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REVIEW 3 major objections 5 minor 18 references

DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read DynaCrys treats the crystallographic space group as part of the evolving diffusion state, revising it jointly with Wyckoff occupations and elements, and reports best-in-class stable, unique, and novel crystal discovery rates on MP-20…

desk verdict Genuinely new mechanism in symmetry-aware crystal generation; strong benchmark evidence, but the best-in-class headline leans on single-run released-sample baselines and omits WyckoffDiff. read the letter →

arxiv 2608.07401 v1 pith:XGM3XM42 submitted 2026-08-07 cond-mat.mtrl-sci cs.LG

Zhuotao Jin , Xiaoyun Wang , Nicholas Brawand , Roman Zubatyuk , Atul Thakur , Eric Qu , Boris Kozinsky , Justin Smith This is my paper · ORCID
classification cond-mat.mtrl-scics.LG
keywords crystalgenerationspace-groupdiffusionWyckoffpositionsgroup-subgrouprelationssymmetrycodebooklegality-constraineddecodingstable-unique-novelratediscrete
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

The paper claims that a crystal generator performs better when the crystallographic space group is not fixed in advance but is revised during generation together with the symbolic description of the crystal. DynaCrys encodes a crystal first as a protostructure—the space group, a set of Wyckoff orbit occupations, and element choices—and applies a coupled discrete diffusion process over these variables, followed by a symmetry-constrained diffusion over lattice and free coordinates. Evaluating about 10,000 candidates per method under two independent relaxation-and-evaluation pipelines, the paper reports that all three DynaCrys configurations outrank every baseline on the strict stable–unique–novel rate and its symmetry-gated variant, and lead the explicit-symmetry block on the metastable thresholds. The same configurations also produce structures that relax with consistently low displacement and sample quickly. If the comparison is fair, dynamic space-group diffusion is an effective foundation for symmetry-aware crystal generation.

What carries the argument

Two mechanisms carry the argument. The first is the coupled symbolic diffusion over protostructures: the space-group channel diffuses over the undirected graph of maximal translationengleiche and klassengleiche group–subgroup relations, while a shared pretrained symmetry codebook supplies embeddings c_G and c_{G,r} for space groups and their Wyckoff rows. The codebook's row vectors act as the clean centers of a continuous row channel, as the tied weights of the space-group-conditional row classifier, and as conditioning for the geometry model, so both stages speak the same Wyckoff vocabulary. The second mechanism is the legality-constrained stochastic decoder: after drawing G, K, and the active-slot set with probabilities proportional to products of active logits—computed by elementary symmetric polynomials e_K(ω)—the decoder rejects skeletons that violate row capacity or atom-count constraints, and Proposition 1 shows the accepted output is an exact sample from the constrained distribution without evaluating its global normalizer. The geometry stage then projects every lattice and coordinate update onto the crystal-family and free-anchor subspaces of G, keeping symmetry exact at intermediate steps.

What would settle it

Re-generate every baseline from its current official checkpoint on the same machine with several independent seeds, run all samples through the identical relaxation, hull, matching, and symmetry pipeline, and compare mean and variance of SUN@0/SSUN@0 on both engines; the claim would fail if any baseline's mean at the strict threshold matches or exceeds the corresponding DynaCrys value on either engine.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that a space group should be treated as a dynamic diffusion variable rather than a conditioning context fixed before sampling. The model state is a protostructure P=(G,K,{(Z_i,r_i)}), where G is the space group, K the number of orbit occupations, r_i a Wyckoff row in that space group, and Z_i the element. The symbolic forward process mixes a structured group–subgroup transition over maximal translationengleiche and klassengleiche relations with a reset to the training marginal, giving the space group a graph-based corruption channel; survivors, births, and padding handle a changing number of occupations. During reverse sampling, a legality-constrained decoder draws from the denoiser's factorized distribution restricted to legal states—groups with valid rows, capacity and atom-count caps—without computing the global normalizer, using an elementary-symmetric-polynomial proposal. The decoded protostructure then conditions a geometry diffusion whose lattice and fractional-coordinate updates are projected onto the subspace allowed by G, so every intermediate geometry obeys the decoded symmetry. Under the common protocol with two independent relaxation-and-evaluation engines, the paper reports that all three configurations of DynaCrys exceed every baseline on SUN@0 and SSUN@0, occupy the top three explicit-symmetry positions on SUN@0.1 and SSUN@0.1, and retain competitive sample-quality, displacement, and speed metrics.

