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A tomographic interpretation of structure-property relations for materials discovery

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A material is not its representation; composition-only models work when a dataset's formulas and structures are nearly one-to-one, and the paper formalizes this with an information-theoretic 'tomographic' view of materials.

desk verdict A genuinely new framing for why simple representations work in materials ML, but the verification doesn't directly test the central claim. read the letter →

arxiv 2501.18163 v1 pith:CJ6VOL5O submitted 2025-01-30 cond-mat.mtrl-sci physics.comp-ph

Raul Ortega-Ochoa , Alán Aspuru-Guzik , Tejs Vegge , Tonio Buonassisi This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.comp-ph
keywords materialsinformaticscomposition-basedmodelsstructure-propertyrelationsinformationtheorypartialdecompositionmachinelearningrepresentationstomographicinterpretation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper addresses a puzzle in machine learning for materials: models that see only the chemical formula, with no crystal structure, often predict properties almost as well as models that see the full structure. The authors argue that this is not a paradox but a consequence of information redundancy: a formula strongly constrains the allowed structures, and many datasets contain only one or a few polymorphs per formula, so formula and structure can be nearly interchangeable within the data. To make this precise, they introduce a 'tomographic interpretation' in which a material is an unseen essence and both representations and measured properties are projections (shadows) of that essence. Using ideas from information theory, and specifically partial information decomposition, they explain when adding one property to a representation should improve prediction of another. They verify the picture with an exhaustive battery of experiments in which each of thirteen properties is added to composition-based and structure-based representations and the change in prediction error on nine target properties is measured.

What carries the argument

The machinery is the tomographic interpretation combined with partial information decomposition (PID), a way of splitting the information that two sources carry about a target into unique, redundant, and synergetic parts. The tomographic interpretation redefines the learning problem: instead of mapping material to property, the model maps one projection of the material to another, and the sufficient information needed for the map is task-dependent. PID then decomposes the information that two source variables (e.g., a base representation and an added property) carry about a target into unique, redundant, and synergetic components; the synergetic component explains why a property can help even when it shares no direct information with the target. The empirical instrument is the feature importance, defined as the relative change in test mean absolute error when a property is added, measured over five seeds with a 60-20-20 split for both a composition-only and a composition-plus-structure version of the same graph neural network.

What would settle it

Take a dataset that contains multiple structurally distinct polymorphs for the same chemical formula with differing values of a target property, and train a composition-only and a structure-based model on it. If the composition-only model's error is much larger, the near-one-to-one correspondence that the argument depends on is absent in that dataset.

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Extended reading notes

Core claim

The paper's central claim is that a material should not be identified with any of its representations. A representation is an approximation of an inaccessible 'material essence,' and a property is also a projection of the same essence; the boundary between representation and property is blurry. The discovery that resolves the composition-only puzzle is that, within typical datasets, the chemical formula and the crystal structure carry nearly the same information: elemental composition and stoichiometry limit the number of polymorphs, and many datasets include only a subset of those polymorphs, so there can be a near one-to-one correspondence between formula and structure. In that regime the structure adds little information for a given task, and the learning problem can be solved from composition alone. The experiments support the framework by showing that a property added to a representation improves prediction only when it encodes non-redundant information about the target, and that structure-specific properties such as spacegroup, density, and volume are already captured in a structure-based representation.

Load-bearing premise

The load-bearing premise of the experimental section is that relative change in test mean absolute error when a feature is added faithfully reflects the mutual-information content of that feature for the target, a proxy the paper itself describes as indirect and does not prove.

