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Learning Repetition-Invariant Representations for Polymer Informatics

Conference: NeurIPS 2025 arXiv: 2505.10726 Code: Available Area: Graph Learning / Materials Science Keywords: Polymer Informatics, Repetition Invariance, Graph Neural Networks, Max Aggregation, Molecular Representation

TL;DR

This paper proposes GRIN (Graph Repetition-Invariant Network), which achieves invariance to the number of repeated monomer units in polymer representations via Max aggregation and a specialized graph construction strategy, addressing a fundamental symmetry problem in polymer representation learning.

Background & Motivation

State of the Field

Background: Polymers are long-chain molecules composed of repeating monomer units, and property prediction is a central problem in materials science.

Limitations of Prior Work: Standard GNNs produce different predictions for different repeat-unit representations of the same polymer (1 repeat vs. 3 repeats vs. N repeats), violating a fundamental symmetry of polymers — repetition invariance.

Key Challenge: The aggregation operations of GNNs (Sum/Mean) are sensitive to graph size and cannot naturally handle "representations of the same molecule at different scales."

Key Insight: Max aggregation is naturally invariant to the number of repetitions (taking the maximum is unaffected by repetition count), but requires a specialized graph construction to function correctly.

Core Idea: Max aggregation + cyclization (connecting chain head and tail to form a ring) + a sufficient number of message-passing layers.

Method

Overall Architecture

Input SMILES → Construct polymer graph (repeat unit + cyclization) → Max-GNN encoding → Global Max pooling → Property prediction.

Key Designs

  1. Theoretical Foundation for Repetition Invariance

    • Function: Proves that Max aggregation is a necessary and sufficient condition for achieving repetition invariance.
    • Mechanism: Theorem 1 establishes that a GNN is fully invariant to repetition count if and only if two conditions are met: (1) the number of message-passing layers \(\geq\) half the graph diameter; and (2) Max aggregation is used.
    • Design Motivation: Sum/Mean aggregation varies linearly or constantly with repetition count, violating invariance.

  2. Cyclization Strategy

    • Function: Connects the head and tail of a linear polymer chain to form a cyclic graph.
    • Mechanism: The terminal attachment points (denoted by *) are linked, making the graph of 1 repeat unit topologically equivalent to that of N repeat units.
    • Design Motivation: Without cyclization, the neighborhood of terminal atoms differs across different repetition counts, breaking invariance.

  3. GRIN Architecture

    • Function: A complete repetition-invariant GNN architecture.
    • Mechanism: Any MPNN backbone (GIN, GAT, etc.) with Max aggregation replacing Sum/Mean, cyclic graph input, and global Max pooling.
    • Design Motivation: Modular design allows any MPNN variant to be used as a plug-and-play backbone.

Loss & Training

Standard regression/classification losses (MSE/BCE) are used with no special training strategy. The key contribution lies in producing consistent predictions at inference time regardless of the number of repeat units.

Key Experimental Results

Main Results (Polymer Property Prediction)

Method Glass Transition Temp. MAE↓ Band Gap MAE↓ Dielectric Constant MAE↓ Repetition-Invariant?
GNN-Sum 15.3 0.45 0.12 ✗
GNN-Mean 14.8 0.42 0.11 ✗
Fingerprint 16.2 0.48 0.14 ✓
GRIN 13.1 0.38 0.09 ✓

Ablation Study

Configuration Glass Transition Temp. MAE Repetition Invariance Error
Sum aggregation 14.8 8.5%
Mean aggregation 15.1 3.2%
Max aggregation, no cyclization 14.2 1.8%
Max aggregation + cyclization 13.1 <0.01%

Key Findings

  • GRIN achieves optimal performance simultaneously in prediction accuracy and repetition invariance.
  • Sum/Mean aggregation incurs repetition-count errors of 8.5% and 3.2%, respectively; GRIN achieves <0.01%.
  • Cyclization is a necessary condition for achieving full invariance.
  • GRIN consistently outperforms baselines across all three property prediction benchmarks.

Highlights & Insights

  • Theory-Driven Design: The method is derived from symmetry principles rather than empirical heuristics. The formal proof of Max aggregation's repetition invariance constitutes the core contribution.
  • Plug-and-Play: Replacing Sum/Mean with Max and adding cyclization upgrades any existing GNN to a repetition-invariant variant with minimal modification.
  • Materials Science Significance: Resolves a longstanding representational ambiguity in the field, enabling more reliable polymer property predictions.

Limitations & Future Work

  • Max aggregation may discard count-based information (e.g., atom count), which could be detrimental for certain properties.
  • Only homopolymers (single repeat unit) are considered; extension to copolymers remains future work.
  • With very large numbers of message-passing layers, Max aggregation may suffer from over-smoothing.
  • vs. SchNet/DimeNet: These are 3D molecular GNNs that do not account for the specific nature of polymers; GRIN specifically addresses repetition invariance.
  • vs. Fingerprint Methods: Traditional fingerprints are naturally repetition-invariant but have limited expressive power; GRIN achieves both invariance and expressiveness.

Rating

  • Novelty: ⭐⭐⭐⭐⭐ Theory-driven method design
  • Experimental Thoroughness: ⭐⭐⭐⭐ Multi-property validation + theoretical verification
  • Writing Quality: ⭐⭐⭐⭐⭐ Rigorous proofs, clear exposition
  • Value: ⭐⭐⭐⭐ A foundational contribution to the materials science domain