cs.LGOct 21, 2026

Fragment-Level Graph Encoding for Interpretable Molecular Property Prediction

Authors: Rafael Lopes Almeida, Ina Pöhner

Organizations: School of Pharmacy, University of Eastern Finland, Kuopio, Finland

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Abstract

Graph neural networks (GNNs) are among the standard tools for molecular property prediction, but the atom-level explanations of their predictions are hard for medicinal chemists to act on. We propose a change of input representation rather than a new model: molecules are encoded as fragment-level graphs from BRICS decomposition, where each node is a synthetically meaningful fragment whose features are the element-wise sum of its atoms' features. Because only the representation changes, any message-passing GNN and any post-hoc attribution method produces explanations at the resolution of functional groups instead of single atoms. Across four architectures, four prediction tasks, and two explainers under scaffold splits, fragment-level encoding matches atom-level test accuracy on roughly five-fold smaller graphs. Integrated-Gradients attributions recover known pharmacophores above chance on two enzyme targets, namely BACE at 1.5 times the chance rate, and PTR1 at 3.2 times. A like-for-like comparison against an aggregated atom-level baseline shows that post-hoc aggregation is not a stable substitute: its BACE hit rate range both exceeds and falls below the fragment model's hit rate depending on two arbitrary aggregation choices, whereas fragment-level training yields a single convention-free attribution at no predictive cost. The code is available at: https://github.com/4D-Lab/frame

