cs.LGSep 4, 2026

GraphNOSE: A Graph Transformer in Olfaction

Authors: Mrityunjay Sharma, Sarabeshwar Balaji, Valentina Parma, Ritesh Kumar

Organizations: CSIR- Central Scientific Instruments Organisation, Sector 30-C, Chandigarh-160030, India · Academy of Scientific and Innovative Research (AcSIR), Ghaziabad-201002, India · Department of Higher Education,Himachal Pradesh,Shimla -171001,India · Indian Institute of Science Education and Research Bhopal(IISERB), Madhya Pradesh-462066,India · 

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Abstract

Predicting olfactory qualities from molecular structure is an open problem in chemoinformatics. Although linear models can link molecular features to odor descriptors, they often fail when extrapolating to novel chemical scaffolds, extreme molecular weights, or complex odor mixtures. To address this, we introduce GraphNOSE, an open-source graph transformer framework that predicts multi-label odor descriptors from simplified molecular-input line-entry system (SMILES) strings for single molecules and binary mixtures. By integrating positional and structural encodings within a transformer-based graph architecture, GraphNOSE achieves strong performance with six times fewer parameters than standard graph neural network (GNN) baseline while consistently outperforming linear models, molecular language model embeddings, molecular fingerprints, and baseline GNNs by an average area under the ROC curve (AUROC) margin of 4.52% (p < 0.01). GraphNOSE achieves an AUROC of 84% on out-of-distribution compounds (OODs). This exceeds the current state-of-the-art GNN for OOD in olfaction (Open-POM: 81%, p < 0.001), and identifies conditions under which linear models empirically fail. Finally, we apply XAI (explainable AI) methods to identify which substructures and molecular features drive odor predictions, yielding insights consistent with chemical intuition and grounded in the model's learned representations. Together, these results establish GraphNOSE as a scalable and interpretable architecture for olfactory prediction that generalizes to structurally distinct compounds underrepresented in current perceptual databases.

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Figure 1: Overview of the GraphNOSE framework architecture for multi-label molecular odor prediction. (A) Raw- input SMILES strings are processed through a custom featurizer using RDKit Landrum et al. (2025) and DeepChem Ramsundar et al. (2019) , constructing undirected molecular graphs G(V,E,Xn,Xe)G(V,E,X_{n},X_{e}) , where atoms and bonds represent nodes and edges, respectively. (B) The structural graph and node features are augmented using a graph positional and structural encoder (GPSE) pre-trained on diverse molecular and graph datasets (e.g., ZINC, ChEMBL, GEOM, PCQM4Mv2, MolPCBA) or standard baseline (RWSE, LapPE) to generate comprehensive spatial representations ( Xn′X^{\prime}_{n} ). (C) The enriched graph representations are fed into a hybrid GraphGPS Rampášek et al. (2022) backbone that integrates local message-passing neural networks (MPNNs) for near-neighbor functional group interactions with global self-attention mechanisms for long-range molecular topology. (D) Finally, the model predicts labels for the input molecule from the 138 odor descriptors (e.g., fruity, sweet, musky, garlic).
FeatureCategories
Atomic number1 (H) to 54 (I), UNK
Valence0, 1, 2, 3, 4, 5, 6, UNK
Degree0, 1, 2, 3, 4, 5, UNK
Formal charge−2-2 , −1-1 , 0, 1, 2, UNK
Number of hydrogens0, 1, 2, 3, 4, 5, 6, 7, 8, UNK
Hybridizationsp, sp 2 , sp 3 , sp 3 d, sp 3 d 2 , UNK
Table 1: Node (atomic) and edge (bond) features used in molecular graphs. All features are one-hot encoded and concatenated into a single bit vector. UNK denotes unknown values and serves as a catch-all category.