Editorial extensions

If this is right

  • If formula and structure are nearly redundant within a dataset, then composition-based screening is a sound first step in discovery campaigns, and inverse design from formula becomes closer to designing the material itself.
  • Property augmentation should be guided by whether the added property supplies unique or synergetic information for the target, not by generic physical intuition about what 'should' matter.
  • Datasets with many polymorphs per formula are precisely where structure-based representations should retain an advantage over composition-only ones.
  • The framework makes forward and inverse design two instances of the same operation, mapping between low- and high-information projections, so tools developed for one can transfer to the other.
  • Counting the number of distinct structures per formula in a dataset gives a practical, a priori indicator of when composition-only models will be sufficient.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the framework would compute or estimate the actual mutual information between formula, structure, and target properties on datasets with known polymorph distributions and compare it with the feature-importance proxy; if the two diverge, the proxy needs correction before the causal story is fully established.
  • The directional asymmetry observed between properties (total magnetization helps energy-per-atom prediction far more than the reverse) suggests that experimental measurement campaigns could prioritize properties by their unique information contribution to a target, a prioritization the paper does not itself derive.
  • The tomographic view implies that multi-property conditioning in generative inverse design should improve reconstruction fidelity up to the point where added properties are fully redundant, which could be tested by measuring how generated-material validity scales with the number of conditioning properties.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a conceptual 'tomographic interpretation' in which a material is a latent essence M, and both representations (e.g., chemical formula, crystal structure) and properties are projections of M. It defines sufficient and minimally sufficient representations via mutual information I(R(M);M), invokes partial information decomposition (PID) to explain when augmenting a representation with an additional property should help, and proposes that composition-based ML succeeds because compositions constrain structures and dataset biases suppress polymorph diversity. To 'verify' the framework, the authors train modified CGCNN models on Materials Project data with composition-only and composition-structure baselines, add each of 13 properties as an extra feature, and measure relative test-MAE changes across 9 target properties; results are presented as heatmaps and summarized in Table 1, with structure-dependent properties identified as being embedded in the structure representation.

Significance. The value of the paper is in providing a vocabulary and an interpretive lens for a genuine empirical phenomenon: simple representations sometimes perform well in materials ML, and property augmentation has task-dependent benefits. The experimental matrix is large and systematic (2340 trained models across two baselines, 9 targets, 13 augmenting properties, and five seeds), and the observation that positive mean changes are generally not robust across seeds is a useful sanity check. However, the central explanatory claim—that composition suffices because of dataset-limited polymorphs—is not directly tested, and the information-theoretic interpretation of the experiments rests on an unvalidated proxy. The contribution is therefore best assessed as an interesting hypothesis-generating framework plus a preliminary augmentation study, rather than a verified theory.

