On the limitations of molecular representations

Acer Blake; Fergus Imrie; Charlotte M. Deane

cs.LGNov 5, 2026

On the limitations of molecular representations

Authors: Acer Blake, Fergus Imrie, Charlotte M. Deane

Organizations: Department of Statistics, University of Oxford, Oxford, UK

Abstract

Molecular representations such as fingerprints and learned embeddings play a central role in cheminformatics and small-molecule machine learning. They serve as the primary input for a diverse array of tasks, including clustering, dataset splitting, and virtual screening, yet their evaluation is often limited to downstream model performance on narrow benchmark tasks. We carried out a systematic investigation of the quality of molecular representations, finding that none of the state-of-the-art molecular embedding models capture graph structure, 3D shape, or ADMET endpoint similarity better than fingerprints or physicochemical descriptors. However, classical fingerprints also revealed their own material limitations. For example, we show that depending on the representation, between 225M and $\sim$ 4B molecules have non-unique representations in the 10.8B Enamine REAL database, with implications for virtual screening. Our findings provide an insight into the current limitations of molecular representations, outlining future research directions for the development of more robust encodings of small molecules.

Figures & tables

Molecular embedding models
Model	Model type	Params	Train set size	Pre-training objective	Loss function	Stereo-aware
MolBERT [ 23 ]	CLM (Transformer)	87M	1.3M	Masked language modelling, SMILES equivalence, descriptor prediction	Multi-task loss	No
ChemBERTa [ 2 ]	CLM (Transformer)	3.4M	77M	Masked language modelling	Categorical cross-entropy	No
MolFormer [ 64 ]	CLM (Transformer)	44.4M	1.1B	Masked language modelling	Multi-class cross-entropy	No
MolCLR [ 71 ]	GNN	2.4M	10M	Contrastive alignment following atom masking, bond deletion, and subgraph removal	Scaled cross-entropy contrastive loss	Yes
CheMeleon [ 6 ]	GNN	9.3M	1M	Prediction of 1,613 molecular descriptors	Masked mean squared error	Yes

Table 1: Molecular representations used in this study

Figure 1: Degeneracy rates for molecular fingerprints across the filtered 10.3 billion molecule Enamine REAL space . (a) Bar chart showing the degeneracy rates for each of the four tested fingerprint types. A molecule is considered to be degenerate if it participates in a group of two or more non-identical molecules that map to the same fingerprint. (b-e) Group sizes for sets of degenerate molecules across FCFP4, topological torsion, ECFP4, and atom pair fingerprints, respectively. Parameter settings for the fingerprints are given in Table 1 .

Figure 2: Degeneracy failure modes across three fingerprint types . The figure depicts a non-exhaustive set of transformations that can be applied to preserve fingerprint identity across ECFP4, atom pair, topological torsion fingerprints, and every intersection between them. Each letter label denotes the fingerprint type(s) for which degeneracy holds, while molecules with the same number have identical fingerprints. All examples are sourced from Enamine and ChEMBL. The Venn diagram at center indicates how many consistent and repeatable failure modes were found for each fingerprint type and combination.

Figure 3: Activity differences for degenerate molecules in ChEMBL . (a) $\delta$ -opioid receptor agonists indistinguishable by all fingerprints [ 48 ] , (b) Amgen TRPV1 antagonists indistinguishable by atom pair fingerprints [ 18 ] . (c) Antitrypanosomals indistinguishable under ECFP4 [ 14 ] . Each example pair is published within one paper and assayed under the same experimental conditions. (d) Number of chiral, 1024-bit ECFP4 degenerate groups in the same ChEMBL assay by maximum within-group fold change.

Figure 4: Disagreement between MCES and similarities defined over molecular representations . (a–l) Poor calibration of cosine similarities (a–i) and Tanimoto similarities (j–l) with respect to global molecular graph topology. Examples for each model are divided into two: the top molecular pair shows high representation similarity and high MCES distance, while the bottom pair shows low relative representation similarity and low MCES distance. Due to their extreme cosine similarity distributions, examples for the MolCLR (a) and COATI (b) models were rescaled using min-max percentile scaling.

Figure 5: Butina cluster leakage . (a) Pairwise Tanimoto similarity distributions for the MCES dataset. (b) Fraction of singleton clusters across Butina thresholds. (c) Fraction of the molecules contained in singleton clusters. (d) Fraction of molecules with $d_{MCES^{w}_{norm}}$ $\leq 0.05$ and $d_{MCES^{w}}$ $<10$ to other molecules in different clusters (edges). (e) Fraction of clusters with at least one edge incident to another cluster using the same threshold as in (d) . (f) Cluster size distributions across a selected Butina Tanimoto threshold range. (g) Edges per cluster across different Butina Tanimoto thresholds. (h) Network showing 2,298 clusters using a Butina threshold of 0.4. Each edge represents a pair of molecules assigned to different clusters with $d_{MCES^{w}_{norm}}\leq 0.05$ and $d_{MCES^{w}}$ $<10$ . Nodes are scaled by molecule count and coloured according to minimum incident $d_{MCES^{w}}$ . (i-m) Average difference across each pair across physicochemical properties. (n) Example molecular pairs from (h) . Each pair contains two molecules from different clusters with low MCES distance. $T_{c}$ denotes the Tanimoto similarity coefficient.

