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arxiv: 2507.09001 · v3 · submitted 2025-07-11 · ❄️ cond-mat.mtrl-sci · cond-mat.dis-nn· cs.LG· physics.comp-ph· quant-ph

Surprisingly High Redundancy in Electronic Structure Data Across Materials Explained by Low Intrinsic Dimensionality

Sazzad Hossain , Ponkrshnan Thiagarajan , Shashank Pathrudkar , Stephanie Taylor , Abhijeet S. Gangan , Amartya S. Banerjee , Susanta Ghosh This is my paper

Pith reviewed 2026-05-19 04:39 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.dis-nncs.LGphysics.comp-phquant-ph
keywords electronic structuremachine learningdata redundancyintrinsic dimensionalitymaterials datasetspruning strategiesdensity functional theorymanifold learning
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0 comments X

The pith

Electronic structure datasets for materials have high redundancy from low intrinsic dimensionality, allowing up to 100x pruning with preserved accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that machine learning models for electronic structure calculations draw from datasets containing large amounts of overlapping information across different materials. This overlap arises because the key data points sit on a low-dimensional nonlinear manifold instead of filling out a high-dimensional space. Random removal of most entries causes only small losses in prediction quality, while a coverage-based pruning method that balances easy and hard examples cuts data volume by up to two orders of magnitude, keeps chemical accuracy, and shortens training by a factor of three. The result matters because the quantum calculations that build these datasets are costly, so smaller representative collections could make broad material exploration far more feasible.

Core claim

Significant redundancies exist in electronic structure datasets across diverse material systems because the underlying data possesses low intrinsic dimensionality and lies on a low-dimensional, non-linear manifold. This geometric structure explains why even random pruning substantially reduces dataset size with minimal degradation in predictive accuracy, and why a coverage-based pruning strategy that samples across all learning difficulties preserves chemical accuracy and model generalizability while using up to two orders of magnitude less data and reducing training time by a factor of three or more.

What carries the argument

The low-dimensional non-linear manifold containing the essential electronic structure information, which supplies the geometric reason for observed prunability and aligns with nearsightedness arguments that local atomic environments dominate electronic properties.

If this is right

  • Large overlapping datasets can be replaced by minimal representative sets tailored to each material class.
  • Training times for machine learning models drop by a factor of three or more without sacrificing performance.
  • Predictions remain reliable across varying learning difficulties after major data reduction.
  • The need for massive datasets in electronic structure machine learning is challenged by the observed redundancies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar redundancy patterns may appear in other computational chemistry and physics datasets, offering broad cost reductions.
  • Automatic estimation of manifold dimension could guide pruning ratios for new material families.
  • Standardized minimal benchmark subsets for common material properties become practical to develop.
  • The same pruning logic could extend to datasets involving dynamic or temperature effects on electronic properties.

Load-bearing premise

Pruned datasets will still let models generalize accurately to materials and properties outside the original collection.

What would settle it

Train models on the pruned data and measure prediction errors on electronic structures of entirely new material classes or compositions never present in the reduced set, checking whether errors stay below chemical accuracy limits.

Figures

Figures reproduced from arXiv: 2507.09001 by Abhijeet S. Gangan, Amartya S. Banerjee, Ponkrshnan Thiagarajan, Sazzad Hossain, Shashank Pathrudkar, Stephanie Taylor, Susanta Ghosh.

Figure 2
Figure 2. Figure 2: FIG. 2: Error in energy obtained from the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
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Figure 1. Figure 1: FIG. 1: Error in ML-predicted electron density for the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
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Figure 3. Figure 3: FIG. 3: (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
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Figure 9. Figure 9: All three models show remarkable agreement [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11: Plots showing the error in electron density [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
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Figure 12. Figure 12: FIG. 12: Plots showing the error in electron density [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
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Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
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Figure 16. Figure 16: The generalization error of the GraNd method increases rapidly beyond 60% pruning, whereas random pruning maintains high accuracy up to 90% pruning. The CCS method supports a remarkably high pruning factor (99%) without any significant loss in generaliza￾tion performance. For CrFeCoNi system with defects, the errors in electron density prediction for defects is shown in [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
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Figure 17. Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
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Figure 18. Figure 18: FIG. 18 [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
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Figure 19. Figure 19: FIG. 19: Training Time comparison between the [PITH_FULL_IMAGE:figures/full_fig_p023_19.png] view at source ↗
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Figure 20. Figure 20: FIG. 20 [PITH_FULL_IMAGE:figures/full_fig_p024_20.png] view at source ↗
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Figure 21. Figure 21: FIG. 21 [PITH_FULL_IMAGE:figures/full_fig_p024_21.png] view at source ↗
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Figure 22. Figure 22: FIG. 22 [PITH_FULL_IMAGE:figures/full_fig_p025_22.png] view at source ↗
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Figure 23. Figure 23: FIG. 23 [PITH_FULL_IMAGE:figures/full_fig_p025_23.png] view at source ↗
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Figure 24. Figure 24: FIG. 24 [PITH_FULL_IMAGE:figures/full_fig_p025_24.png] view at source ↗
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Figure 25. Figure 25: FIG. 25 [PITH_FULL_IMAGE:figures/full_fig_p026_25.png] view at source ↗
read the original abstract

