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GraphNOSE: A Graph Transformer in Olfaction

Mrityunjay Sharma, Sarabeshwar Balaji, Valentina Parma, Ritesh Kumar

arXiv:2609.05694v1cs.LG

TL;DR

Predicting odor perception from molecular structure remains challenging, and linear models degrade on structurally novel molecules. GraphNOSE combines global attention with GPSE-based encodings for multi-label odor prediction across single molecules and binary mixtures. It outperforms existing message-passing and quantum-informed models with fewer parameters and generalizes to binary odor mixtures.

  • Problem

    Predicting human odor perception from molecular structure remains challenging, while linear models degrade on molecules with properties unlike those in training, including structurally novel compounds.

    Source: Introduction · p. 3

  • Method

    GraphNOSE is an open-source graph-transformer architecture using global attention and GPSE-based encodings to predict multi-label odor descriptors for single molecules and binary mixtures.

    Source: Introduction · p. 6

  • Results

    GraphNOSE outperforms existing message-passing and quantum-informed models with fewer parameters and generalizes to binary odor mixtures.

    Source: Conclusions · p. 27

  • Takeaways & Limitations

    The authors conclude that this parameter-efficient architecture extends odor prediction to binary mixtures as well as single molecules.

    Source: Conclusions · pp. 26–27

    Linear models show marked degradation when predicting structurally novel molecules, including compounds with physico-chemical properties unlike those in training.

    Source: Introduction · p. 3

Abstract

from arXiv · show

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.

Introduction

The introduction frames challenges in predicting odor from molecular structure, including limits in generalization and perceptual context. It motivates GraphNOSE’s global-attention graph-transformer approach with GPSE to predict multi-label odor descriptors for single molecules and binary mixtures, and sets out the hypotheses and research questions guiding the experiments.

Introduction

  • Structurally similar molecules can evoke qualitatively different odors, exposing the difficulty of predicting perception from molecular structure.The introduction describes this as a disconnect between structure and perceived odor.Source: Introduction · p. 3
  • Linear models reach about 80% AUROC but degrade on structurally novel compounds, especially extreme molecular weights, and fail to generalize to unseen mixtures [7,10,11].These failures limit their use for ecological olfactory stimuli [12–17].Source: Introduction · p. 3
  • Public odor datasets combining chemical features and odor descriptors lack standardization, are typically small (about 10^2–10^3 molecules versus millions of samples in other domains), and have sparse, inconsistent annotations [18,19].The discussion identifies stimulus intensity as important to the ecological validity of odor perception.Source: Introduction · pp. 3–4
  • Existing graph-based odor approaches remain monomolecular and do not cover mixtures, while MPNNs require many layers to propagate information across distant atoms [32].Source: Introduction · p. 5
  • Although odor descriptors depend on a molecule’s overall geometry and topology rather than isolated functional groups, global architectures—particularly graph transformers (GTs) [35,36]—had not yet been applied to structure–odor prediction.Source: Introduction · p. 5
  • Traditional graph transformers ignore molecular geometry, while positional and structural encodings add geometric context; GPSE derives transferable encodings from connectivity alone [40].No principled rule guides encoding selection for a downstream task, and concatenating encodings adds overhead without proportional gains.Source: Introduction · p. 6
  • GraphNOSE combines global attention with GPSE to predict multi-label odor descriptors for single molecules and binary mixtures.The model was trained and evaluated on a benchmark dataset of 4,983 molecules and 138 descriptors, described as the largest available for olfaction (10,30).Source: Introduction · pp. 6–7
  • The authors hypothesize that GPSE provides more informative positional and structural information than common encodings, improving odor-descriptor prediction across attention architectures.They also hypothesize that GraphNOSE will outperform state-of-the-art MPNNs on held-out AUROC, OOD generalization, and robustness with reduced training data.Source: Introduction · p. 7
  • The experiments address four questions: which GPSE pretraining corpus best informs odor prediction, how GraphNOSE compares with GNN baselines under OOD and low-data conditions, and whether it generalizes to binary mixtures.A further question asks whether the learned odor space preserves label hierarchies and perceptual similarity beyond structural similarity.Source: Introduction · p. 7
  • The four analysis groups cover GPSE pretraining, benchmark comparisons and data efficiency, learned odor-space structure and perceptual hierarchies, and binary-mixture generalization.These groups correspond to research questions Q1–Q4.Source: Introduction · p. 7

Methods

The Methods section describes how GraphNOSE represents odor-labeled molecules and combines message passing, global attention, and pretrained structural encodings. It also outlines model training and imbalance-aware evaluation, including an out-of-distribution test that holds out molecules with extreme physicochemical properties.

