Aligning Molecular Graph Explanations with Chemical Identity via InChIfied Invariants

Problem Statement
Machine learning models for molecular graphs increasingly require explainability to gain the trust of experimental chemists. A critical, yet often overlooked, requirement for chemical meaningfulness is that explanations must be consistent across chemically equivalent graph representations. Currently, different drawings of the same molecule (e.g., varying atom orderings, tautomers, metal disconnections, or charge distributions) can induce different molecular representations in standard featurization methods. This leads to inconsistent predictions and, more critically, divergent attributions (explanations) for the same chemical entity. Existing methods, such as standard Daylight invariants, fail to guarantee that chemically identical structures yield identical feature vectors, thereby undermining the reliability of model explanations.

Methodology: INCHIFIED INVARIANTS
The authors introduce INCHIFIED INVARIANTS, a class of node, edge, and graph features designed to be invariant under transformations that preserve chemical identity. The methodology leverages the International Chemical Identifier (InChI), a standard developed by IUPAC, to define the equivalence relation. The construction mimics the InChI Technical Manual through a sequential 10-step workflow applied to the input molecular graph:

1. Preparation: Calculation of total molecular charge, conversion of aromatic bonds to Kekulé forms (single/double), and marking hydrogen atoms as "phantom" atoms (removing them from the graph while storing their count and isotope information in the attributes of attached heavy atoms).
2. Disconnection: Separation of metal atoms by increasing their charge and decreasing the charge of attached atoms, effectively removing metal-ligand bonds and associated stereochemistry.
3. Normalization: Application of SMARTS-based transformations to redistribute formal charges and bond orders (e.g., handling zwitterions and charge-separated forms).
4. Deprotonation: Removal of protons from positively charged heteroatoms and specific chain patterns to neutralize charges.
5. Neutralization: Attempting to neutralize molecular fragments by adjusting charges and hydrogens on specific heteroatoms.
6. Valence Reduction: Removal of excess hydrogens from non-metal atoms to reduce valence to standard levels.
7. Movable Charge Detection: Identification of alternating bond chains connecting positive charges on nitrogen atoms, tagging them as "aromatic" to handle resonance.
8. Tautomerism Detection: Iterative detection of tautomeric patterns (e.g., keto-enol shifts), removing mobile hydrogens, and tagging bonds as "aromatic" to capture equivalence across tautomers.
9. Hydrogen Isotopes: Handling of mobile protiums, deuteriums, and tritiums by removing phantom tags where appropriate and recording isotope counts.
10. Stereochemistry: Assignment of R/S and E/Z labels based on Cahn–Ingold–Prelog (CIP) rules, dropping labels for cases not treated as stereogenic by InChI.

The final INCHIFIED INVARIANTS consist of:

• Node features: Atomic number, isotope, degree, ring membership, hydrogen counts (total and specific isotopes), and CIP codes.
• Edge features: Bond CIP codes.
• Graph features: Total molecular charge.

Phantom atoms are retained in the graph structure with zero-valued features to preserve original atom indexing for visualization purposes but are ignored during feature extraction.

Key Contributions

1. Novel Featurization: Introduction of a feature set that enforces invariance to chemical identity transformations, serving as a drop-in replacement for standard molecular graph features.
2. Large-Scale Validation: Demonstration on 1 million molecular graphs from PubChem that INCHIFIED INVARIANTS produce identical representations for chemically equivalent graphs (same InChI) in 99.62% of cases, compared to only 0.35% for standard Daylight invariants.
3. Performance Preservation: Validation on MoleculeNet benchmark tasks showing that predictive performance is preserved while significantly improving consistency across alternative graph depictions.
4. Attribution Consistency: Quantitative analysis showing that explanations generated with standard features vary substantially across chemically equivalent graphs, whereas INCHIFIED INVARIANTS enforce near-perfect consistency by construction.
5. Open-Source Release: Provision of software to integrate these invariants into existing machine learning pipelines.

Results

• Representation Consistency: In a dataset of 1 million SMILES strings, INCHIFIED INVARIANTS achieved a 99.62% match rate for graphs sharing the same InChI Key, whereas standard Daylight invariants matched only 0.35%. Conversely, when InChI Keys differed, both methods produced different fingerprints in >99.98% of cases.
• Predictive Performance: On original MoleculeNet test sets, models using INCHIFIED INVARIANTS performed comparably to those using benchmark features. However, on alternative-depiction datasets (graphs of the same molecule generated via SMILES $\to$ InChI $\to$ SMILES conversion), models using INCHIFIED INVARIANTS showed significantly better performance (e.g., lower RMSE on ESOL, FreeSolv, and Lipo; higher ROC-AUC on HIV, BACE, BBBP) than benchmark models. This indicates that benchmark models are sensitive to graph depiction, while INCHIFIED INVARIANTS reduce this sensitivity.
• Explanation Consistency: Using Integrated Gradients on models trained on ClinTox and HIV, the authors measured the Kendall's tau correlation between attributions for pairs of SMILES with the same InChI.
  • With Benchmark features, agreement varied widely (e.g., median Kendall's tau of 0.78 for NeuralFP on HIV, dropping to 0.35 for AttentiveFP).
  • With INCHIFIED INVARIANTS, agreement was nearly perfect (median Kendall's tau of 1.00 across all configurations).
• Computational Overhead: The preprocessing cost is higher than standard Daylight invariants (median runtime increases from ~0.02ms to ~0.29ms for small molecules) but remains negligible relative to model training and inference times.

Significance and Claims
The paper posits that consistency is a necessary (though not sufficient) prerequisite for explanations to be chemically meaningful. By aligning molecular graph representations with the international standard of chemical identity (InChI), INCHIFIED INVARIANTS ensure that two drawings of the same molecule yield the same predictions and attributions. The authors emphasize that this approach does not replace InChI for database indexing but brings the same chemical standard into graph-based machine learning as usable features. The work addresses a gap in the literature where explanation methods (e.g., LIME, SHAP, GNNExplainer) are typically evaluated on fixed inputs without considering whether different valid inputs for the same molecule yield consistent explanations. The authors conclude that INCHIFIED INVARIANTS provide a practical, architecture-agnostic method to improve the reliability of molecular machine learning without requiring changes to downstream models or explanation algorithms.