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From Human Labels to Literature: Semi-Supervised Learning of NMR Chemical Shifts at Scale

Yongqi Jin, Yecheng Wang, Jun-jie Wang, Rong Zhu, Guolin Ke, Weinan E

TL;DR

The paper tackles the data bottleneck in NMR chemical shift prediction by leveraging millions of unassigned literature spectra through a semi-supervised, permutation-invariant learning framework. It replaces combinatorial bipartite matching with a sorting-based loss, enabling stable, scalable training that combines atom-level labels with large-scale unlabeled data. By incorporating solvent embeddings, the approach captures solvent-induced shifts and achieves substantial gains on both the standard NMRShiftDB2 benchmark and the large ShiftDB-Lit dataset, including heteroatom shifts. The study demonstrates that literature-derived, weakly structured data can power accurate, solvent-aware predictions at scale, suggesting a broad potential for data-centric AI in science.

Abstract

Accurate prediction of nuclear magnetic resonance (NMR) chemical shifts is fundamental to spectral analysis and molecular structure elucidation, yet existing machine learning methods rely on limited, labor-intensive atom-assigned datasets. We propose a semi-supervised framework that learns NMR chemical shifts from millions of literature-extracted spectra without explicit atom-level assignments, integrating a small amount of labeled data with large-scale unassigned spectra. We formulate chemical shift prediction from literature spectra as a permutation-invariant set supervision problem, and show that under commonly satisfied conditions on the loss function, optimal bipartite matching reduces to a sorting-based loss, enabling stable large-scale semi-supervised training beyond traditional curated datasets. Our models achieve substantially improved accuracy and robustness over state-of-the-art methods and exhibit stronger generalization on significantly larger and more diverse molecular datasets. Moreover, by incorporating solvent information at scale, our approach captures systematic solvent effects across common NMR solvents for the first time. Overall, our results demonstrate that large-scale unlabeled spectra mined from the literature can serve as a practical and effective data source for training NMR shift models, suggesting a broader role of literature-derived, weakly structured data in data-centric AI for science.

From Human Labels to Literature: Semi-Supervised Learning of NMR Chemical Shifts at Scale

TL;DR

The paper tackles the data bottleneck in NMR chemical shift prediction by leveraging millions of unassigned literature spectra through a semi-supervised, permutation-invariant learning framework. It replaces combinatorial bipartite matching with a sorting-based loss, enabling stable, scalable training that combines atom-level labels with large-scale unlabeled data. By incorporating solvent embeddings, the approach captures solvent-induced shifts and achieves substantial gains on both the standard NMRShiftDB2 benchmark and the large ShiftDB-Lit dataset, including heteroatom shifts. The study demonstrates that literature-derived, weakly structured data can power accurate, solvent-aware predictions at scale, suggesting a broad potential for data-centric AI in science.

Abstract

Accurate prediction of nuclear magnetic resonance (NMR) chemical shifts is fundamental to spectral analysis and molecular structure elucidation, yet existing machine learning methods rely on limited, labor-intensive atom-assigned datasets. We propose a semi-supervised framework that learns NMR chemical shifts from millions of literature-extracted spectra without explicit atom-level assignments, integrating a small amount of labeled data with large-scale unassigned spectra. We formulate chemical shift prediction from literature spectra as a permutation-invariant set supervision problem, and show that under commonly satisfied conditions on the loss function, optimal bipartite matching reduces to a sorting-based loss, enabling stable large-scale semi-supervised training beyond traditional curated datasets. Our models achieve substantially improved accuracy and robustness over state-of-the-art methods and exhibit stronger generalization on significantly larger and more diverse molecular datasets. Moreover, by incorporating solvent information at scale, our approach captures systematic solvent effects across common NMR solvents for the first time. Overall, our results demonstrate that large-scale unlabeled spectra mined from the literature can serve as a practical and effective data source for training NMR shift models, suggesting a broader role of literature-derived, weakly structured data in data-centric AI for science.
Paper Structure (31 sections, 2 theorems, 16 equations, 5 figures, 9 tables)

This paper contains 31 sections, 2 theorems, 16 equations, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Data Source and Preprocessing
  5. Semi-supervised Training Framework
  6. Supervised atom-level loss.
  7. Weakly-supervised molecule-level loss.
  8. Permutation-invariant loss equivalence.
  9. Overall objective.
  10. Model Architecture
  11. Embedding Solvent Information
  12. Experiments
  13. Implementation Details
  14. Overall Performance Comparison
  15. Incorporation of Solvent Information
  16. ...and 16 more sections

Key Result

Lemma 6.1

If $x_1 \leq x_2$ and $y_1 \leq y_2$, then for a monotonically increasing and convex function $f(x)$, we have:

Figures (5)

  • Figure 1: Framework of semi-supervised learning for chemical shift prediction models.
  • Figure 2: (a) Strategies to incorporate solvent information into the model: (1) [CLS]-token injection; (2) atom-token pre-backbone injection; (3) atom-token post-backbone injection; (4) simple correction (applied after prediction). (b) Comparison of these strategies on ShiftDB-Lit in terms of mean absolute error (MAE). The baseline corresponds to the model without solvent information.
  • Figure 3: Model performance under different values of the weakly-supervised weight $\lambda$ (MAE metric).
  • Figure 4: Statistics of NMRShiftDB2 and ShiftDB-Lit datasets.
  • Figure 5: Atom-wise prediction deviations for $^{1}\mathrm{H}$ and $^{13}\mathrm{C}$ NMR shifts under different solvent conditions. The two shaded blue regions indicate where solvent conditioning yields lower errors than the solvent-agnostic baseline.

Theorems & Definitions (4)

  • Lemma 6.1: Monotonicity and Convexity Lemma
  • proof
  • Theorem 6.2: Optimal Bipartite Matching for Monotonically Increasing and Convex Loss Functions
  • proof