Dataset and Molecular Graphs

  • OpenPOM contains 4,983 molecules with up to 138 binary odor labels, whose strong class imbalance creates a minority-class generalization challenge.Frequent labels such as fruity and sweet substantially outnumber rare labels such as musk and garlic.Source: Dataset and Molecular Graphs · p. 8
  • SMILES are converted to undirected atom–bond graphs with 92 atomic and 7 bond attributes, but non-isomeric inputs omit stereochemistry.Consequently, molecules differing only in 3D configuration, including enantiomers, have indistinguishable input representations.Source: Dataset and Molecular Graphs · pp. 8, 10

Model

  • GraphNOSE pairs edge-featured GINE local message passing with global attention, then mean-pools node representations for graph-level odor prediction.GraphNOSElin uses linear attention to avoid the computational overhead of quadratic standard self-attention in GraphNOSEtrans.Source: Model · pp. 11–12

Positional and Structural Encoding

  • Pretrained GPSE latent embeddings augment node features with positional and structural information and remain frozen during odor-model training.The evaluated GPSE variants were pretrained on MolPCBA, PCQM4Mv2, GEOM-Drugs, and ZINC/ChEMBL.Source: Positional and Structural Encoding · pp. 12–13

Training

  • The GS-LF dataset is split 80:20 into training and test sets, with 20% of the training portion reserved for validation and iterative stratification preserving label-combination distributions.The split follows Lee et al.10.Source: Training · p. 13
  • Training used Bayesian optimization with Optuna, Adam at 6.82 × 10−4, batch size 16, and up to 150 epochs, without data augmentation.Source: Training · p. 13
  • An imbalance-weighted binary cross-entropy loss weighted odor descriptors inversely to training frequency, while performance metrics were macro-averaged across labels.Source: Training · p. 13
  • Paired t-tests compared seed-matched runs, treating random seeds as paired observations, with p-values uncorrected for multiple comparisons.Source: Training · p. 13

Physico-chemical Out-of-Distribution Splitting

Results and Discussion

The Results and Discussion evaluates GraphNOSE’s performance across benchmark, out-of-distribution, low-data, and binary-mixture settings, and examines its learned representations and chemically meaningful attributions. It also considers dataset scope and open questions about scalability and robustness to label noise and concentration-dependent perceptual shifts.

GPSE pre-training corpora and inductive bias (Q1)

  • GPSE pre-training on varied chemical datasets consistently outperformed explicit PSEs, and performance was robust across corpora despite MolPCBA yielding the highest numerical result.The authors hypothesize that MolPCBA’s advantage may reflect alignment between biological assay targets and olfactory receptor-binding mechanisms; differences across corpora were largely statistically indistinguishable.Source: GPSE pre-training corpora and… · p. 15
  • GraphNOSElin and GraphNOSEtrans performed equivalently across most encodings, with gaps ≤0.12%, but GraphNOSEtrans degraded markedly with RWSE.The authors attribute the RWSE exception to attention collapse toward local structural features, whereas Performer’s low-rank approximation and LapPE’s graph-Laplacian construction avoid this issue.Source: GPSE pre-training corpora and… · pp. 15–16
  • With 314K parameters, GraphNOSE significantly outperformed OpenPOM (p = 0.0028, d = 2.94), LDMGCN (p = 3.73 × 10−5, d = 8.92), and LDMDMPNN (p = 8.34 × 10−5, d = 7.28); logistic regression with MACCS reached 84.76% AUROC.OpenPOM has 2M parameters and the LDM baselines approximately 670K.Source: Table 3 · p. 16, Table 4 · p. 17, GPSE pre-training corpora and… · p. 18

GraphNOSE outperforms GNNs in extreme out-of-distribution (OOD) setting

  • GraphNOSE variants outperformed baseline GNNs by an average 4.65% in the extreme physico-chemical OOD split (p < 0.001), while logistic regression with MACCS reached 78.46% AUROC.The authors hypothesize that global attention, GPSE structural priors, and parameter efficiency help preserve useful long-range dependencies when local scaffolds change.Source: GraphNOSE outperforms GNNs in extreme… · pp. 19–20, Table 5 · p. 19

hierarchies (Q3)

  • The authors examined GraphNOSElin’s learned space using its 512-dimensional penultimate-layer activations, choosing the linear-attention variant for computational efficiency and comparable performance to GraphNOSEtrans.This analysis follows experiments by Lee et al.10.Source: hierarchies (Q3) · p. 20
  • The descriptive evaluation yielded 86.91% AUROC for GraphNOSElin versus 79.73% for Morgan fingerprints, illustrating that the embedding space efficiently captures perceptual similarity in local neighborhoods.Source: hierarchies (Q3) · p. 21
  • GraphNOSE embeddings separated distinct odor families while preserving hierarchical relationships, whereas Morgan-fingerprint KDE boundaries between categories were largely indistinct.The learned space distinguished broad perceptual classes while also capturing fine-grained subcategory relationships.Source: hierarchies (Q3) · p. 21, Figure 4 · p. 22

