VIANA: character Value-enhanced Intensity Assessment via domain-informed Neural Architecture

Abstract: Predicting the perceived intensity of odorants remains a fundamental challenge in sensory science due to the complex, non-linear behavior of their response, as well as the difficulty in correlating molecular structure with human perception. While traditional deep learning models, such as Graph Convolutional Networks (GCNs), excel at capturing molecular topology, they often fail to account for the biological and perceptual context of olfaction. This study introduces VIANA, a novel "tri-pillar" framework that integrates structural graph theory, character value embeddings, and phenomenological behavior. This methodology systematically evaluates knowledge transfer across three distinct domains: molecular structure via GCNs, semantic odor character values via Principal Odor Map (POM) embeddings, and biological dose-response logic via Hill's law. We demonstrate that knowledge transfer is not inherently positive; rather, a balance must be maintained in the volume of information provided to the model. While raw semantic data led to "information overload" in domain-informed models, applying Principal Component Analysis (PCA) to distill the 95% most impactful semantic variance yielded a superior "signal distillation" effect. Results indicate that the synthesis of these three knowledge transfer pillars significantly outperforms baseline structural models, with VIANA achieving a peak R^2 of 0.996 and a test Mean Squared Error (MSE) of 0.19. In this context, VIANA successfully captures the physical ceiling of saturation, the sensitivity of detection thresholds, and the nuance of odor character value expression, providing a domain grounded simulation of the human olfactory experience. This research provides a robust framework for digital olfaction, effectively bridging the gap between molecular informatics and sensory perception.

• The paper introduces VIANA, a graph neural network that combines molecular structure, Hill-law dose-response constraints, and PCA-compressed odor embeddings to predict olfactory intensity.
• VIANA achieved a test MSE of 0.19 and R² of 0.996 on 209 molecules, substantially outperforming a structure-only GCN with MSE 195.44 and R² 0.010.
• The results show that distilled semantic features can improve domain-informed models, while raw high-dimensional embeddings may cause information overload and reduce prediction stability.

Motivation and positioning

Predicting perceived odor intensity from molecular structure is complicated by the fact that intensity is not a static molecular property but a sigmoidal function of gas-phase concentration, shaped by receptor saturation kinetics and by neural encoding that relies on response latency and population synchrony rather than a simple rate code. The authors argue that existing ML approaches treat intensity as a static, descriptor-based property and ignore this dose-response structure. VIANA addresses this gap by combining three "pillars" of knowledge transfer: (1) molecular structure via GCNs, (2) phenomenological dose-response logic via Hill's law as an architectural inductive bias, and (3) semantic odor character via embeddings transferred from the Principal Odor Map (POM) of Lee et al., a GNN trained on roughly 5,000 labeled molecules that achieved human-panel-level performance on odor quality prediction.

The work extends a line of domain-informed modeling developed by the same group—PUFFIN for vapor pressure with an Antoine-equation bias node, ExPUFFIN for viscosity with an Andrade bias (37% RMSE reduction over a baseline GNN), and HybridGamma for thermodynamically consistent activity coefficients—and transposes that strategy to sensory science, following the dose-response curve database approach of Wakayama et al.

Methodology

The dataset derives from Wakayama et al.'s dose-response database augmented with vapor pressures retrieved via PubChemPy. For each molecule, a 100-point synthetic concentration grid is generated on a log scale between an estimated detection threshold and saturation defined by vapor pressure; after scrubbing missing values, 209 molecules remain, split 80/10/10 into training/validation/test sets. Each data point pairs the molecular graph (75-dimensional atom features) with log-vapor pressure and concentration scalars.

Six configurations are evaluated:

1. GCN baseline: three GCNConv layers, dual global mean/max pooling, MLP head predicting intensity directly.
2. Domain-informed model: the head instead predicts the three Hill parameters ($I_{max}$, $C$, $D$), with softplus activations enforcing positivity on $I_{max}$ and $D$; the final output is computed through the constrained sigmoidal equation.
3. Character value-enhanced GCN: concatenation of the 128-d structural embedding with the raw 256-d POM embedding, POM contribution weight tuned via Optuna (0.1–2).
4. Character value-enhanced domain-informed model: fused structural + POM features drive prediction of the Hill parameters.
5. Reduced-dimensionality variants: PCA applied to the POM embeddings, retaining components explaining 95% of variance (93 components).
6. VIANA: the full integration—structural graph features plus PCA-distilled POM embeddings feeding the Hill-parameter head.