Load-bearing premise

The comparison's load-bearing premise is that the baseline numbers are honest representatives of each baseline's typical performance—one released sample or single run, evaluated under the same protocol—so the reported margins mean DynaCrys is genuinely ahead rather than ahead of unusually weak baseline sets.

Editorial extensions

If this is right

  • Across both engines, all three DynaCrys configurations are reported to exceed every baseline on SUN@0 and SSUN@0; the canonical configuration reaches 9.39% and 9.55% on the two engines.
  • At the metastable threshold, the three configurations take the top three explicit-symmetry spots on SUN@0.1 and SSUN@0.1.
  • Replacing the state-dependent space-group proposal with the training-set marginal drops the canonical configuration's SUN@0 from 9.28% to 3.01% at a fixed seed, identifying the coupling as the active ingredient.
  • The reduced-size DynaCrys-small is 1.59× faster than the canonical configuration while staying ahead of every timed baseline on all four SUN/SSUN columns.
  • Generated structures relax with lower mean RMSD than every baseline except one, with matched-pair rates around 96%, so the symmetry-enforced geometries are close to their relaxed endpoints.

Reading between the lines

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

  • If the coupling is the mechanism rather than the architecture, the same symbolic diffusion could be attached to a different geometry model or to property-conditioned objectives (band gap, formation energy, synthesizability) with minimal changes.
  • The group–subgroup kernel uses only maximal one-hop relations; extending it to longer paths or to experimentally observed transformation mechanisms might alter discovery rates and would test whether maximal relations are the right transition geometry.
  • The exact constrained-decoder idea is not crystal-specific: any discrete diffusion whose target is a subset of finite states can use an elementary-symmetric rejection proposal whenever the unconstrained density factorizes over slots, provided acceptance rates stay practical.
  • Because novelty is defined only against the MP-20 training partition, a natural external validation would be to search generated 'novel' candidates against broader experimental and computed structure databases and to test the most stable ones with higher-fidelity relaxation.
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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

3 major / 5 minor

Summary. DynaCrys is a two-stage generative model for crystals in which the space group is part of the evolving diffusion state. A symbolic diffusion process jointly samples the space group, Wyckoff-row occupations, and elements, using a space-group transition kernel built from maximal translationengleiche and klassengleiche group–subgroup relations and a frozen, pretrained symmetry codebook. A legality-constrained stochastic decoder, whose exactness is stated in Proposition 1, produces a legal protostructure, and a symmetry-constrained geometry diffusion model generates the lattice and free Wyckoff coordinates. The method is evaluated on MP-20 with approximately 10,000 candidates per method, using two independent relaxation-and-evaluation engines (CHGNet and MACE-MP-0), and compared with seven baselines. The paper reports that all three DynaCrys configurations outperform every baseline on SUN@0 and SSUN@0, occupy the top three positions in the explicit-symmetry block at the metastable threshold, achieve low median relaxed hull energies, low relaxation-induced RMSD, and competitive sampling times. Ablations include replacing the learned space-group proposal with a marginal distribution, varying the geometry reverse schedule, and checking symmetry-detection tolerance sensitivity.