PSEGraphNOSElin\text{GraphNOSE}_{\text{lin}}GraphNOSEtrans\text{GraphNOSE}_{\text{trans}}
RWSE87.356±0.15∗∗∗87.356\pm{\scriptstyle 0.15}^{***}84.474±1.04∗∗∗84.474\pm{\scriptstyle 1.04}^{***}
LapPE87.796±0.13∗∗∗87.796\pm{\scriptstyle 0.13}^{***}88.378±0.06∗∗∗88.378\pm{\scriptstyle 0.06}^{***}
GPSEChEMBL\text{GPSE}_{\text{ChEMBL}}88.864±0.0888.864\pm{\scriptstyle 0.08}89.084±0.0789.084\pm{\scriptstyle 0.07}
GPSEGEOM\text{GPSE}_{\text{GEOM}}88.916±0.0588.916\pm{\scriptstyle 0.05}89.124±0.1389.124\pm{\scriptstyle 0.13}
GPSEPCQM4Mv2\text{GPSE}_{\text{PCQM4Mv2}}88.930±0.1288.930\pm{\scriptstyle 0.12}88.990±0.0988.990\pm{\scriptstyle 0.09}
GPSEZINC\text{GPSE}_{\text{ZINC}}88.958±0.1888.958\pm{\scriptstyle 0.18}89.026±0.1089.026\pm{\scriptstyle 0.10}
Table 2: Different PSE augmentations. These macro AUROC scores are averaged over five random seeds. Positional and structural encodings (PSEs) are explicitly augmented to the node features to provide topological context to the global attention mechanism. GraphNOSElin\text{GraphNOSE}_{\text{lin}} uses a linear transformer Choromanski et al. (2020) for global attention, while GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} uses standard self-attention Vaswani et al. (2017) with quadratic complexity. Significance levels ( ∗\ast denote paired tt -test comparisons relative to the GPSEMolPCBA\text{GPSE}_{\text{MolPCBA}} ): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
ClassModelROC (%)pp -valueCohen’s dd
Linear [logistic regression (LR)]LR (TopTorsion) Nilakantan et al. (1987)80.8280.82––
LR (RDKit) Landrum et al. (2025)82.0582.05––
LR (AtomPair) Carhart et al. (1985)82.8382.83––
LR (Morgan_ECFP4) Rogers and Hahn (2010)83.5683.56––
LR (MACCS) Durant et al. (2002)84.7684.76––
LLM embeddingChemBERTa Chithrananda et al. (2020)84.78±0.04∗∗∗84.78\pm{\scriptstyle 0.04}^{***}4.93×10−74.93\times 10^{-7}26.4026.40
Table 3: Baselines . Models are grouped into descriptor-based methods, LLM embedding approaches, standard GNN architectures, other GNN variants, and the proposed method. Linear models using the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) solver are deterministic and therefore do not report standard deviations, paired pp -values, or effect sizes. Significance levels and effect sizes ( ∗\ast denote paired tt -test comparisons and Cohen’s dd relative to the GraphNOSElin\text{GraphNOSE}_{\text{lin}} baseline): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 . LR, logistic regression; RF, random forest.
ModelParameters
OpenPOM2M
LDMDMPNN\text{LDM}_{\text{DMPNN}}674K
LDMGCN\text{LDM}_{\text{GCN}}671K
GraphNOSE314K
Table 4: Parameter counts for single molecule odor prediction models , reported in thousands (K) and millions (M).
Figure 2: Impact of training set size on model performance: Mean predictive performance on the held-out test set as a function of the training data proportion. Error bars represent the standard deviation across 5 random seeds. While all architectures exhibit performance gains as the training set size increases, both GraphNOSE variants consistently outperform baseline GNNs (OpenPOM and LDM variants) across all sampling rates, demonstrating superior data efficiency even in low-data regimes.
ModelAUROC (%)pp -valueCohen’s dd
GraphNOSEtrans\text{GraphNOSE}_{\text{trans}}84.34 ± 0.18\boldsymbol{84.34\>\pm\>}{\scriptstyle\boldsymbol{0.18}}––
GraphNOSElin\text{GraphNOSE}_{\text{lin}}84.26±0.3384.26\pm{\scriptstyle 0.33}––
OpenPOM80.84±0.35∗∗∗80.84\pm{\scriptstyle 0.35}^{***}4.39×10−74.39\times 10^{-7}27.1927.19
LDMGCN\text{LDM}_{\text{GCN}}79.13±0.44∗∗∗79.13\pm{\scriptstyle 0.44}^{***}1.52×10−51.52\times 10^{-5}11.1811.18
LDMDMPNN\text{LDM}_{\text{DMPNN}}79.03±0.73∗∗∗79.03\pm{\scriptstyle 0.73}^{***}5.63×10−55.63\times 10^{-5}8.048.04
LR (MACCS)78.46––
Table 5: Out-of-distribution (OOD) training results for molecule odor prediction across five random seeds . As linear models using the LBFGS solver are deterministic, they do not report standard deviations, paired pp -values, or effect sizes. The best-performing score is highlighted in bold. LR, logistic regression. Significance levels ( ∗\ast denote paired tt -test comparisons relative to the GraphNOSElin\text{GraphNOSE}_{\text{lin}} baseline): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
Figure 3: Nearest neighbor retrieval for a reference molecule.a) Reference molecule b) Top five nearest neighbors retrieved using cosine similarity on GraphNOSE continuous embeddings. c) Top five nearest neighbors retrieved using Tanimoto distance on bit-based Morgan fingerprints (serving as the established baseline in chemo-informatics Jasial et al. (2016) ).
Figure 4: Analysis of odor space: Kernel density estimation (KDE) plots for Morgan fingerprint (a) and predicted labels by OpenPOM (b) and GraphNOSE (c) Shaded and contoured areas are kernel density estimates of the distribution of labeled data. Colors denote odor categories, with shaded areas for broad classes and contours for specific descriptors (e.g., lavender, roasted).