Figures & tables

Figure 1: Atom-level versus BRICS fragment-level graph construction for celecoxib. (a) The atom graph: every atom is a node (26 nodes, 34-dimensional features) and every bond an edge, with nodes ringed and coloured by BRICS fragment and cut bonds in red. (b) The fragment-level graph (4 fragment nodes with element-wise summed features), each node a recognizable substructure.
Figure 2: Integrated Gradients (IG) attribution at three resolutions for a correctly-predicted BACE inhibitor. (a) Raw atom-level attribution is fine-grained but noisy. (b) Atom attributions aggregated into fragments (SME-style control). (c) Native fragment-level attribution concentrates on the aminothienopyran recognition element. Each panel is scaled to its own maximum.
DatasetTaskNNScaf.Label
BACE (cls)cls1512649690/1512 pos (46%)
BACE (reg)reg15126492.54–10.52 ( μ\mu =6.52)
BBBPcls196510201495/1965 pos (76%)
PTR1reg2501193.19–10.00 ( μ\mu =5.61)
Table 1: Datasets used. NN is the molecule count and Scaf. the number of unique Bemis–Murcko scaffolds. The two regression targets carry different constants: BACE is pIC 50 and PTR1 is pK i{}_{\text{i}} . Graph sizes are in Table 10 .
 BACE (cls)BBBP
BackboneMCC aMCC fMCC aMCC f
AttentiveFP0.530  ± 0.073\,\pm\,0.0730.565  ± 0.050\,\pm\,0.0500.291  ± 0.040\,\pm\,0.0400.186  ± 0.042\,\pm\,0.042
GATv20.439  ± 0.057\,\pm\,0.0570.552  ± 0.058\,\pm\,0.0580.140  ± 0.020\,\pm\,0.0200.176  ± 0.065\,\pm\,0.065
GIN0.385  ± 0.087\,\pm\,0.0870.476  ± 0.104\,\pm\,0.1040.163  ± 0.050\,\pm\,0.0500.183  ± 0.051\,\pm\,0.051
PNA0.453  ± 0.085\,\pm\,0.0850.587  ± 0.030\,\pm\,0.0300.175  ± 0.027\,\pm\,0.0270.151  ± 0.057\,\pm\,0.057
Table 2: Classification: primary test metric (MCC) per architecture and encoding, atom (a) vs. fragment (f). Values are mean ±\pm std over five training seeds, with the best mean per block in bold. Full metrics in Appendix C .
 BACE (reg)PTR1
BackboneCCC aCCC fCCC aCCC f
AttentiveFP0.846  ± 0.013\,\pm\,0.0130.861  ± 0.007\,\pm\,0.0070.267  ± 0.027\,\pm\,0.0270.439  ± 0.033\,\pm\,0.033
GATv20.818  ± 0.009\,\pm\,0.0090.814  ± 0.031\,\pm\,0.0310.261  ± 0.061\,\pm\,0.0610.229  ± 0.034\,\pm\,0.034
GIN0.797  ± 0.009\,\pm\,0.0090.800  ± 0.056\,\pm\,0.0560.298  ± 0.035\,\pm\,0.0350.379  ± 0.053\,\pm\,0.053
PNA0.858  ± 0.007\,\pm\,0.0070.845  ± 0.010\,\pm\,0.0100.300  ± 0.044\,\pm\,0.0440.377  ± 0.040\,\pm\,0.040
Table 3: Regression: primary test metric (CCC) per architecture and encoding, atom (a) vs. fragment (f). Values are mean ±\pm std over five training seeds, with the best mean per block in bold. Full metrics in Appendix C .
DataApproachnnHit IG↑{}_{\text{IG}}\uparrowHit IG∗↑{}^{\ast}_{\text{IG}}\uparrowHit GX↑{}_{\text{GX}}\uparrowGini IG↑{}_{\text{IG}}\uparrowGini GX↑{}_{\text{GX}}\uparrowρIG,GX↑\rho_{\text{IG,GX}}\uparrow
BACEAtom-level1480.4050.4650.3450.4780.122-0.029
 Aggregated1480.3990.4570.5140.5320.4030.053
 Native frag.1480.2770.3180.4800.5180.2820.330
 reachable ceiling 0.872     
BBBPAtom-level1660.723—0.7410.2580.0750.155
 Aggregated1660.711—0.7230.4550.4340.812
Table 4: Explanation quality by approach. Hit: fragment hit rate against known pharmacophores (BBBP: directional TPSA), with the reachable ceiling imposed by BRICS given below the BACE and PTR1 blocks. BBBP has no discrete pharmacophore and thus no ceiling. Hit IG∗{}^{\ast}_{\text{IG}} : the same IG hit rate normalized by that ceiling, i.e. the rate among molecules that can register a hit at all, which makes targets with different ceilings comparable; interval estimates for it are given in Section 3.4 . The best value per dataset block is set in bold, and exact ties are left unbolded. Gini: attribution concentration, corrected by the maximum attainable at each vector length, so atom- and fragment-level values are comparable. ρIG,GX\rho_{\text{IG,GX}} : per-molecule IG vs. GNNExplainer Spearman agreement. The aggregated row uses the default signed-sum convention, and Appendix D gives its full range.
Figure 3: Fragment hit rate using IG by target and approach, with 95% intervals conditional on reachability: for BACE and PTR1 the interval is estimated over the molecules that can register a hit and rescaled by the ceiling, so it cannot exceed it; BBBP has no ceiling and uses a Wilson interval on the raw proportion. Dashed lines mark the random-chance rate per target, solid rules the reachable ceiling. BACE and PTR1 attributions exceed chance for all approaches. The three PTR1 bars coincide at the ceiling, where all three approaches select the same 18 of 23 molecules (Appendix H ). BBBP uses the directional TPSA criterion.
Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