major comments (4)
  1. [Section 2.1, footnote 7] The central causal mechanism—that composition is sufficient because elemental composition and stoichiometry constrain structure and because datasets limit the number of polymorphs—is not tested by the reported experiments. Footnote 7 reports that 59.08% of the Materials Project snapshot has a one-to-one material–formula correspondence, but this does not establish a near one-to-one correspondence for the other 41% of entries, and no conditional entropy H(structure|formula) is computed for the dataset actually used. The experiments in Section 2.2 compare augmented versus non-augmented representations, not composition-only versus composition-with-structure test errors, so they cannot determine whether structure is redundant given composition. Please add a direct comparison (same architecture, same splits, with and without structure), stratify the performance gap by the number of polymorphs per formula, and report H(structure|formula), or else explicitly recast the claim as a hypothesis rather than a verified result.
  2. [Section 2.2] The paper identifies feature importance (relative change in test MAE) with the mutual-information quantities in the PID decomposition without validation. The sentence 'we aim to indirectly assess this quantity through the feature importance' is an assertion, not an argument; relative test-MAE changes can be driven by optimization ease, model capacity, regularization, feature scaling, and finite-sample overfitting. The theoretical statement that performance cannot be harmed by including more information because mutual information is non-negative applies to expected information, not to an empirical test error on a finite dataset, and footnote 8 already concedes that poorly scaled features can hurt. Because the PID interpretation of Figures 4 and 5 and the construction of Table 1 depend on this proxy, please validate the proxy (for example, on synthetic data with known PID/MI terms, or by comparing against direct MI estimates on low-dimensional subsets) or restrict the conclusions to observations about test-error changes.
  3. [Section 2.2, Table 1] The significance criterion used throughout the results is not statistically valid. The authors call the min-max range over five repetitions a 'confidence interval,' but a range of five values is not a confidence interval and carries no stated error control; the rule that significance requires the min-max range not to overlap zero is an ad hoc criterion, and no multiple-comparison correction is applied across the 9 targets and 13 augmenting properties. Since Table 1 and the conclusions about which properties 'had an impact' are derived from this criterion, please report the per-seed/split distributions, use a proper paired test (e.g., a paired bootstrap or signed test), and justify or correct for multiple comparisons.
  4. [Section 2.1, Eq. (3)] The empirical verification is partly circular. The framework asserts that if adding a property improves performance, the property must encode unique or synergistic information about the target; but 'improvement' is exactly the operational definition of feature importance used in the experiments, so the observed improvements are a restatement of the proxy rather than an independent confirmation of the tomographic or PID interpretation. The heatmaps are genuine empirical observations about property augmentation, but they do not test the core framework claims—that representations are projections of a material essence, that all projections together determine the essence, or that sufficiency is task-dependent. Please separate the confirmable empirical predictions (e.g., under controlled normalization and sufficient data, augmentation does not harm; augmentation benefits are asymmetric) from the post-hoc interpretations, and state which framework claims the experiments could in principle falsify.
minor comments (6)
  1. [Section 2.2] The experimental count appears inconsistent: the text says the process is repeated for 'five different dataset splits' after stating that a constant 60-20-20 split was used for five seeds, while footnote 9 counts five seeds and two models per setting (giving 2340 models). Please clarify the number of seeds, splits, and the total model count.
  2. [Figures 4 and 5] The heatmaps should include an explicit colorbar and a precise definition of the plotted quantity (percentage change in test MAE of augmented versus non-augmented representation), since the text's blue/red significance discussion depends on that scale.
  3. [Section 2.1] The notation 'I(Ra(M); M) > I(Rb(M); M) ∀M ∈ M' conflates the material as a random variable with the set of materials; please introduce a random-variable convention (e.g., lowercase m for a sample, M for the random variable) to make the information-theoretic statements precise.
  4. [Section 3, Table 1] The column header 'In Struct. but not Comp.' is confusing: it lists properties that improve the composition-restricted baseline but not the composition-structure baseline, meaning the structure representation already captures that information. Please rename the column or define it more explicitly.
  5. [Section 4] The concluding statement that multi-property inverse design should improve with more properties is not derived from the formalism and ignores finite-sample and redundancy considerations; please qualify it.
  6. [References] Reference [15] is cited without a venue or identifier; please provide the preprint or publication details.

Circularity Check

1 steps flagged · score 4.0 of 10

The property-augmentation explanation in the verification section is partly definitional, but the paper's core tomographic framework is a conceptual proposal rather than a derived prediction.

  1. self definitional [Section 2.2, Verification Experiments (paragraph defining feature importance)]
    "In terms of feature importance, adding some new property/feature encoding non-redundant information needed for predicting some target will result in a decrease in the error with respect to the non-augmented baseline, and in the case it does not encode relevant information, or the information was already accounted for, then there will be no change in the error with respect to the non-augmented baseline, because the performance can not be harmed by including more information since mutual information is non-negative."

    The paper defines feature importance as relative change in test MAE and then uses that same definition to conclude that a property which reduces MAE encodes non-redundant task information. Thus the 'verification' that property augmentation works because of unique or synergistic PID terms is a restatement of the operational definition rather than an independent test. Any significant negative feature importance is reinterpreted as evidence for the PID explanation simply because the explanation was defined in terms of performance change. This makes the confirmatory part of the framework self-definitional.