Figure 5: Explainability through integrated gradients Sundararajan et al. (2017) of different odor descriptors. The visualizations highlight the molecular features most important for predicting each odor category. Green highlights atom-level contributions; red highlights bond-level contributions. Node and edge importance are visualized by the opacity and are proportional to the values. For more examples in each category, see Supplementary Material, Figure S4.
ModelPSE / FeaturesROC (%)pp -valueCohen’s dd
GraphNOSElin\text{GraphNOSE}_{\text{lin}}GPSEMolPCBA\text{GPSE}_{\text{MolPCBA}}77.96±0.5877.96\pm{\scriptstyle 0.58}––
GPSEChEMBL\text{GPSE}_{\text{ChEMBL}}77.84±0.5477.84\pm{\scriptstyle 0.54}0.7780.7780.140.14
GPSEpcqmv2\text{GPSE}_{\text{pcqmv2}}77.64±0.9977.64\pm{\scriptstyle 0.99}0.3490.3490.470.47
GPSEzinc\text{GPSE}_{\text{zinc}}77.58±0.6777.58\pm{\scriptstyle 0.67}0.3960.3960.420.42
LapPE77.54±1.2477.54\pm{\scriptstyle 1.24}0.6010.6010.250.25
GPSEGeom\text{GPSE}_{\text{Geom}}77.24±0.63∗77.24\pm{\scriptstyle 0.63}^{*}0.0380.0381.361.36
Table 6: Results for binary odor mixture prediction. Scores are macro AUROC scores averaged over five random seeds. Linear models (LR, logistic regression) are deterministic and therefore do not report standard deviations, paired pp -values, or effect sizes. Significance levels ( ∗\ast denote paired tt -test comparisons relative to GPSEMolPCBA\text{GPSE}_{\text{MolPCBA}} ): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
Figure 6: Figure S1: Structural similarity does not imply perceptual similarity. Perceptual odor similarity to a reference molecule (here, m-cresol, a) can be observed among some structurally related molecules (e.g., o-cresol, b) but not others (e.g., 3-methylcyclohexanol, c) , and structurally dissimilar molecules (e.g., a complex bicyclic ketone, d) can show odor similarity. Molecules sourced from the GF-LS dataset. Luebke (2019) ; Leffingwell (2005)
Figure 7: Figure S2: Dataset insights: (a) Frequency distribution of the top 30 odor labels among 138. (b) Number of labels per molecule in the GS-LF dataset Barsainyan et al. (2023a) (total n = 4983).
DatasetPrimary SourceLicenseUnique Graphs
MolPCBAMoleculeNet Hu et al. (2020)MIT323,555
ZINCZINC Database Gómez-Bombarelli et al. (2018)Apache 2.0 License249,455
GEOMAxelrod & Gomez-Bombarelli Axelrod and Gomez-Bombarelli (2022)CC0 1.0169,925
ChEMBLGaulton et al. Gaulton et al. (2012)CC BY-SA 3.0970,963
PCQM4Mv2PubChemQC Hu et al. (2021)CC BY 4.0273,920
Table 12.1 : Table S2: Summary of molecular datasets used in pretraining of GPSE.
HyperparameterSearch SpaceOptimal Value
Architecture Parameters
Hidden dimension{64, 128, 256, 288, 352, 512}64
Classifier dimension{128, 256, 512, 1024}512
Heads{1, 2, 4}1
No. of GPS layers{4, 5, 6, 7}4
Dropout[0.0, 0.5]0.440
Table 13.2 : Table S3: Hyperparameters for GraphNOSE
Sampled TrainSeed 1Seed 10Seed 100Seed 21Seed 42pp -val (vs. GraphNOSElin\text{GraphNOSE}_{\text{lin}} )pp -val (vs. GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} )
30%82.3281.8882.6280.5582.401.51×10−3 ∗∗1.51\times 10^{-3\,**}1.43×10−3 ∗∗1.43\times 10^{-3\,**}
40%83.9183.5284.1284.0184.064.39×10−4 ∗∗∗4.39\times 10^{-4\,***}1.55×10−4 ∗∗∗1.55\times 10^{-4\,***}
50%84.3584.3584.0184.9584.562.95×10−4 ∗∗∗2.95\times 10^{-4\,***}1.06×10−4 ∗∗∗1.06\times 10^{-4\,***}
60%85.0185.5485.3885.1585.203.00×10−5 ∗∗∗3.00\times 10^{-5\,***}2.80×10−5 ∗∗∗2.80\times 10^{-5\,***}
70%86.7286.9686.5886.9086.517.59×10−4 ∗∗∗7.59\times 10^{-4\,***}1.10×10−4 ∗∗∗1.10\times 10^{-4\,***}