Hyperparameters are optimized with Optuna (30 trials for the baseline, 50 with MedianPruner for domain-informed variants), tuning learning rate, dropout, hidden units, batch size, and POM weight. Training uses Adam with gradient clipping at norm 1.0 and early stopping (patience 50).

Results

The progression across architectures is stark:

Architecture	Test MSE	$R^2$
GCN baseline	195.44	0.010
Domain-informed	0.46	0.991
Character value-enhanced GCN	23.47	0.881
Character value-enhanced domain-informed	0.55	0.989
Reduced dim. char. value-enhanced GCN	33.46	0.830
VIANA	0.19	0.996

The baseline GCN collapses to near-mean predictions (clustering all outputs in the 10–12 range), demonstrating that structural topology alone cannot capture sensory behavior on this dataset. Introducing Hill's law as an architectural constraint produces the single largest improvement—an MSE reduction of more than two orders of magnitude—because the shift from direct regression to parameter estimation acts as a strong regularizer guaranteeing physically plausible curves. Residual dispersion remains at high intensities (8+), indicating the model still needed qualitative information to pin down $I_{max}$ for complex molecules.

The semantic pillar reveals a genuinely contradictory finding central to the paper's argument: knowledge transfer is not inherently positive. Adding raw 256-d POM embeddings improves the unconstrained GCN substantially ($R^2$ from 0.010 to 0.881) but degrades the domain-informed model (MSE from 0.46 to 0.55). The authors attribute this to "information overload": the Hill parameters are sensitive to input variation, and redundant semantic dimensions compete with critical physical features like vapor pressure, destabilizing gradient descent. Conversely, PCA compression hurts the GCN ($R^2$ drops to 0.830)—which apparently relied on fine-grained semantic detail to compensate for its lack of physical logic—but benefits the domain-informed model, yielding VIANA's peak performance (MSE 0.19, $R^2$ 0.996) with smooth convergence and a near-Gaussian residual distribution centered at zero. Per-molecule comparisons confirm that VIANA tracks both extremes of the intensity range accurately (e.g., p-tolualdehyde predicted at 15.10 vs. true 15.19; alpha-terpineol at 0.83 vs. true 0.77).

The implication is that the optimal form of auxiliary knowledge depends on the presence of an architectural inductive bias: unconstrained models benefit from maximum feature granularity, while constrained models require distilled, low-noise inputs to preserve stability of the phenomenological parameters.

Limitations and open questions

Several constraints bound these results. The training corpus contains only 209 molecules with synthetic dose-response points interpolated from a curve database rather than measured directly, so the reported $C$0 reflects fit to modeled—not experimentally observed—intensity data, and generalization to broader chemical space is untested. The paper itself concedes that validation is bounded by the existing experimental landscape and that a larger, more diverse intensity repository would be essential. Subject-level variability (genetic receptor differences, cognitive and demographic modifiers) is discussed as motivation but is not modeled; the framework predicts a population-level percept without accounting for inter-individual differences. Mixture effects, which are central to perfumery practice, are also outside the current scope. Whether the PCA-based distillation threshold (95% variance) is robust across datasets, or whether the "information overload" effect persists with larger training corpora, remain open questions.

Conclusion

VIANA demonstrates that olfactory intensity prediction benefits from a deliberate composition of knowledge sources: structural graph encoding, hard-coded sigmoidal dose-response physics, and semantically distilled odor-character embeddings. Its principal empirical finding—that raw high-dimensional transfer can harm a domain-constrained model while dimensionality-reduced transfer helps it—offers a concrete design principle for domain-informed architectures beyond olfaction. The framework's practical utility, however, depends on validation against directly measured human intensity data across a wider chemical space, which the current 209-molecule, database-derived dataset does not provide.