Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

XIMP: Cross Graph Inter-Message Passing for Molecular Property Prediction

Anatol Ehrlich, Lorenz Kummer, Vojtech Voracek, Franka Bause, Nils M. Kriege

TL;DR

XIMP tackles molecular property prediction by enabling cross-graph inter-message passing among multiple chemistries-informed abstractions, specifically the junction tree and extended reduced graph, in addition to the molecular graph. By integrating both indirect (I2MP) and direct (DIMP) communication across these abstractions, XIMP expands expressivity beyond prior schemes like HIMP and learns interpretable, chemistry-aligned priors that improve generalization in low-data regimes. Across ten diverse tasks, XIMP outperforms state-of-the-art GNN baselines and fixed fingerprints, particularly on ADMET and pharmacophore-driven properties, while maintaining linear scaling with graph size and quadratic scaling with the number of abstractions. The framework provides a versatile, domain-agnostic approach to multi-view graph learning, with potential applications in drug discovery and beyond, and lays groundwork for extending to additional reductions and protein design.

Abstract

Accurate molecular property prediction is central to drug discovery, yet graph neural networks often underperform in data-scarce regimes and fail to surpass traditional fingerprints. We introduce cross-graph inter-message passing (XIMP), which performs message passing both within and across multiple related graph representations. For small molecules, we combine the molecular graph with scaffold-aware junction trees and pharmacophore-encoding extended reduced graphs, integrating complementary abstractions. While prior work is either limited to a single abstraction or non-iterative communication across graphs, XIMP supports an arbitrary number of abstractions and both direct and indirect communication between them in each layer. Across ten diverse molecular property prediction tasks, XIMP outperforms state-of-the-art baselines in most cases, leveraging interpretable abstractions as an inductive bias that guides learning toward established chemical concepts, enhancing generalization in low-data settings.

XIMP: Cross Graph Inter-Message Passing for Molecular Property Prediction

TL;DR

XIMP tackles molecular property prediction by enabling cross-graph inter-message passing among multiple chemistries-informed abstractions, specifically the junction tree and extended reduced graph, in addition to the molecular graph. By integrating both indirect (I2MP) and direct (DIMP) communication across these abstractions, XIMP expands expressivity beyond prior schemes like HIMP and learns interpretable, chemistry-aligned priors that improve generalization in low-data regimes. Across ten diverse tasks, XIMP outperforms state-of-the-art GNN baselines and fixed fingerprints, particularly on ADMET and pharmacophore-driven properties, while maintaining linear scaling with graph size and quadratic scaling with the number of abstractions. The framework provides a versatile, domain-agnostic approach to multi-view graph learning, with potential applications in drug discovery and beyond, and lays groundwork for extending to additional reductions and protein design.

Abstract

Accurate molecular property prediction is central to drug discovery, yet graph neural networks often underperform in data-scarce regimes and fail to surpass traditional fingerprints. We introduce cross-graph inter-message passing (XIMP), which performs message passing both within and across multiple related graph representations. For small molecules, we combine the molecular graph with scaffold-aware junction trees and pharmacophore-encoding extended reduced graphs, integrating complementary abstractions. While prior work is either limited to a single abstraction or non-iterative communication across graphs, XIMP supports an arbitrary number of abstractions and both direct and indirect communication between them in each layer. Across ten diverse molecular property prediction tasks, XIMP outperforms state-of-the-art baselines in most cases, leveraging interpretable abstractions as an inductive bias that guides learning toward established chemical concepts, enhancing generalization in low-data settings.
Paper Structure (39 sections, 10 theorems, 20 equations, 5 figures, 8 tables)

This paper contains 39 sections, 10 theorems, 20 equations, 5 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Related Work
  4. Preliminaries
  5. Molecular Graphs and Reduced Graphs
  6. Message Passing Graph Neural Networks
  7. Hierarchical Inter-Message Passing
  8. Cross Graph Inter-Message Passing
  9. Input and Formalism
  10. Indirect Inter-Message Passing (I2MP)
  11. Direct Inter-Message Passing (DIMP)
  12. Overall Framework
  13. Expressivity and Complexity
  14. Assumptions and Limitations
  15. Experimental Evaluation
  16. ...and 24 more sections

Key Result

Proposition 3.1

Let $\bm{S}_k \in \{0,1\}^{|V(G)|\times |V(T_k)|}$ and $\bm{S}_i \in \{0,1\}^{|V(G)|\times |V(T_i)|}$ represent left-total relations between the nodes of $G$ and those of $T_k$ and $T_i$, respectively. Let $\widetilde{\bm{S}}_{ik}$ be defined according to Eq. eq:dimp:norm and $\widetilde{\bm{M}}_{k\

Figures (5)

  • Figure 1: Molecular graph abstractions: (\ref{['fig:junction_tree']}) junction tree and (\ref{['fig:erg']}) extended reduced graph. Arrows indicate node mappings between the graphs; their colors encode singleton or group memberships.
  • Figure 2: Visualization of communication flows in XIMP and HIMP. XIMP employs DIMP, I2MP, and MP, while HIMP uses only IMP and MP. Node colors denote graph semantics; arrows indicate bidirectional message passing: red/green for one-to-many ring–abstraction relations, blue for one-to-one cross-graph relations, and yellow for one-to-one within-graph relations.
  • Figure 3: Performance profiles of architectures on ADMET, Potency, and MoleculeNet, computed from Tables \ref{['tab:potency-admet-moleculenet']} and \ref{['tab:potency-admet-moleculenet-extended']}. Panels 1-2 (left): Empirical Cumulative Distribution Functions (ECDFs) of the performance ratio $\rho=\text{MAE}(\text{model},\text{task})/\min_{\text{arch}}\text{MAE}(\text{task})$, where $\rho=1$ is best and $\rho>1$ quantifies degradation; curves closer to the top-left indicate better overall performance. Panels 3-4 (right): discrete summaries across tasks. Bars show the fraction of tasks a model wins ($\rho=1$) or is within a practical tolerance ($\rho\le\tau$, here $\tau=1.05$). Panels 1, 3 use test MAE with hyperparameters chosen by validation; panels 2, 4 use test MAE under best hyperparameters per model and dataset.
  • Figure 4: Validation MAE (x-axis) versus test MAE (y-axis) across hyperparameter configurations. For each task, the lowest test MAE is marked by a green circle and the lowest validation MAE by a red circle. Each panel reports the Pearson correlation ($r$) and $R^2$ score. Points closer to the lower left indicate better performance. To improve readability, non-optimal runs (neither red nor green) were randomly subsampled at $150$ per architecture.
  • Figure 5: Relative test error across ErG/JT settings per architecture with medians across targets. Each panel shows $\Delta$ in milli-MAE by target task (x-axis), colored by whether ErG, JT or a combination is used. Here $\Delta = 1000 \times (\mathrm{MAE} - \min_{\text{cfg}}\mathrm{MAE})$, so the best setting is $0$; the other bars report the gap. Bar labels report exact $\Delta$ values, and a horizontal line at $0$ marks the per-target optimum.

Theorems & Definitions (17)

  • Proposition 3.1
  • Theorem 3.2
  • Proposition 3.3
  • Theorem 9.1: equiv. Theorem \ref{['thm:mono']})
  • proof
  • Proposition 9.2: equiv. Proposition \ref{['prop:stru']}
  • proof
  • Proposition 10.1: equiv. Proposition \ref{['prop:dimpnorm']}
  • proof
  • Lemma 10.2: Row-stochasticity
  • ...and 7 more