Significance. If the empirical claims hold, DynaCrys is a meaningful advance in symmetry-aware crystal generation: it makes the space group a dynamically revised variable rather than a fixed conditioning input, and it provides a principled legality-constrained decoder with a stated exactness guarantee. The evaluation is unusually careful in several respects: two independent MLIP relaxation rulers, a common downstream protocol, approximately 10,000 candidates per method, five-run means with standard deviations for the proposed model and SGEquiDiff, and sensitivity analyses for symmetry detection, geometry steps, and the space-group coupling ablation. These strengths make the comparison substantially more credible than typical crystal-generation benchmarks. However, the headline 'best-in-class' claim is only as strong as the fairness of the baseline comparison, and the paper currently lacks statistical support for some of the small reported deltas and omits at least one direct symmetry-aware competitor. The contribution is therefore promising but needs strengthening before the central benchmark claim can be regarded as definitive.

major comments (3)
  1. [§5.1, Table 1, Appendix G.3, Appendix H.1] The central claim that all three DynaCrys configurations outperform every baseline on SUN@0 and SSUN@0 is not yet supported by a significance analysis. All baselines except SGEquiDiff are single evaluated sets, and SGEquiDiff and DynaCrys are each summarized by only five runs. In the MACE-MP-0 panel, for example, DynaCrys-B has SUN@0 9.26±0.40 versus SGEquiDiff 9.11±0.23, so the mean gap is smaller than the reported dispersion; the same is true for DynaCrys-C under CHGNet (9.18±0.30 versus 8.45±0.34). The paper reports no paired or unpaired significance tests, and the deltas against the closest baseline are on the order of 0.1–0.9 percentage points. Because the 'best-in-class' wording depends on these orderings, the authors should either provide multi-seed baseline evaluations or formal significance tests, and they should describe how representative the released baseline sample sets are of each method's performance under the common protocol.
  2. [§2, Table 1] WyckoffDiff is discussed in Related Work as a symmetry-aware generator that represents Wyckoff occupations with space-group-specific discrete variables, yet it is absent from the evaluation. The headline claim is specifically about being best-in-class among symmetry-aware generative models, so omitting a directly competing method of this class weakens the claim. If WyckoffDiff cannot be evaluated under the common protocol, the authors should state this explicitly and qualify the 'best-in-class' wording to the set of methods actually compared; otherwise they should add it to Table 1.
  3. [§4.3, Appendix E.4, Eq. (9)] The exactness statement in Proposition 1 is conditional on acceptance, but the sampling procedure does not specify what the reverse sampler does when all R proposal attempts are rejected. Appendix E.4 says only that the decoder 'reports a rejection to the reverse sampler.' If the reverse process then falls back to an unconstrained sample, stops, or re-noises, the final generated distribution is no longer the claimed constrained target, and the exactness guarantee in Eq. (9) does not cover the actual procedure. The authors should specify the rejection fallback precisely and analyze its effect on the generated distribution, or modify the sampler so that the claimed conditional distribution is realized.
minor comments (5)
  1. [§5.1, Appendix G.1] The text says 'approximately 10,000 candidates per method,' but Appendix G.1 states that WyFormer's released set contains 9,999 structures; a more precise phrasing would avoid implying an exact common budget.
  2. [§6] The conclusion says DynaCrys models 'lead symmetry-aware generators,' while the abstract says 'best-in-class.' These formulations are not equivalent, and the stronger wording should be supported or softened consistently throughout the paper.
  3. [Figure 1] The inline notation in Figure 1 appears corrupted, for example '𝑥!(#)∈𝒳%&’(%,' and '𝑍!,#𝑍$,#'; these fragments should be replaced with the intended mathematical expressions.
  4. [Appendix A.1] The model vocabulary contains only 168 of the 230 space-group types. The paper should state prominently that generation is restricted to training-supported space groups and discuss the implications for coverage and for the Eff. SGs comparison in Table 2.
  5. [Table 4] The quality–efficiency comparison includes only five methods, and the timing rows for the other baselines are absent; the sentence 'DynaCrys-small exceeds every baseline in this comparison' should make clear that the 'baselines' here are only those with same-machine timing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are empirical benchmark results with independently defined components and held-out ablations.