Explainability: Structure-Odor Relationship

  • Integrated-gradients attributions highlighted hydroxyl groups for alcoholic odors, phenolic OH and adjacent aromatic carbons for phenolic odors, and sulfur atoms and adjacent carbon chains for sulfurous odors.These attribution patterns were consistent with chemical intuition about odor-influencing functional groups.Source: Explainability: Structure-Odor… · pp. 21, 23, Figure 5 · p. 23
  • Attributions emphasized carbonyl groups and α-carbons for ketonic odors, muscone for musk, and ester groups for fruity odors.The reported patterns were consistent with chemical intuition about functional groups that influence olfaction.Source: Figure 5 · p. 23, Explainability: Structure-Odor… · p. 23

Generalization to binary odor mixtures (Q4)

Conclusions

GraphNOSE combines chemical priors with global attention in a parameter-efficient graph transformer for olfactory prediction. The conclusions emphasize its benchmark performance, generalization to binary mixtures, and potential as a scalable architecture.

Conclusions

  • GraphNOSE is presented as a graph-transformer framework bridging the complex nonlinear gap between molecular structure and odor perception.Source: Conclusions · p. 26
  • Pre-trained structural and positional embeddings provide richer inductive biases than traditional explicitly constructed encodings.Source: Conclusions · p. 26
  • GraphNOSE outperforms existing message-passing and quantum-informed models while requiring significantly fewer parameters.The conclusions describe it as establishing a new benchmark.Source: Conclusions · p. 27
  • Linear attention supports scalable prediction for single molecules, while GraphNOSE also generalizes to binary odor mixtures.Source: Conclusions · p. 27

Data and Software Availability

Notes

The notes state that the authors declare no competing financial interests. The supplementary material includes an explainability figure about integrated gradients across odors.

Notes

  • The authors declare no competing financial interests.Source: Notes · p. 27

S11. Explainability Analysis of Compounds

S1. The Complex Relationship Between Molecular Struc-

Structural and perceptual odor similarity do not consistently align: related molecules may differ perceptually, while dissimilar molecules may smell alike.

  • Structurally related o-cresol can share perceptual odor similarity with reference m-cresol, but another related molecule, 3-methylcyclohexanol, may not.Source: Figure S1 · p. 29
  • A structurally dissimilar complex bicyclic ketone can nevertheless show odor similarity to m-cresol.Source: Figure S1 · p. 29
  • The examples illustrate that structural similarity does not reliably imply perceptual odor similarity.Source: Figure S1 · p. 29

S2. Dataset Analysis

The dataset analysis describes odor-label frequency and label counts per molecule, and the accompanying table lists labels in the curated dataset.

  • Figure S2 summarizes the frequency distribution of the top 30 odor labels among 138 and the number of labels per molecule in GS-LF (n = 4983).Source: Figure S2 · p. 30
  • Table S1 lists the odor labels used in the curated dataset.Source: Table S1 · p. 31

S3. Model Architecture

GraphNOSE builds on GraphGPS, combining molecular node features with positional and structural encodings before processing graphs through four GPS layers. Global mean pooling and an MLP produce multi-label predictions.

S3. Model Architecture

  • GraphNOSE projects positional and structural encodings into node features, maps edge attributes to a hidden dimension, and processes the graph through four GPS layers.Unlike the referenced implementation, it does not update edge attributes.Source: S3. Model Architecture · pp. 31–32
  • Global mean pooling aggregates the final node embeddings, which an MLP then uses for multi-label classification.Source: S3. Model Architecture · p. 32
  • Hyperparameter search fixed the GPS global attention type to Performer and selected GPSE pre-trained on MoLPCBA as the optimal positional and structural encoding setting.Source: S3. Model Architecture · p. 32

S4. Loss Function

The section motivates label-imbalance handling by noting that highly imbalanced odor datasets can yield high micro-averaged ROC scores but low macro-averaged ROC scores. It defines an imbalance ratio per label and uses it to weight the loss.