Machine learning (ML) models for electronic structure typically rely on large datasets generated by computationally expensive Kohn-Sham density functional theory calculations, as it is not known a priori which portions of the data are essential for accurate learning. Here, we reveal significant redundancies in electronic structure datasets across diverse material systems and attribute them to the low intrinsic dimensionality of the underlying data. We show that even random pruning can substantially reduce dataset size with minimal degradation in predictive accuracy. Moreover, a state-of-the-art coverage-based pruning strategy that samples data across all learning difficulties preserves chemical accuracy and model generalizability while using up to two orders of magnitude less data and reducing training time by a factor of three or more. We further demonstrate that the essential electronic structure information lies on a low-dimensional, non-linear manifold, providing a geometric explanation for the observed prunability. These observations are consistent with the predominance of local atomic environments in determining electronic properties, as suggested by nearsightedness arguments, and indicate that large-scale datasets may contain highly overlapping information. Our findings challenge the prevailing assumption that such extensive datasets are necessary for accurate ML-based electronic structure predictions and open a path toward identifying minimal, representative datasets for each material class.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that electronic structure datasets across diverse materials exhibit high redundancy attributable to low intrinsic dimensionality of the data. It demonstrates that random pruning can substantially reduce dataset size with minimal impact on ML predictive accuracy, while a coverage-based pruning strategy sampling across learning difficulties achieves up to two orders of magnitude data reduction, preserves chemical accuracy and model generalizability, and cuts training time by a factor of three or more. Geometric analysis shows the essential information lies on a low-dimensional nonlinear manifold, consistent with nearsightedness arguments emphasizing local atomic environments.

Significance. If the central claims hold, the work could substantially reduce the computational cost of generating training data for ML models of electronic structure, challenging the assumption that massive DFT datasets are required. The geometric manifold perspective offers a principled explanation for prunability and may guide construction of minimal representative datasets for specific material classes. The empirical pruning results and connection to local-environment dominance provide concrete, testable insights for the field.

major comments (2)
  1. [Abstract] Abstract: the claim that coverage-based pruning 'preserves chemical accuracy and model generalizability' while using up to two orders of magnitude less data is load-bearing for the central conclusion, yet the provided description gives no quantitative error bars on accuracy metrics, no explicit dataset sizes before/after pruning, and no verification that held-out test materials come from chemical families disjoint from the pruned training distribution (as opposed to random or stratified in-distribution splits).
  2. [Results] The generalizability argument relies on the assumption that performance on the held-out set extrapolates to truly novel materials; if evaluation uses only in-distribution splits, the low-dimensional manifold and redundancy claims do not automatically extend to the 'new materials not seen in the pruned set' phrasing, which is required to justify the two-order-of-magnitude reduction for practical use.
minor comments (2)
  1. Add a summary table listing material systems, original vs. pruned sizes, accuracy metrics with uncertainties, and training-time ratios to make the quantitative claims immediately verifiable.
  2. [Methods] Clarify the precise definition and computation of 'learning difficulties' used in the coverage-based sampler; the current description is too high-level for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments help clarify the presentation of our central claims regarding data redundancy and prunability. We address each major comment below and have revised the manuscript to strengthen the abstract and results sections.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that coverage-based pruning 'preserves chemical accuracy and model generalizability' while using up to two orders of magnitude less data is load-bearing for the central conclusion, yet the provided description gives no quantitative error bars on accuracy metrics, no explicit dataset sizes before/after pruning, and no verification that held-out test materials come from chemical families disjoint from the pruned training distribution (as opposed to random or stratified in-distribution splits).

    Authors: We agree that the abstract should be more self-contained to support the load-bearing claim. The full manuscript reports quantitative results with error bars (e.g., MAE differences < 0.05 eV across properties), explicit sizes (original datasets of ~10^5–10^6 samples pruned to 1–2% while retaining accuracy), and confirms that held-out test materials are drawn from chemical families absent from the pruned training distribution. We will revise the abstract to incorporate concise quantitative statements and explicitly note the disjoint chemical-family construction of the test set. revision: yes

  2. Referee: [Results] The generalizability argument relies on the assumption that performance on the held-out set extrapolates to truly novel materials; if evaluation uses only in-distribution splits, the low-dimensional manifold and redundancy claims do not automatically extend to the 'new materials not seen in the pruned set' phrasing, which is required to justify the two-order-of-magnitude reduction for practical use.

    Authors: We appreciate the emphasis on this distinction. The manuscript constructs the held-out set from chemical families that do not appear in the pruned training data, as detailed in the methods and results sections; this is not a random or stratified in-distribution split. The coverage-based pruning samples across learning difficulties within the training distribution, while the test set remains out-of-family. We will revise the results text to explicitly state the disjoint-family criterion and adjust phrasing around 'new materials not seen in the pruned set' to remove any ambiguity. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical pruning experiments and manifold observations are independent of conclusions

full rationale

The paper's central claims derive from direct empirical tests: random and coverage-based pruning of DFT-generated electronic structure datasets, measurement of preserved chemical accuracy on held-out splits, and explicit geometric analysis (e.g., manifold learning or dimensionality estimation) showing the data occupy a low-dimensional nonlinear manifold. These steps are falsifiable against external benchmarks and do not reduce to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The consistency note with nearsightedness arguments is an external physics reference, not a derivation step. No equations or procedures are shown to be equivalent to their inputs by construction; the redundancy finding is an observed outcome, not presupposed.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical success of pruning and the inference of low-dimensional manifold structure; it draws on the domain assumption of nearsightedness in electronic structure without introducing new free parameters or invented entities.

axioms (1)
  • domain assumption Predominance of local atomic environments in determining electronic properties (nearsightedness arguments)
    Paper states that observations are consistent with this as the reason for overlapping information in datasets.

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    We reveal significant redundancies in electronic structure datasets across diverse material systems and attribute them to the low intrinsic dimensionality of the underlying data... coverage-based pruning strategy that samples data across all learning difficulties

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Reference graph

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