HyperparameterRange / choices
hidden channels[32, 256]
layers[2, 4]
dropout[0.2, 0.6]
pooling{mean, add, max}
learning rate[0.0001, 0.005] (log)
weight decay[1e-06, 0.001] (log)
Appendix
Table 5: Hyperparameter search space.
ExperimentEnc.Best configuration
BACE (cls)/AttentiveFPAh234, L4, d0.23, lr2.8e-03, timesteps2
BACE (cls)/AttentiveFPFh95, L3, d0.26, lr3.1e-03, timesteps3
BACE (cls)/GATAh213, L3, d0.24, lr3.7e-03, add, heads2, v1
BACE (cls)/GATFh149, L4, d0.28, lr4.9e-03, mean, heads4, v1
BACE (cls)/GINAh126, L2, d0.55, lr2.3e-03, mean
BACE (cls)/GINFh170, L3, d0.48, lr2.7e-03, max
Appendix
Table 6: Best configurations (atom / fragment).
DatasetModel / Enc.accacc_balf1precrecmccavg_precroc_auc
BACE (cls)AttentiveFP/A0.777  ± 0.074\,\pm\,0.0740.781  ± 0.033\,\pm\,0.0330.666  ± 0.050\,\pm\,0.0500.590  ± 0.092\,\pm\,0.0920.790  ± 0.059\,\pm\,0.0590.530  ± 0.073\,\pm\,0.0730.747  ± 0.025\,\pm\,0.0250.867  ± 0.015\,\pm\,0.015
 AttentiveFP/F0.815  ± 0.032\,\pm\,0.0320.794  ± 0.019\,\pm\,0.0190.688  ± 0.032\,\pm\,0.0320.642  ± 0.066\,\pm\,0.0660.750  ± 0.039\,\pm\,0.0390.565  ± 0.050\,\pm\,0.0500.760  ± 0.027\,\pm\,0.0270.864  ± 0.029\,\pm\,0.029
 GAT/A0.726  ± 0.067\,\pm\,0.0670.737  ± 0.029\,\pm\,0.0290.605  ± 0.037\,\pm\,0.0370.515  ± 0.071\,\pm\,0.0710.761  ± 0.090\,\pm\,0.0900.439  ± 0.057\,\pm\,0.0570.651  ± 0.055\,\pm\,0.0550.817  ± 0.017\,\pm\,0.017
 GAT/F0.816  ± 0.025\,\pm\,0.0250.784  ± 0.030\,\pm\,0.0300.678  ± 0.041\,\pm\,0.0410.647  ± 0.050\,\pm\,0.0500.715  ± 0.056\,\pm\,0.0560.552  ± 0.058\,\pm\,0.0580.745  ± 0.014\,\pm\,0.0140.854  ± 0.013\,\pm\,0.013
 GIN/A0.662  ± 0.086\,\pm\,0.0860.712  ± 0.049\,\pm\,0.0490.575  ± 0.054\,\pm\,0.0540.450  ± 0.073\,\pm\,0.0730.820  ± 0.063\,\pm\,0.0630.385  ± 0.087\,\pm\,0.0870.615  ± 0.064\,\pm\,0.0640.816  ± 0.025\,\pm\,0.025
 GIN/F0.737  ± 0.097\,\pm\,0.0970.756  ± 0.053\,\pm\,0.0530.633  ± 0.068\,\pm\,0.0680.536  ± 0.102\,\pm\,0.1020.800  ± 0.050\,\pm\,0.0500.476  ± 0.104\,\pm\,0.1040.632  ± 0.145\,\pm\,0.1450.805  ± 0.057\,\pm\,0.057
Appendix
Table 7: Classification test metrics (A: atom, F: fragment). Abbreviations: acc: accuracy; acc_bal: balanced accuracy (the mean per-class recall); f1: F1F_{1} score; prec: precision; rec: recall (f1, prec and recall for the positive class); mcc: Matthews correlation coefficient [ 6 ] ; avg_prec: average precision (area under the precision–recall curve); roc_auc: area under the ROC curve. All except avg_prec and roc_auc are computed at a fixed 0.5 probability threshold, while avg_prec and roc_auc use continuous scores and are threshold-free.
DatasetModel / Enc.r2rmsemaerto_r2cccroy_croy_c_invdelta
BACE (reg)AttentiveFP/A0.686  ± 0.039\,\pm\,0.0390.750  ± 0.047\,\pm\,0.0470.579  ± 0.034\,\pm\,0.0340.720  ± 0.028\,\pm\,0.0280.846  ± 0.013\,\pm\,0.0130.579  ± 0.085\,\pm\,0.0850.601  ± 0.062\,\pm\,0.0620.032  ± 0.013\,\pm\,0.013
 AttentiveFP/F0.730  ± 0.016\,\pm\,0.0160.673  ± 0.020\,\pm\,0.0200.499  ± 0.017\,\pm\,0.0170.743  ± 0.011\,\pm\,0.0110.861  ± 0.007\,\pm\,0.0070.655  ± 0.051\,\pm\,0.0510.659  ± 0.040\,\pm\,0.0400.026  ± 0.017\,\pm\,0.017
 GAT/A0.620  ± 0.026\,\pm\,0.0260.827  ± 0.028\,\pm\,0.0280.611  ± 0.028\,\pm\,0.0280.671  ± 0.010\,\pm\,0.0100.818  ± 0.009\,\pm\,0.0090.483  ± 0.047\,\pm\,0.0470.547  ± 0.041\,\pm\,0.0410.010  ± 0.007\,\pm\,0.007