80%87.0387.0786.9287.4886.652.87×10−4 ∗∗∗2.87\times 10^{-4\,***}5.70×10−4 ∗∗∗5.70\times 10^{-4\,***}
Table 14.3 : Table S4: AUROC on the held-out test set across five random seeds and paired tt -test pp -values comparing OpenPOM against GraphNOSElin\text{GraphNOSE}_{\text{lin}} and GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} across training data proportions (30% – 90%). Significance levels ( ∗ denote paired tt -test comparison): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
Sampled TrainSeed 1Seed 10Seed 100Seed 21Seed 42pp -val (vs. GraphNOSElin\text{GraphNOSE}_{\text{lin}} )pp -val (vs. GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} )
30%82.7177.3180.9782.0981.561.50×10−2 ∗1.50\times 10^{-2\,*}1.29×10−2 ∗1.29\times 10^{-2\,*}
40%83.5783.4582.7483.2483.855.10×10−5 ∗∗∗5.10\times 10^{-5\,***}3.60×10−5 ∗∗∗3.60\times 10^{-5\,***}
50%83.8084.8083.8784.9784.722.79×10−4 ∗∗∗2.79\times 10^{-4\,***}2.11×10−4 ∗∗∗2.11\times 10^{-4\,***}
60%84.6884.9183.8384.4385.101.38×10−4 ∗∗∗1.38\times 10^{-4\,***}1.80×10−4 ∗∗∗1.80\times 10^{-4\,***}
70%85.0185.3085.8585.3185.561.60×10−5 ∗∗∗1.60\times 10^{-5\,***}2.30×10−5 ∗∗∗2.30\times 10^{-5\,***}
80%86.1686.1886.1386.0886.561.00×10−5 ∗∗∗1.00\times 10^{-5\,***}2.31×10−7 ∗∗∗2.31\times 10^{-7\,***}
Table 14.4 : Table S5: AUROC on the held-out test set across five random seeds and paired tt -test pp -values comparing LDMGCN\text{LDM}_{\text{GCN}} against GraphNOSElin\text{GraphNOSE}_{\text{lin}} and GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} across training data proportions (30% – 90%). Significance levels ( ∗ denote paired tt -test comparison): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
Sampled TrainSeed 1Seed 10Seed 100Seed 21Seed 42pp -val (vs. GraphNOSElin\text{GraphNOSE}_{\text{lin}} )pp -val (vs. GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} )
30%81.7682.4082.1081.8181.673.00×10−6 ∗∗∗3.00\times 10^{-6\,***}1.66×10−6 ∗∗∗1.66\times 10^{-6\,***}
40%83.9683.9083.3981.8283.691.70×10−3 ∗∗1.70\times 10^{-3\,**}2.55×10−3 ∗∗2.55\times 10^{-3\,**}
50%83.8783.3082.9583.5884.033.71×10−4 ∗∗∗3.71\times 10^{-4\,***}1.62×10−4 ∗∗∗1.62\times 10^{-4\,***}
60%85.4984.7684.7085.0284.865.20×10−5 ∗∗∗5.20\times 10^{-5\,***}3.40×10−5 ∗∗∗3.40\times 10^{-5\,***}
70%85.8885.6385.4685.7483.941.46×10−3 ∗∗1.46\times 10^{-3\,**}1.06×10−3 ∗∗1.06\times 10^{-3\,**}
80%85.9486.0886.3285.7086.127.50×10−5 ∗∗∗7.50\times 10^{-5\,***}1.90×10−5 ∗∗∗1.90\times 10^{-5\,***}
Table 14.5 : Table S6: AUROC on the held-out test set across five random seeds and paired tt -test pp -values comparing LDMDMPNN\text{LDM}_{\text{DMPNN}} against GraphNOSElin\text{GraphNOSE}_{\text{lin}} and GraphNOSEtrans\text{GraphNOSE}_{\text{trans}} across training data proportions (30% – 90%). Significance levels ( ∗ denote paired tt -test comparison): ∗∗∗p<0.001{}^{***}p<0.001 , ∗∗p<0.01{}^{**}p<0.01 , and ∗p<0.05{}^{*}p<0.05 .
Figure 15.1 : Figure S3: Analysis of odor space: KDE plot for true label. Shaded and contoured areas are kernel density estimates of the distribution of labeled data. Colors denote odor categories, with shaded areas for broad classes and contours for specific descriptors (e.g., lavender, roasted).
Figure 16.2 : Figure S4: Explainability through integrated gradients Sundararajan et al. (2017) for different odor descriptors: (a) alcohol, (b) sulfurous, (c) phenolic, (d) fruity, (e) musk, and (f) ketonic. Green indicates atom-level contributions; red, bond-level contributions. Opacity indicates node and edge importance and is proportional to the values.
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