Panel of Figure 7 — List of extendedfigures 1 Graph similarity evaluations . (a) An example of normalized weighted MCES distance between two molecules. (b-m) Hexbin relative density plots with marginal distributions showing the Spearman correlation between Tanimoto similarity (b-d) and cosine similarity (e-m) against normalized weighted MCES distance across 12 representations. After preprocessing, a total of 4,348,627 pairwise comparisons are plotted for each hexbin plot. All $d_{MCES^{w}}$ values are $<10$ .

List of extendedfigures 2 Shape evaluations for molecular representations . (a) Bar chart showing the Spearman correlation between Tanimoto and cosine similarity against maximum pairwise conformational overlap score for randomly sampled molecules from ZINC. Overlap scores are given by RDKit shape and color score returned by the RDKit AlignMol API. For each representation, 1,000 total molecular pairs were uniformly sampled according to the given model’s similarity distribution. Each model’s distribution was divided into ten equal-width intervals and up to 100 pairs were randomly sampled per similarity bin. 10 conformers were generated per molecule and the maximum pairwise score was taken for each pair. (b-m) Rolling shape and color Spearman correlations for each of the 12 representations across binned (200-molecular pairs) intervals with a step size of 25 and shaded regions representing 95% confidence intervals estimated from 300 bootstrap resamples with replacement.

List of extendedfigures 3 Chemical similarity evaluations for molecular representations . (a-d) ADMET endpoint similarity for the Biogen dataset across similarity thresholds. Each plot shows the median absolute endpoint difference for the top closest 100,000, 10,000 and 1,000 molecular pairs by representation similarity. (e-h) Jaccard similarity triangles indicating the fraction of molecules that overlap in the top 1,000 of molecular pairs by representation similarity.

List of extendedfigures 4 QSAR roughness and performance . (a) ROGI-XD roughness for the representations with the lowest ROGI-XD values. ROGI-XD is computed across all molecules for which endpoint measurements are available. Lower values indicate representations that induce a smoother landscape. (b) Box plots for mean 5-fold RMSE for the top 5 representations across each endpoint and model. (c) Pearson correlation between ROGI-XD roughness and cross-validated RMSE.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 1: Quinoline inversion construction for atom pair fingerprints. The figure shows how the nitrogen atom in a quinoline functional group (a) can be relocated to the same position on the opposite fused ring (b) while maintaining fingerprint identity. R groups here signify that provided the same structure is substituted for both placeholders in subfigures (a) and (b) , the resulting molecule will have the same fingerprint. Numerical annotations represent the bond distance from the highlighted nitrogen to each atom. Atom pair fingerprints encode features using a three-tuple of the form

(a_{1},d,a_{2})

where

a_{1}

and

a_{2}

are the atom environments of two distinct atoms and

d

is the bond distance between them. Atom environments are encoded using atomic number, number of

\pi

electrons, and degree. None of these values are changed by the relocation of the nitrogen. Further, because of the symmetry of the quinoline functional group, bond distances are matched by the relocation of the nitrogen. Subfigures (c) and (d) show an example pair of degenerate molecules satisfying the rule depicted.

Figure 2: Ring expansion for ECFP4 fingerprints. The figure shows how non-aromatic rings can be expanded while maintaining fingerprint identity for ECFP4 fingerprints. R groups here signify that provided the same structure is substituted for both placeholders in subfigures (a) and (b) , the resulting molecule will have the same fingerprint. Note that there is no limit as to how large the rings can be made in the cases of subfigures (b) and (d) . The maintenance of fingerprint identity can be attributed to the fact that no new radial substructures up to a bond distance of 2 are generated. Note that it is not necessary for rings to be cycloalkanes for ring expansion to be possible. It is possible to replace these with heterocycles in some instances.

Figure 3: Ring insertion for ECFP4 fingerprints. The figure shows how additional benzene groups can be inserted into a molecular structure while maintaining fingerprint identity. R groups here signify that provided the same structure is substituted for both structures in subfigures (a) and (b) , the resulting molecule will have the same fingerprint. Note that there is no limit as to how many rings may be inserted into the structures of (b) and (d) . The maintenance of fingerprint identity can be attributed to the fact that no new radial substructures up to a bond distance of 2 are generated. Ring insertion is a specific case of substructure insertion, wherein molecules degenerate under the ECFP4 fingerprint can be constructed by repeatedly appending repeated substructures to a reference molecule. Provided the attachment points for the repeated substructures do not introduce a new substructure, these molecules will maintain an identical fingerprint.