full rationale

The paper's derivation chain is self-contained rather than circular. The space-group symbolic state, Wyckoff row vocabulary, and legality constraints are defined from external crystallographic tables (Aroyo; PyXtal), not from the paper's outputs. The shared symmetry codebook is pretrained from crystallographic descriptors via retrieval and separation losses, then frozen; it is a learned representation, not a fitted prediction of the evaluation metrics. The core SUN/SSUN claims are empirical benchmark comparisons on MP-20 under two independent relaxation engines, computed from generated structures with a fixed evaluation protocol; no fitted parameter of DynaCrys is reused as evidence for the same parameter. The legality-constrained decoder's exactness claim (Proposition 1) is derived algebraically from the factorized clean-state distribution and the legality indicator, with the elementary-symmetric factors canceling explicitly; it does not assume the target distribution. The Marginal-G ablation in Appendix K compares the learned state-dependent space-group proposal against the training marginal under a fixed seed, which is a genuine controlled test rather than a circular validation. The geometry stage builds on the external DiffCSP++ framework, not on the authors' own unverified prior result, and no uniqueness theorem or analogous self-citation is load-bearing. The only substantive evaluation concern is that several baselines are single evaluated sets using publicly released samples, which affects the strength of the 'best-in-class' comparison; that is a benchmark-fairness risk, not a circularity of the derivation. Accordingly, no circular step is identified and the score is 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The model rests on a standard crystallographic vocabulary, a learned codebook, and a set of hand-chosen hyperparameters. The evaluation additionally assumes that machine-learning potentials and the MP-20 snapshot are adequate stability proxies, a limitation acknowledged in Section 6. No invented physical entities are introduced.

free parameters (6)
  • Per-row occupancy capacity qtrain_0.99(G,r) = By-row 99th percentiles from MP-20 training partition
    Defines legal multiplicity constraints in Eq. (11), directly shaping the legal state space sampled by the decoder.
  • Maximum conventional-cell atom count Nmax = 80
    Hand-chosen cap in the atom-count legality constraint (Eq. 12), affects achievable compositions and legal states.
  • Orbit slot count M = 20
    Hand-chosen padded state width; limits the maximum number of Wyckoff occupations in a protostructure.
  • Graph diffusion rate beta_max = 4
    Controls the speed of space-group graph diffusion in Eq. (16); chosen, not derived.
  • Orbit-count prior shrinkage alpha_K = 20
    Smoothing pseudo-count in Eq. (15) blending conditional and global orbit-count priors.
  • Symbolic loss weights = w_K=w_m=w_r=w_Z=1; w_cap=0.1; w_N=w_comp=0.01; lambda_FiLM=1e-4
    Set by hand; balance auxiliary legality and composition losses in the training objective Eq. (35).
assumptions (4)
  • standard math The 230 space-group types and Wyckoff position tables from International Tables and PyXtal are complete and correct.
    The entire symbolic state space and legality constraints are built on these crystallographic tables (Section 3 and Appendix A).
  • domain assumption The maximal translationengleiche and klassengleiche group-subgroup graph captures the feasible space-group transitions used for corruption.
    The forward space-group kernel in Eq. (3) and Eq. (17) diffuses over this graph; if the graph omits relevant relations, the corruption process is misspecified.
  • domain assumption MP-20 training data and the Materials Project hull snapshot are adequate proxies for thermodynamic stability.
    All stability metrics use MLIP relaxation against a fixed DFT hull snapshot; the authors acknowledge in Section 6 that this does not imply synthesizability.
  • ad hoc to paper The frozen shared codebook, pretrained from symmetry-operation descriptors, generalizes across space groups and Wyckoff rows.
    The codebook ties the symbolic and geometry stages (Section 4.1 and Appendix C); poor generalization would degrade both stages.