 GAT/F0.606  ± 0.074\,\pm\,0.0740.810  ± 0.074\,\pm\,0.0740.619  ± 0.052\,\pm\,0.0520.646  ± 0.054\,\pm\,0.0540.814  ± 0.031\,\pm\,0.0310.496  ± 0.093\,\pm\,0.0930.571  ± 0.077\,\pm\,0.0770.010  ± 0.006\,\pm\,0.006
 GIN/A0.551  ± 0.029\,\pm\,0.0290.898  ± 0.029\,\pm\,0.0290.687  ± 0.024\,\pm\,0.0240.621  ± 0.018\,\pm\,0.0180.797  ± 0.009\,\pm\,0.0090.410  ± 0.047\,\pm\,0.0470.515  ± 0.033\,\pm\,0.0330.021  ± 0.014\,\pm\,0.014
 GIN/F0.558  ± 0.169\,\pm\,0.1690.848  ± 0.150\,\pm\,0.1500.640  ± 0.095\,\pm\,0.0950.603  ± 0.171\,\pm\,0.1710.800  ± 0.056\,\pm\,0.0560.451  ± 0.154\,\pm\,0.1540.552  ± 0.076\,\pm\,0.0760.058  ± 0.078\,\pm\,0.078
Appendix
Table 8: Regression test metrics (A: atom, F: fragment). Abbreviations: r2: coefficient of determination; rmse: root-mean-square error and mae: mean absolute error, both in target units; rto_r2 ( r02r_{0}^{2} ): R2R^{2} of a zero-intercept fit of observed on predicted values; ccc the concordance correlation coefficient [ 26 ] ; roy_c and roy_c_inv: Roy’s rm2=r2(1−∣r2−r02∣)r_{m}^{2}=r^{2}(1-\sqrt{|r^{2}-r_{0}^{2}|}) and its inverse rm′2r_{m}^{\prime 2} computed with observed and predicted values swapped [ 41 ] ; delta ( Δr02\Delta r_{0}^{2} ): the Golbraikh–Tropsha statistic ∣r02−r0′2∣|r_{0}^{2}-r_{0}^{\prime 2}| [ 16 ] . Higher is better except for rmse, mae and delta, with conventional acceptance thresholds rm2>0.5r_{m}^{2}>0.5 and Δr02<0.3\Delta r_{0}^{2}<0.3 .
AggregationBACE (cls)PTR1
Signed, sum (SME default)0.3990.783
Signed, size-normalised0.2230.696
Absolute, sum0.4260.783
Absolute, size-normalised0.2570.739
Native fragment model0.2770.783
Appendix
Table 9: Fragment hit rate of the aggregated atom-level baseline under each aggregation convention, against the convention-free native fragment model.
DatasetTrainValTestScaf.Singl.BRICS excl.Avg. atom/frag. nodes
BACE (cls)12101511516494525 (0.3%)34.1/7.2
BACE (reg)12101511516494525 (0.3%)34.1/7.2
BBBP15721961971020776254 (12.9%)24.0/4.5
PTR120025251198211 (4.4%)23.3/4.4
Appendix
Table 10: Scaffold, BRICS-exclusion, and graph-size statistics.
SourceYearReportedCurated
Khalaf et al. [ 19 ]20147146
Linciano et al. [ 29 ]20193535
Pöhner et al. [ 37 ]20223434
Borsari et al. [ 4 ]20164229
Spinks et al. [ 47 ]20112622
Santucci et al. [ 42 ]20211414
Appendix
Table 11: Primary sources of the PTR1 dataset, ordered by the number of compounds each contributes after curation. “Reported” is the number of measurements in the source table and “Curated” the number surviving the removal of qualitative or unavailable readings.
Figure 4: Native fragment-level IG attributions, each map scaled to its own maximum. (a) BACE actives; titles give the predicted probability and the top fragment’s pharmacophore class. (b) PTR1 test molecules whose top-ranked fragment is pharmacophoric; titles give the predicted pK i{}_{\text{i}} and the top fragment’s pharmacophore class. Class labels mark fragments carrying a SAR-defined recognition element (Section 3.4 ); for BACE, the hydroxyethylamine motif spans a BRICS cut, so no single fragment can carry it whole.
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