S4. Loss Function

  • Highly imbalanced datasets can show high micro-averaged ROC scores but low macro-averaged ROC scores when models fail to generalize to under-represented descriptors.The section identifies label-set distribution and degree of imbalance as important to generalizability and predictive accuracy.Source: S4. Loss Function · p. 32
  • IRLbl is the frequency of the most common label divided by the frequency of a specific label.The most frequent label has an IRLbl of 1; higher values indicate greater imbalance for that descriptor.Source: S4. Loss Function · pp. 32–33
  • The study weights its loss by log(1 + class_imbalanceratio), motivated by the per-label imbalance measure used in POM.Source: S4. Loss Function · pp. 32–33

S5. Baselines

The section describes OpenPOM and four baseline approaches spanning conventional molecular features, quantum-mechanical features, and binary-mixture prediction. Their datasets, featurizers, and model designs provide comparison contexts for GraphNOSE.

OpenPOM

  • OpenPOM uses a message-passing neural network to predict probabilities for 138 possible odor descriptors per molecule, using an odor dataset of 4,983 molecules curated by merging GoodScents and Leffingwell PMP.OpenPOM provides a standardized benchmark bridging chemical structure to odor.Source: OpenPOM · pp. 33–34

Matrices (AIMLDM)

  • AIMLDM uses quantum-mechanical features as node and edge features alongside chemically grounded featurizers, training on 4,872 molecules with IRLbl-weighted summed binary cross-entropy.Source: Matrices (AIMLDM) · p. 34

LDMDMPNN

  • LDMDMPNN concatenates embeddings from quantum-feature and DMPNN-featurizer branches before a feed-forward network.The quantum branch uses localization and delocalization indices as node and edge features; the chemical branch uses 133 node and 14 edge features.Source: LDMDMPNN · p. 34

LDMGCN

  • LDMGCN achieves better performance than the odor-prediction model that employs the LDM matrix.LDMGCN uses the same GNN architecture as LDMDMPNN but a MolGraph-ConvFeaturizer with 30 node and 11 edge features.Source: LDMGCN · p. 35

MPNN model: Aroma Blend Prediction

  • For binary odor mixtures, the MPNN model groups molecule pairs into a two-component graph and uses graph carving to form a 50:50 train/test split.The evaluation uses 74 shared odor labels, prevents molecule overlap between partitions, and follows the split proposed by Sisson et al.Source: MPNN model: Aroma Blend Prediction · p. 35

S6. Positional and structural encoding

GraphNOSE uses random-walk structural encodings (RWSE) and Laplacian positional encodings (LapPE) to represent molecular-graph topology. RWSE describes local structure through return probabilities, while LapPE uses graph-Laplacian eigenvectors.

S6. Positional and structural encoding

Random-walk structural encodings (RWSE)

  • RWSE represents node i with random-walk return probabilities after k steps, capturing local cycle density and motifs such as aromatic rings and functional groups.The experiments use k = 16.Source: Random-walk structural encodings (RWSE) · p. 36

Laplacian Eigenvector Positional Encodings (LapPE)

  • LapPE derives positional encodings from graph-Laplacian eigenvectors and uses the graph's 8 non-trivial eigenvectors.The eigenvectors are ordered by nondecreasing eigenvalue.Source: Laplacian Eigenvector Positional… · p. 36

S7. Pre-training datasets

The supplementary material catalogs GPSE pretraining datasets and hyperparameter choices, documents held-out AUROC comparisons, and provides odor-space and integrated-gradients visualizations.

S7. Pre-training datasets

S8. Hyperparameter Search

  • RF baselines were tuned over tree settings and fingerprint radius, alongside common hyperparameters such as batch size and learning rate.The listed tree settings include depth, split and leaf sample counts, and features considered for each split.Source: S8. Hyperparameter Search · p. 37
  • KNN tuning covered k for GraphNOSE and Mordred embeddings, plus Mordred fingerprint radius and length; LLM embeddings used a tuned MLP hidden dimension.The LLM embeddings came from MoLFormer and ChemBERTa.Source: S8. Hyperparameter Search · p. 37

mance

  • Tables S4–S6 report held-out-test AUROC across five seeds and training proportions from 30% to 90%, comparing OpenPOM, LDMGCN, and LDMDMPNN with GraphNOSE variants.The captions specify paired t-tests for the comparisons but provide no cell values.Source: Table S4 · p. 39, Table S5 · p. 39, Table S6 · p. 39

S10. KDE Plot for True Labels

  • The true-label odor-space KDE plot uses color for odor categories, shading for broad classes, and contours for specific descriptors.Lavender and roasted are given as examples of specific descriptors.Source: Figure S3 · p. 40

S11. Explainability Analysis of Compounds

  • Integrated-gradients visualizations show atom-level and bond-level contributions for six odor descriptors, with opacity proportional to importance.Green encodes atom contributions and red encodes bond contributions.Source: Figure S4 · p. 41

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