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Cite this review

Pith. "Pith review of DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion." pith.science (2026). https://pith.science/paper/XGM3XM42

@misc{pith2026260807401,
  author       = {Pith},
  title        = {Pith review of: DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGM3XM42}},
  note         = {Machine review of arXiv:2608.07401}
}
read the original abstract

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires jointly modeling discrete crystallographic symmetry, elemental composition, and continuous geometry. We introduce DynaCrys, a generative model for crystals in which the space group co-evolves with Wyckoff occupations and elements through a coupled symbolic diffusion process. The structured space-group transitions follow crystallographic group-subgroup relations. As the space group changes, a shared, pretrained symmetry codebook provides both the legality-constrained stochastic decoder and the symmetry-constrained crystal-geometry model with a common representation of the corresponding Wyckoff vocabulary. Across large-scale evaluations using two independent relaxation-and-evaluation engines, DynaCrys achieves best-in-class performance in symmetry-aware discovery of stable, unique, and novel crystals, both overall and under the additional requirement of nontrivial post-relaxation symmetry. It also enables fast sampling while generating structures with consistently low relaxation-induced structural displacements.

Figures

Figures reproduced from arXiv: 2608.07401 by the authors.

Figure 1
Figure 1. Overview of DynaCrys. The symbolic stage jointly updates the space group, Wyckoff [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Wyckoff positions and crystallographic group–subgroup relations. (a) Selected positions in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Space-group distributions of as-generated DynaCrys structures and the MP-20 test reference. [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Sensitivity of canonical DynaCrys to the geometry reverse schedule. The four schedules [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]

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Works this paper leans on

18 extracted references · 9 canonical work pages

  1. [1]

    BecauseP Z∈Zpi(Z|G,r i) = 1 for every occupied slot, marginalizing Eq

    Let s= (G,K,A,r) denote the symbolic skeleton, and letSlegal be the projection ofXlegal onto these variables. BecauseP Z∈Zpi(Z|G,r i) = 1 for every occupied slot, marginalizing Eq. (40) overZgives pskel θ (s|x t) =c 0pG(G)pK(K) Y i∈A ωipi(ri|G), c 0 = MY i=1 (1−π i).(46) LetZK =P kpK(k)ek(ω). One proposal attempt has density q(s) =p G(G)pK(K)eK(ω) ZK Q i∈...

    work page 2024

  2. [3]

    End-to-end object detection with transformers

    Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. InComputer Vision – ECCV 2020, volume 12346 ofLecture Notes in Computer Science, pp. 213–229. Springer,

    work page 2020

  3. [4]

    SGs is an effective count

    Rates, validity, coverage, and matched fractions are percentages; medianehull is in eV/atom, RMSD is in Å, and the two distribution distances retain the units of Table 2; Eff. SGs is an effective count. All entries are computed per run and then averaged without pooling. CHGNet discovery and energy Method SUN@0 SSUN@0 SUN@0.1 SSUN@0.1 Med.e hull SGEquiDiff...

    work page

  4. [5]

    SLayerGen: a Crystal Generative Model for all Space and Layer Groups

    Rees Chang, Andrew Novick, Ryan P. Adams, and Elif Ertekin. SLayerGen: a crystal generative model for all space and layer groups. arXiv preprint arXiv:2605.08262,

    work page Pith review arXiv

  5. [9]

    Ethan Perez, Florian Strub, Harm de Vries, Vincent Dumoulin, and Aaron Courville

    doi: 10.1016/j.commatsci.2012.10.028. Ethan Perez, Florian Strub, Harm de Vries, Vincent Dumoulin, and Aaron Courville. FiLM: Visual reasoning with a general conditioning layer. InProceedings of the AAAI Conference on Artificial Intelligence,

    doi:10.1016/j.commatsci.2012.10.028 2012

  6. [11]

    Biao Zhang and Rico Sennrich

    doi: 10.1038/s41586-025-08628-5. Biao Zhang and Rico Sennrich. Root mean square layer normalization. InAdvances in Neural Information Processing Systems, volume 32,

    doi:10.1038/s41586-025-08628-5

  7. [13]

