GNN	5.3 (9)	3.5 (13)	4.3 (22)	Yes (GIN)
WEECFP-SuRGE Ensemble* (ours)	3.9 (9)	5.9 (13)	5.1 (22)	No
MiniMol	6.4 (9)	4.2 (12)	5.2 (21)	Yes
WEECFP-NoSuRGE Ensemble* (ours)	4.1 (9)	6.2 (13)	5.3 (22)	No
MapLight	5.4 (9)	6.0 (13)	5.8 (22)	No
CFA	9.2 (9)	7.2 (12)	8.0 (21)	No

Table 4

Figure 3: Effect of graph-distance filtering on molecular reconstruction. Fragment-level matches (A) and radius-1 shell-atom handshakes (B) are shown without filtering, after applying distances recovered from SuRGE, and after distance filtering with iterative pair matching and symmetry resolution. Green nodes and edges denote exclusively matched shell atoms and confirmed handshakes; gray edges denote unresolved alternatives; the remaining node colors encode the number of unmatched alternatives. The example model shown is 5-(dimethylamino)-N-[3-(2,4,6-triphenylpyridin-1-ium-1-yl)propyl]naphthalene-1-sulfonamide (TAPY-Dans), which is a large high-symmetry theoretical molecule for illustration.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Ensemble member	Regression (RMSE ↓)							Classification (ROC-AUC ↑)
	FreeSolv N=642	ESOL 1,128	Lipo 4,200	QM9 $\mu$ 133,885	QM9 gap 133,885	QM9 $\alpha$ 133,885	QM9 $C_{v}$ 133,885	ClinTox 1,478	BACE 1,513	BBBP 2,039	Tox21 7,831	HIV 41,127
WEECFP- SuRGE (Input, md)	2.229 3 ± 0.248	1.011 1 ± 0.177	0.725 3 ± 0.010	0.843 ± 0.105	0.0125 3 ± 0.0007	1.045 ± 0.229	0.468 2 ± 0.052	0.754 ± 0.122	0.778 3 ± 0.080	0.855 ± 0.033	0.676 ± 0.069	0.741 ± 0.036
WEECFP- SuRGE+AE (Input, md)	2.308 ± 0.218	1.237 3 ± 0.252	0.752 ± 0.012	0.919 ± 0.106	0.0127 3 ± 0.0008	1.569 ± 0.744	0.641 ± 0.300	0.684 ± 0.059	0.789 3 ± 0.061	0.886 ± 0.002	0.662 ± 0.067	0.767 ± 0.054
Morgan- SuRGE (Input, md)	2.972 ± 0.243	1.225 2 ± 0.249	0.765 ± 0.020	0.859 ± 0.111	0.0131 ± 0.0007	1.228 ± 0.195	0.511 ± 0.035	0.695 ± 0.089	0.805 3 ± 0.037	0.862 ± 0.038	0.648 ± 0.046	0.761 ± 0.047
Morgan- SuRGE+AE (Input, md)	2.428 ± 0.122	1.242 3 ± 0.231	0.740 ± 0.013	0.897 ± 0.102	0.0125 3 ± 0.0011	1.470 ± 0.621	0.654 ± 0.291	0.696 ± 0.060	0.785 3 ± 0.061	0.874 ± 0.016	0.656 ± 0.052	0.780 ± 0.050
MLP + WEECFP+AE	1.881 2 ± 0.257	1.002 1 ± 0.067	0.723 3 ± 0.019	0.861 ± 0.087	0.0117 2 ± 0.0010	1.405 ± 0.263	0.670 ± 0.161	0.682 ± 0.089	0.772 3 ± 0.048	0.891 ± 0.028	0.666 ± 0.049	0.810 3 ± 0.027