full rationale

The paper does not derive its central composition-sufficiency claim from the experiments. The causal mechanism of §2.1, that composition and stoichiometry constrain structure and that datasets further limit polymorphs, is a plausible conjecture supported only by the footnote-7 statistic that 59.08% of Materials Project entries have one-to-one formula-to-material correspondence, which is not a near-one-to-one result. The verification experiments measure a different quantity: they record relative MAE changes when a third property is added to composition or composition-structure representations, interpreted through an unvalidated feature-importance proxy for mutual information. The main circular step is the identification of 'encoding non-redundant information' with 'decreasing test error,' which makes the observed heatmaps illustrations of the definition rather than tests of an independent quantitative prediction. The self-citation to Tian et al. (reference [15]), which includes a co-author of this paper, is not load-bearing for the framework's central claim. Overall, the paper is a conceptual framework with genuine empirical observations, but the verification of the property-augmentation explanation is partly circular; the central composition-sufficiency conjecture remains under-supported rather than circularly derived.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The framework's central claims rest on a small set of postulates: an unobservable material essence, a tomographic completeness principle, and a proxy assumption that feature importance measures information. None of these is independently validated, and the proxy assumption is the most load-bearing for the experiments.

free parameters (1)
  • Significance criterion for feature importance = Non-overlap of min-max confidence interval with 0%
    Chosen to decide which properties have a 'meaningful impact'; this threshold influences the summary in Table 1.
assumptions (4)
  • domain assumption The material essence exists and is only accessible through projections
    Postulated in Section 2.1 to ground the definition of representations and properties.
  • ad hoc to paper All projections together fully determine the material essence
    The tomographic analogy is declared without proof; Section 2.1 'if we have all the possible projections... then we have as much information as the essence itself'.
  • domain assumption Relative MAE change (feature importance) is a valid proxy for mutual information content
    Section 2.2: 'we aim to indirectly assess this quantity through the feature importance'.
  • standard math Data processing inequality and non-negativity of mutual information
    Used to argue that adding a feature cannot reduce the information available in the input; Section 2.1.
invented entities (1)
  • Material essence
    purpose: An abstract, unobservable object of which representations and properties are projections; serves as the anchor for defining information content and sufficiency.
    No operational definition or falsifiable handle is given; it functions as a philosophical construct.

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Cite this review

Pith. "Pith review of A tomographic interpretation of structure-property relations for materials discovery." pith.science (2026). https://pith.science/paper/CJ6VOL5O

@misc{pith2026250118163,
  author       = {Pith},
  title        = {Pith review of: A tomographic interpretation of structure-property relations for materials discovery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CJ6VOL5O}},
  note         = {Machine review of arXiv:2501.18163}
}
read the original abstract

Recent advancements in machine learning (ML) for materials have demonstrated that "simple" materials representations (e.g., the chemical formula alone without structural information) can sometimes achieve competitive property prediction performance in common-tasks. Our physics-based intuition would suggest that such representations are "incomplete", which indicates a gap in our understanding. This work proposes a tomographic interpretation of structure-property relations of materials to bridge that gap by defining what is a material representation, material properties, the material and the relationships between these three concepts using ideas from information theory. We verify this framework performing an exhaustive comparison of property-augmented representations on a range of material's property prediction objectives, providing insight into how different properties can encode complementary information.

Figures

Figures reproduced from arXiv: 2501.18163 by the authors.

Figure 1
Figure 1. With enough shadows, we can uniquely identify the underlying object. Given the projections [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. PID diagram of the unique, synergetic and redundant information contributions of two source [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Schematic process of calculating feature importance for “Property A” in the task of predicting [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Percentage change in MAE of an augmented vs a non-augmented composition-structure rep [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Percentage change in MAE of an augmented vs a non-augmented composition-restricted rep [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Reference graph

Works this paper leans on

40 extracted references · 39 canonical work pages · cited by 1 Pith paper

  1. [1]

    Inverse design in search of materials with target functionalities

    Alex Zunger. Inverse design in search of materials with target functionalities. Nature Reviews Chemistry, 2(4):0121, 03 2018

    work page 2018

  2. [2]

    Inverse molecular design using ma- chine learning: Generative models for matter engineering

    Benjamin Sanchez-Lengeling and Al´ an Aspuru-Guzik. Inverse molecular design using ma- chine learning: Generative models for matter engineering. Science, 361(6400):360–365, 2018

    work page 2018

  3. [3]

