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Learning Repetition-Invariant Representations for Polymer Informatics

Yihan Zhu, Gang Liu, Eric Inae, Tengfei Luo, Meng Jiang

TL;DR

Polymers require representations that are invariant to the number of repeating units, but standard graph neural networks trained on a single repeating unit fail to generalize to longer chains. The authors propose GRIN, which combines maximum-spanning-tree aligned aggregation with repeat-unit augmentation to learn repetition-invariant polymer embeddings, together with dual theoretical guarantees (model-wise and data-wise) that outline when invariance is achieved. They prove that a minimal augmentation of $3$ repeating units suffices and show that GRIN achieves state-of-the-art performance on four homopolymers and two copolymers, with strong extrapolation to unseen repeat counts and robust invariance across sizes. The practical impact is improved, size-robust property prediction for polymers, enabling reliable design and screening of long-chain polymers in various applications.

Abstract

Polymers are large macromolecules composed of repeating structural units known as monomers and are widely applied in fields such as energy storage, construction, medicine, and aerospace. However, existing graph neural network methods, though effective for small molecules, only model the single unit of polymers and fail to produce consistent vector representations for the true polymer structure with varying numbers of units. To address this challenge, we introduce Graph Repetition Invariance (GRIN), a novel method to learn polymer representations that are invariant to the number of repeating units in their graph representations. GRIN integrates a graph-based maximum spanning tree alignment with repeat-unit augmentation to ensure structural consistency. We provide theoretical guarantees for repetition-invariance from both model and data perspectives, demonstrating that three repeating units are the minimal augmentation required for optimal invariant representation learning. GRIN outperforms state-of-the-art baselines on both homopolymer and copolymer benchmarks, learning stable, repetition-invariant representations that generalize effectively to polymer chains of unseen sizes.

Learning Repetition-Invariant Representations for Polymer Informatics

TL;DR

Polymers require representations that are invariant to the number of repeating units, but standard graph neural networks trained on a single repeating unit fail to generalize to longer chains. The authors propose GRIN, which combines maximum-spanning-tree aligned aggregation with repeat-unit augmentation to learn repetition-invariant polymer embeddings, together with dual theoretical guarantees (model-wise and data-wise) that outline when invariance is achieved. They prove that a minimal augmentation of repeating units suffices and show that GRIN achieves state-of-the-art performance on four homopolymers and two copolymers, with strong extrapolation to unseen repeat counts and robust invariance across sizes. The practical impact is improved, size-robust property prediction for polymers, enabling reliable design and screening of long-chain polymers in various applications.

Abstract

Polymers are large macromolecules composed of repeating structural units known as monomers and are widely applied in fields such as energy storage, construction, medicine, and aerospace. However, existing graph neural network methods, though effective for small molecules, only model the single unit of polymers and fail to produce consistent vector representations for the true polymer structure with varying numbers of units. To address this challenge, we introduce Graph Repetition Invariance (GRIN), a novel method to learn polymer representations that are invariant to the number of repeating units in their graph representations. GRIN integrates a graph-based maximum spanning tree alignment with repeat-unit augmentation to ensure structural consistency. We provide theoretical guarantees for repetition-invariance from both model and data perspectives, demonstrating that three repeating units are the minimal augmentation required for optimal invariant representation learning. GRIN outperforms state-of-the-art baselines on both homopolymer and copolymer benchmarks, learning stable, repetition-invariant representations that generalize effectively to polymer chains of unseen sizes.
Paper Structure (43 sections, 2 theorems, 16 equations, 4 figures, 14 tables)

This paper contains 43 sections, 2 theorems, 16 equations, 4 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Invariant Representation Learning
  4. Neural Algorithmic Alignment
  5. Methodology
  6. Problem Definition
  7. Message Passing with Max Aggregation
  8. Theoretical Guarantee of Invariant Representation Learning
  9. Model-Wise: Algorithm Alignment with Maximum-Spanning-Tree
  10. Max vs. Mean, Sum.
  11. Data-Wise: Minimal Repeat Size for Invariant Representation
  12. Hyperchain Message Passing.
  13. Hyperdegree-2 Supervision
  14. Experiments
  15. Experimental Settings
  16. ...and 28 more sections

Key Result

Proposition 3.2

Under def:polymer_hyperchain and let $\theta^\star\!\in\!\arg\min\mathcal{L}(\theta)$, for every test hyperchain $P_m$ with $m\ge2$, the prediction is

Figures (4)

  • Figure 1: Graph representations of homopolymers and block copolymers. Left and right: Prior graph learning methods model polymers as small molecules using a single repeat unit (e.g., -A- or -A-B-B-), which may not capture the long-chain features of polymers. Middle and right: Repeating the unit multiple times better approximates realistic polymer structures and serves as an effective data augmentation strategy.
  • Figure 2: Figure 2: t‑SNE visualization of polymer embeddings from GCN and GRIN (ours) across repeat sizes (1–20 RUs) on the glass transition task. Points are colored by repeat count (light=1RU, dark=20RU). (a) GCN produces inconsistent embeddings for different repeat sizes of the same polymer, clustering by size (same color) rather than identity; our augmentation introduces light-to-dark stripes, indicating improved alignment of repeat variants. (b) GRIN learns repeat‑invariant representations: each polymer’s variants form tight, size‑independent clusters, further improved with augmentation.
  • Figure 3: Performance improvement of GRIN over GRIN-RepAug (without augmentation) under different training schemes (GIN-based). The test sets include 1 repeating unit (a) and 60 repeating units (b) for MeltingTemp (homopolymer) and IP (copolymer), respectively. In both cases, training on the $\{1,3\}$ pair reaches the best improvement, while further increasing the merging size leads to convergence.
  • Figure 4: Property distributions of homopolymer datasets (a) GlassTemp, (b) MeltingTemp, (c) PolyDensity, (d) O$_2$Perm and copolymer datasets (e) Electron Affinity, (f) Ionization Potential. The x‑axis denotes property value and the y‑axis denotes frequency. For clarity, the O$_2$Perm histogram with long tail is truncated to the 0–50 value range.

Theorems & Definitions (3)

  • Definition 3.1: Polymer Hyperchain
  • Proposition 3.2: Latent Repetition‐Invariance
  • Proposition 3.3: Accumulated Gradient Norm