Appendix

Table 6

Fingerprint	Regression (RMSE ↓)							Classification (ROC-AUC ↑)
	FreeSolv N=642	ESOL 1,128	Lipo 4,200	QM9 $\mu$ 133,885	QM9 gap 133,885	QM9 $\alpha$ 133,885	QM9 $C_{v}$ 133,885	ClinTox 1,478	BACE 1,513	BBBP 2,039	Tox21 7,831	HIV 41,127
AtomPair	2.445 ± 0.164	1.272 3 ± 0.130	0.851 ± 0.012	0.890 ± 0.103	0.0169 ± 0.0024	2.168 ± 0.357	0.986 ± 0.113	0.573 ± 0.046	0.824 1 ± 0.033	0.831 ± 0.033	0.709 2 ± 0.053	0.790 3 ± 0.034
Avalon	2.052 2 ± 0.149	1.631 ± 0.212	0.829 ± 0.008	0.850 ± 0.098	0.0154 ± 0.0024	5.121 ± 1.052	2.243 ± 0.545	0.576 ± 0.047	0.796 3 ± 0.056	0.838 ± 0.036	0.691 3 ± 0.064	0.832 1 ± 0.020
ErG	2.667 ± 0.097	1.857 ± 0.303	0.857 ± 0.020	1.017 ± 0.118	0.0330 ± 0.0011	5.825 ± 0.798	2.888 ± 0.341	0.769 ± 0.029	0.754 ± 0.062	0.898 3 ± 0.019	0.711 2 ± 0.056	0.747 ± 0.042
MACCS	1.690 1 ± 0.167	1.593 ± 0.367	0.920 ± 0.013	0.886 ± 0.102	0.0165 ± 0.0020	6.211 ± 3.231	2.249 ± 1.038	0.598 ± 0.067	0.781 3 ± 0.049	0.839 ± 0.029	0.711 2 ± 0.053	0.801 3 ± 0.036
MHFP6	2.762 ± 0.267	1.701 ± 0.079	0.885 ± 0.012	0.897 ± 0.098	0.0178 ± 0.0028	4.445 ± 0.745	1.983 ± 0.266	0.601 ± 0.047	0.802 3 ± 0.038	0.835 ± 0.031	0.693 3 ± 0.059	0.793 3 ± 0.029

Appendix

Table 7

Fingerprint	Regression (RMSE ↓)							Classification (ROC-AUC ↑)
	FreeSolv N=642	ESOL 1,128	Lipo 4,200	QM9 $\mu$ 133,885	QM9 gap 133,885	QM9 $\alpha$ 133,885	QM9 $C_{v}$ 133,885	ClinTox 1,478	BACE 1,513	BBBP 2,039	Tox21 7,831	HIV 41,127
AtomPair	2.612 ± 0.158	1.231 2 ± 0.136	0.910 ± 0.036	0.911 ± 0.111	0.0144 ± 0.0012	1.653 ± 0.286	0.824 ± 0.209	0.655 ± 0.067	0.821 2 ± 0.040	0.891 ± 0.022	0.614 ± 0.073	0.752 ± 0.039
Avalon	2.064 3 ± 0.178	1.681 ± 0.074	0.870 ± 0.016	0.900 ± 0.086	0.0153 ± 0.0056	4.404 ± 1.134	1.870 ± 0.593	0.697 ± 0.049	0.736 ± 0.050	0.876 ± 0.022	0.652 ± 0.059	0.803 3 ± 0.025
ErG	3.109 ± 0.427	2.011 ± 0.266	0.891 ± 0.033	1.029 ± 0.121	0.0318 ± 0.0019	5.881 ± 0.876	2.922 ± 0.395	0.713 ± 0.042	0.724 ± 0.081	0.850 ± 0.033	0.668 ± 0.035	0.740 ± 0.024
MACCS	1.888 2 ± 0.241	1.523 ± 0.308	0.938 ± 0.051	0.901 ± 0.092	0.0147 ± 0.0007	4.280 ± 1.336	1.636 ± 0.492	0.844 2 ± 0.046	0.773 3 ± 0.062	0.867 ± 0.034	0.699 3 ± 0.074	0.783 ± 0.041
MHFP6	2.886 ± 0.256	1.882 ± 0.138	0.946 ± 0.024	0.915 ± 0.092	0.0136 ± 0.0013	4.083 ± 0.449	1.919 ± 0.220	0.776 ± 0.063	0.769 3 ± 0.043	0.853 ± 0.032	0.646 ± 0.058	0.751 ± 0.021