    Austin H. Cheng, Cher Tian Ser, Marta Skreta, Andr´ es Guzm´ an-Cordero, Luca Thiede, Andreas Burger, Abdulrahman Aldossary, Shi Xuan Leong, Sergio Pablo-Garc ´ ıa, Felix Strieth-Kalthoff, and Al´ an Aspuru-Guzik. Spiers memorial lecture: How to do impactful research in artificial intelligence for chemistry and materials science. Faraday Discuss., pages –, 2025

    work page 2025

  4. [4]

    Formation energy prediction of crystalline com- pounds using deep convolutional network learning on voxel image representation

    Ali Davariashtiyani and Sara Kadkhodaei. Formation energy prediction of crystalline com- pounds using deep convolutional network learning on voxel image representation. Commu- nications Materials, 4(1):105, 12 2023

    work page 2023

  5. [5]

    Descriptor engineering in machine learning re- gression of electronic structure properties for 2d materials

    Minh Tuan Dau, Mohamed Al Khalfioui, Adrien Michon, Antoine Reserbat-Plantey, St´ ephane V´ ezian, and Philippe Boucaud. Descriptor engineering in machine learning re- gression of electronic structure properties for 2d materials. Scientific Reports, 13(1):5426, 04 2023

    work page 2023

  6. [6]

    Interplay between superconductivity and the strange-metal state in fese

    Xingyu Jiang, Mingyang Qin, Xinjian Wei, Li Xu, Jiezun Ke, Haipeng Zhu, Ruozhou Zhang, Zhanyi Zhao, Qimei Liang, Zhongxu Wei, Zefeng Lin, Zhongpei Feng, Fucong Chen, Peiyu Xiong, Jie Yuan, Beiyi Zhu, Yangmu Li, Chuanying Xi, Zhaosheng Wang, Ming Yang, Junfeng Wang, Tao Xiang, Jiangping Hu, Kun Jiang, Qihong Chen, Kui Jin, and Zhongxian Zhao. Interplay bet...

    work page 2023

  7. [7]

    Exploring diamondlike lattice thermal conductivity crystals via feature-based transfer learning

    Shenghong Ju, Ryo Yoshida, Chang Liu, Stephen Wu, Kenta Hongo, Terumasa Tadano, and Junichiro Shiomi. Exploring diamondlike lattice thermal conductivity crystals via feature-based transfer learning. Phys. Rev. Mater. , 5:053801, 05 2021

    work page 2021

  8. [8]

    Ludwig, and Bakhtiyor Ra- sulev

    Rahil Ashtari Mahini, Gerardo Casanola-Martin, Simone A. Ludwig, and Bakhtiyor Ra- sulev. Mixturemetrics: A comprehensive package to develop additive numerical features to describe complex materials for machine learning modeling. SoftwareX, 28:101911, 2024

    work page 2024

Show all 40 references
  1. [9]

    Benchmarking materials property prediction methods: the matbench test set and automatminer reference algorithm

    Alexander Dunn, Qi Wang, Alex Ganose, Daniel Dopp, and Anubhav Jain. Benchmarking materials property prediction methods: the matbench test set and automatminer reference algorithm. npj Computational Materials , 6(1):138, 09 2020

    2020

  2. [10]

    Matbench leaderboard-property: General purpose algorithms, 2024

    MatBench. Matbench leaderboard-property: General purpose algorithms, 2024. Accessed: 1 November 2024. 11

    2024

  3. [11]

    Lunger, Aik Rui Tan, Mingrou Xie, Jiayu Peng, and Rafael G´ omez-Bombarelli

    James Damewood, Jessica Karaguesian, Jaclyn R. Lunger, Aik Rui Tan, Mingrou Xie, Jiayu Peng, and Rafael G´ omez-Bombarelli. Representations of materials for machine learning. Annual Review of Materials Research , 53(Volume 53, 2023):399–426, 2023

    2023

  4. [12]

    Kauwe, Ryan J

    Anthony Yu-Tung Wang, Steven K. Kauwe, Ryan J. Murdock, and Taylor D. Sparks. Compositionally restricted attention-based network for materials property predictions. npj Computational Materials , 7(1):77, 05 2021