Figure 4: Macrocyclization for ECFP4 fingerprints. The figure shows how a 6-membered heterocycle with heteroatoms at the 1 and 4 positions and an attached side-chain can be resized into a 12-membered macrocycle while maintaining fingerprint identity. R groups here signify that provided the same structure is substituted for the side chains in subfigures (a) and (b) , the resulting molecules (subfigures (c) and (d) ) will have the same fingerprint. The atoms denoted

\eta_{1}

\eta_{2}

may be any heteroatoms satisfying valence rules. The maintenance of fingerprint identity can be attributed to the fact that the constructed 12-membered macrocycle maintains the same radius 2 substructures as the 6-membered heterocycle throughout. Indeed, provided the period of repeated heteroatoms and side-chains repeats with the same frequency, the heterocycle can be expanded infinitely.

Figure 5: Ring swap for ECFP4 and topological torsion fingerprints. The figure shows how two substituted rings can be exchanged with respect to a shared skeleton while maintaining fingerprint identity. R groups here signify that provided the same structures are substituted for both

R_{1}

and

R_{2}

in figures (a) and (b) , the resulting molecule will have the same fingerprint. The wavy double bonds indicate that the rings may be either aromatic or saturated. Further, the asterisks indicate that the given atoms may be heteroatoms. The maintenance of identical ECFP4 and topological torsion fingerprints can be attributed to the fact that no new radial substructures are introduced (accounting for ECFP4 identity) nor are any new length 4 sequences of atoms (accounting for topological torsion identity). Note that the construction is not limited to two substituted rings being exchanged. In fact, provided the rings follow the same structure as in (a) and (b) any number of rings can be swapped. Figures (c) and (d) provide a concrete example of ring swaps that maintain fingerprint identity.

Figure 6: Cage substitution for ECFP4, topological torsion and atom pair fingerprints. The figure depicts how diazatricyclodecane functional groups can be substituted for each other while maintaining fingerprint identity. Subfigure (a) depicts a 9,10-diazatricyclo[4.2.1.1 2 , 5 ]decane ring, while (b) represents a 2,7-diazatricyclo[4.4.0.0 3 , 8 ]decane ring. The R groups here signify that provided the same structures are substituted for both

R_{1}

and

R_{2}

in figures a and b, the resulting molecule will have the same fingerprint. Figures ( c ) and ( d ) provide a concrete example of two molecules sharing the same fingerprint with substituted diazatricyclodecane groups.

Figure 7: Linker extension for ECFP4 and topological torsion fingerprints. The figure shows how a carbon chain can be extended in length while maintaining fingerprint identity. R groups here signify that provided the same structure is substituted for both structures in figures (a) and (b) , the resulting molecule will have the same fingerprint. Note that the parity of the length of the original linker may be required to be equivalent for degeneracy to hold. Figures ( c ) and ( d ) provide a concrete example of two molecules sharing the same fingerprint with carbon-chain linkers of varying lengths.

Figure 8: Substituent swap and duplication for ECFP4 fingerprints. The figure shows how ring substituents can be relocated and duplicated on unsubstituted rings within the same molecule while maintaining fingerprint identity. R groups here signify that provided the same structure is substituted for the corresponding structures in subfigures (a) and (b) , the resulting molecule will have the same fingerprint. Figures ( c ) and ( d ) provide two examples of substituent swaps and duplications for molecules that maintain fingerprint identity.

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Benchmarking Pretrained Molecular Embedding Models For Molecular Representation Learning

Mateusz Praski, Jakub Adamczyk, Wojciech Czech

Faculty of Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland

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Pretrained molecular embedding models spanning graph neural networks, text transformers, and hybrid architectures have been widely used in drug discovery, yet no large-scale, rigorous comparison of their representations existed. We evaluated 28 models across 25 classification datasets under a controlled framework using hierarchical Bayesian Bradley-Terry statistical testing. All neural models except CheMeleon failed to outperform the classical ECFP count fingerprint; CheMeleon was the only model rated as better. However, further testing on external validation datasets, based on scaffold cross-validation and a Bayesian hierarchical correlated t-test, revealed no definite advantage of either embedding method. As a practical takeaway, we recommend evaluating both ECFP fingerprints and CheMeleon embeddings in novel QSAR/QSPR studies. Overall, in the context of all neural networks evaluated, these results also challenge the perceived progress in molecular representation learning and highlight the need for rigorous evaluation standards in the field.

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