Appendix

Table 8

Method	Regression (RMSE ↓)							Classification (ROC-AUC ↑)
	FreeSolv N=642	ESOL 1,128	Lipo 4,200	QM9 $\mu$ 133,885	QM9 gap 133,885	QM9 $\alpha$ 133,885	QM9 $C_{v}$ 133,885	ClinTox 1,478	BACE 1,513	BBBP 2,039	Tox21 7,831	HIV 41,127
Morgan Transformer	2.829 ± 0.311	1.223 2 ± 0.098	0.758 ± 0.025	0.835 ± 0.098	0.0136 ± 0.0007	2.679 ± 0.462	1.218 ± 0.351	0.805 ± 0.078	0.769 3 ± 0.059	0.881 ± 0.032	0.647 ± 0.065	0.774 ± 0.039
WEECFP- NoSuRGE	2.159 3 ± 0.459	0.932 1 ± 0.061	0.719 3 ± 0.027	0.872 ± 0.108	0.0138 ± 0.0006	2.462 ± 0.296	1.238 ± 0.281	0.829 3 ± 0.060	0.774 3 ± 0.081	0.873 ± 0.022	0.690 3 ± 0.045	0.759 ± 0.058
WEECFP- InputSuRGE (md)	1.852 2 ± 0.203	0.861 1 ± 0.085	0.711 2 ± 0.027	0.852 ± 0.095	0.0126 3 ± 0.0007	1.062 ± 0.138	0.449 2 ± 0.020	0.809 ± 0.068	0.783 3 ± 0.054	0.853 ± 0.029	0.689 3 ± 0.057	0.756 ± 0.031
WEECFP- InputSuRGE (ref3)	2.074 3 ± 0.330	0.864 1 ± 0.056	0.723 3 ± 0.029	0.872 ± 0.102	0.0129 3 ± 0.0007	1.257 ± 0.180	0.596 ± 0.146	0.836 3 ± 0.065	0.787 3 ± 0.062	0.862 ± 0.031	0.689 3 ± 0.058	0.756 ± 0.046
WEECFP- LayerSuRGE (md)	2.241 3 ± 0.422	0.866 1 ± 0.050	0.706 2 ± 0.028	0.845 ± 0.109	0.0129 3 ± 0.0008	1.977 ± 0.124	0.891 ± 0.131	0.827 ± 0.044	0.785 3 ± 0.055	0.889 ± 0.013	0.689 3 ± 0.054	0.766 ± 0.030

Appendix

Table 9

Figure 4: Cedrol token t3 and its SuRGE-rotated representation. Left: Cedrol with the radius-2 source fragment centered at token t3 highlighted in blue and the center atom highlighted in red. Right: selected unrotated token values (blue circles), rotated token values (red squares), and fragment-retrieval weights (black dashed line, right axis).

Seq. length S	Pairwise (MiB, fp16)	Ref3 (KiB, fp32)	Ratio
50	19.5	818.8	48.9×
100	78.1	1,637.5	97.7×
200	312.5	3,275.0	195.4×
500	1,953.1	8,187.5	488.5×
1,000	7,812.5	16,375.0	977.1×

Appendix

Table 11

Benchmark	Metric	LB #1 (method)	LB #1 NoPT (method)	SuRGE Ensemble	NoSuRGE Ensemble	Rank [#all, #NoPT]
Caco-2	MAE ↓	0.256 (CaliciBoost)	0.256 (CaliciBoost)	0.276	0.284	[4, 4]
Lipophil.	MAE ↓	0.456 (MiniMol)	0.467 (Chemprop-RDKit)	0.447*	0.460	[1, 1]
Solubility	MAE ↓	0.741 (MiniMol)	0.761 (Chemprop-RDKit)	0.745	0.762	[2, 1]
PPBR	MAE ↓	7.440 (Gradient Boost)	7.440 (Gradient Boost)	7.569	7.499	[3, 2]
VDss	Spearman ↑	0.713 (MapLight+GNN)	0.707 (MapLight)	0.617	0.619	[5, 4]
Half-life	Spearman ↑	0.576 (CFA)	0.576 (CFA)	0.431	0.433	[9, 7]

Appendix

Table 12

Benchmark	Metric	LB #1 (method)	LB #1 NoPT (method)	SuRGE Ensemble	NoSuRGE Ensemble	Rank [#all, #NoPT]
HIA (Hou)	AUROC ↑	0.993 (MiniMol)	0.990 (DeepMol (AutoML))	0.9914	0.9932*	[2, 1]
Pgp (Broccatelli)	AUROC ↑	0.938 (MapLight+GNN)	0.935 (ZairaChem)	0.9452*	0.9383*	[1, 1]
Bioavailability (Ma)	AUROC ↑	0.942 (MiniMol)	0.935 (ZairaChem)	0.7056	0.6869	[21, 17]
BBB (Martins)	AUROC ↑	0.924 (MiniMol)	0.920 (CFA)	0.9161	0.9159	[3, 2]
CYP2C9 Inhib. (Veith)	AUPRC ↑	0.859 (MapLight+GNN)	0.789 (ADMETrix)	0.7684	0.7684	[9, 5]
CYP2D6 Inhib. (Veith)	AUPRC ↑	0.790 (MapLight+GNN)	0.723 (MapLight)	0.6969	0.6853	[7, 3]

Appendix

Table 13

Hyperparameter	Value
Token dimension	1024 (WEECFP); 3387 (+AE variants)
d_model	$128$ (transformer and CNN)
Feed-forward width	256 (transformer)
Layers L	3 (transformer) / 3 residual Conv1D blocks (CNN)
Heads	$8$ (transformer); $d_{\mathrm{head}}=16$
Max sequence length	300 tokens (+1 [CLS])

Appendix

Table 14

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