    2021

  5. [13]

    Predicting materials properties without crystal struc- ture: Deep representation learning from stoichiometry

    Rhys EA Goodall and Alpha A Lee. Predicting materials properties without crystal struc- ture: Deep representation learning from stoichiometry. Nature Communications, 11(1):1–9, 2020

    2020

  6. [14]

    Large language models for inorganic synthesis predictions

    Seongmin Kim, Yousung Jung, and Joshua Schrier. Large language models for inorganic synthesis predictions. Journal of the American Chemical Society , 146(29):19654–19659, 07 2024

    2024

  7. [15]

    What information is necessary and sufficient to predict materials properties using machine learning?, 2022

    Siyu Isaac Parker Tian, Aron Walsh, Zekun Ren, Qianxiao Li, and Tonio Buonassisi. What information is necessary and sufficient to predict materials properties using machine learning?, 2022

    2022

  8. [16]

    Anubhav Jain, Shyue Ping Ong, Geoffroy Hautier, Wei Chen, William Davidson Richards, Stephen Dacek, Shreyas Cholia, Dan Gunter, David Skinner, Gerbrand Ceder, and Kristin A. Persson. Commentary: The Materials Project: A materials genome approach to accelerating materials innov...

    2013

  9. [17]

    Deep learning and the information bottleneck principle

    Naftali Tishby and Noga Zaslavsky. Deep learning and the information bottleneck principle. In 2015 IEEE Information Theory Workshop (ITW) , pages 1–5, 2015

    2015

  10. [18]

    Opening the black box of deep neural networks via information, 2017

    Ravid Shwartz-Ziv and Naftali Tishby. Opening the black box of deep neural networks via information, 2017

    2017

  11. [19]

    3d reconstruction from cryo-em projection images using two spherical embeddings

    Yonggang Lu, Jiaxuan Liu, Li Zhu, Bianlan Zhang, and Jing He. 3d reconstruction from cryo-em projection images using two spherical embeddings. Communications Biology , 5(1):304, 04 2022

    2022

  12. [20]

    Paris and J

    M. Paris and J. ˇReh´ aˇ cek, editors.Quantum State Estimation , volume 649 of Lecture Notes in Physics . Springer Berlin Heidelberg, 2004

    2004

  13. [21]

    Castelli, Thomas Olsen, Soumendu Datta, David D

    Ivano E. Castelli, Thomas Olsen, Soumendu Datta, David D. Landis, Søren Dahl, Kris- tian S. Thygesen, and Karsten W. Jacobsen. Computational screening of perovskite metal oxides for optimal solar light capture. Energy Environ. Sci. , 5:5814–5819, 2012

    2012

  14. [22]

    Information theoretical analysis of multivariate correlation

    Satosi Watanabe. Information theoretical analysis of multivariate correlation. IBM Journal of Research and Development , 4(1):66–82, 1960

    1960

  15. [23]

    W.R. Garner. Uncertainty and Structure as Psychological Concepts . Wiley, 1962

    1962

  16. [24]

    Studen´ y and J

    M. Studen´ y and J. Vejnarov´ a.The Multiinformation Function as a Tool for Measuring Stochastic Dependence, pages 261–297. Springer Netherlands, Dordrecht, 1998

    1998

  17. [25]

    A measure for brain complexity: relating func- tional segregation and integration in the nervous system

    G Tononi, O Sporns, and G M Edelman. A measure for brain complexity: relating func- tional segregation and integration in the nervous system. Proceedings of the National Academy of Sciences, 91(11):5033–5037, 05 1994

    1994

  18. [26]

    William J. McGill. Multivariate information transmission. Psychometrika, 19(2):97–116, 06 1954. 12

    1954

  19. [27]

    Multiple mutual informations and multiple interactions in frequency data

    Te Sun Han. Multiple mutual informations and multiple interactions in frequency data. Information and Control , 46(1):26–45, 1980

    1980

  20. [28]

    A. J. Bell. The co-information lattice. In ica03, pages 921–926, Nara, Japan, 04 2003

    2003

  21. [29]

    How independent are the messages carried by adjacent inferior temporal cortical neurons? Journal of Neuroscience , 13(7):2758–2771, 1993

    TJ Gawne and BJ Richmond. How independent are the messages carried by adjacent inferior temporal cortical neurons? Journal of Neuroscience , 13(7):2758–2771, 1993

    1993

  22. [30]

    Williams and Randall D

    Paul L. Williams and Randall D. Beer. Nonnegative decomposition of multivariate infor- mation, 2010

    2010

  23. [31]

    Kay, Joseph T

    Michael Wibral, Viola Priesemann, Jim W. Kay, Joseph T. Lizier, and William A. Phillips. Partial information decomposition as a unified approach to the specification of neural goal functions. Brain and Cognition , 112:25–38, 2017. Perspectives on Human Probabilistic Inferences...

    2017

  24. [32]

    Tianfan Jin, Veerupaksh Singla, Hsuan-Hao Hsu, and Brett M. Savoie. Large property models: a new generative machine-learning formulation for molecules. Faraday Discuss., 256:104–119, 2025

    2025

  25. [33]

    Aberle, Shijing Sun, Xiaonan Wang, Yi Liu, Qianx- iao Li, Senthilnath Jayavelu, Kedar Hippalgaonkar, Yousung Jung, and Tonio Buonassisi

    Zekun Ren, Siyu Isaac Parker Tian, Juhwan Noh, Felipe Oviedo, Guangzong Xing, Jiali Li, Qiaohao Liang, Ruiming Zhu, Armin G. Aberle, Shijing Sun, Xiaonan Wang, Yi Liu, Qianx- iao Li, Senthilnath Jayavelu, Kedar Hippalgaonkar, Yousung Jung, and Tonio Buonassisi. An invertible c...

    2022

  26. [34]

    Butler, and Aron Walsh

    Anthony Onwuli, Keith T. Butler, and Aron Walsh. Ionic species representations for materials informatics. APL Machine Learning , 2(3):036112, 09 2024

    2024

  27. [35]

    Incorporating long-range electrostatics in neural network potentials via variational charge equilibration from shortsighted ingredients

    Yusuf Shaidu, Franco Pellegrini, Emine K¨ u¸ c¨ ukbenli, Ruggero Lot, and Stefano de Gironcoli. Incorporating long-range electrostatics in neural network potentials via variational charge equilibration from shortsighted ingredients. npj Computational Materials , 10(1):47, 03 2024

    2024

  28. [36]

    Bartel, and Gerbrand Ceder

    Bowen Deng, Peichen Zhong, KyuJung Jun, Janosh Riebesell, Kevin Han, Christopher J. Bartel, and Gerbrand Ceder. Chgnet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nature Machine Intelligence, 5(9):1031–1041, Sep 2023

    2023

  29. [37]

    Unke, Stefan Chmiela, Michael Gastegger, Kristof T

    Oliver T. Unke, Stefan Chmiela, Michael Gastegger, Kristof T. Sch¨ utt, Huziel E. Sauceda, and Klaus-Robert M¨ uller. Spookynet: Learning force fields with electronic degrees of freedom and nonlocal effects. Nature Communications, 12(1):7273, 12 2021

    2021

  30. [38]

    Estimating mutual infor- mation

    Alexander Kraskov, Harald St¨ ogbauer, and Peter Grassberger. Estimating mutual infor- mation. Phys. Rev. E , 69:066138, 06 2004

    2004

  31. [39]

    Accurate estimation of the normal- ized mutual information of multidimensional data

    Daniel Nagel, Georg Diez, and Gerhard Stock. Accurate estimation of the normal- ized mutual information of multidimensional data. The Journal of Chemical Physics , 161(5):054108, 08 2024

    2024

  32. [40]

    Grossman

    Tian Xie and Jeffrey C. Grossman. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett., 120:145301, 04 2018. 13

    2018

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