    The resulting cG,cG,r, andcpad tables are frozen

    with cosine decay learning rate3×10 −3 stage-1 / stage-2 weight decay 0 / 0.01 retrieval temperature / noise draws 0.1 / 4 separation marginm/ weightλ sep 0.5 / 1 After training, every nonzero vector is normalized as c← √ d c ∥c∥2 ,(30) so each vector has unit root-mean-square coordinate magnitude. The resulting cG,cG,r, andcpad tables are frozen. C.3 USE...

    work page 2019

  8. [16]

    SSUN counts only structures successfully identified as non-P1

    through SpacegroupAnalyzer, using symprec= 0.1 Å and angle_tolerance= 5◦. SSUN counts only structures successfully identified as non-P1. G.2 METRICS AND ACCOUNTING For a thresholdτ, RelStab@τ counts relaxed structures withehull≤τ , SUN@τ additionally requires uniqueness and novelty, and SSUN@τfurther requires a non-P1space group. For each geometry-relaxed...

    work page 2025

Show all 18 references
  1. [18]

    The resulting quantity retains every evaluated pair while using the same as-generated structures and relaxation endpoints as the main-text RMSD comparison

    When the common matcher does not recover a correspondence, the penalty-inclusive mean assigns that pair the finite cap used by the common MatterGen-style evaluator before averaging. The resulting quantity retains every evaluated pair while using the same as-generated structure...

    1991

  2. [2013]

    Rui Jiao, Wenbing Huang, Peijia Lin, Jiaqi Han, Pin Chen, Yutong Lu, and Yang Liu

    doi: 10.1063/1.4812323. Rui Jiao, Wenbing Huang, Peijia Lin, Jiaqi Han, Pin Chen, Yutong Lu, and Yang Liu. Crystal structure prediction by joint equivariant diffusion. InAdvances in Neural Information Processing Systems, volume 36,

    doi

  3. [2016]

    doi: 10.1107/97809553602060000114

    ISBN 9780470974230. doi: 10.1107/97809553602060000114. URL https://it.iucr.org/Ac/. Jacob Austin, Daniel D. Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. Structured denoising diffusion models in discrete state-spaces. InAdvances in Neural Information Processing...

    doi

  4. [2019]

    A.1 SYMBOLIC STATE SPACE Let G={G:n train G >0} be the model vocabulary of 168 training-supported space groups

    12 A SYMBOLICSTATESPACE ANDLEGALITY This appendix defines the finite state space of the symbolic model and the legal clean states used by the decoder. A.1 SYMBOLIC STATE SPACE Let G={G:n train G >0} be the model vocabulary of 168 training-supported space groups. Using PyXtal’s...

    2021

  5. [2020]

    Rees Chang, Angela Pak, Alex Guerra, Ni Zhan, Nick Richardson, Elif Ertekin, and Ryan P

    doi: 10.1007/978-3-030-58452-8_13. Rees Chang, Angela Pak, Alex Guerra, Ni Zhan, Nick Richardson, Elif Ertekin, and Ryan P. Adams. Space group equivariant crystal diffusion. InAdvances in Neural Information Processing Systems, volume 38,

    doi

  6. [2021]

    doi: 10.1016/j.cpc.2020.107810. Rhys E. A. Goodall, Abhijith S. Parackal, Felix A. Faber, Rickard Armiento, and Alpha A. Lee. Rapid discovery of stable materials by coordinate-free coarse graining.Science Advances, 8(30): eabn4117,

    2020

  7. [2022]

    Jonathan Ho, Ajay Jain, and Pieter Abbeel

    doi: 10.1126/sciadv.abn4117. Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. InAdvances in Neural Information Processing Systems, volume 33,

    doi

  8. [2023]

    They define two separate evaluation rulers: values are compared across methods within an engine, not across engines

    is the primary relaxation engine, and the same as-generated structures are independently re-relaxed and analyzed with MACE-MP-0 (Batatia et al., 2025). They define two separate evaluation rulers: values are compared across methods within an engine, not across engines. Energy a...

    2025

  9. [2024]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N

    doi: 10.1080/27660400.2024.2384822. Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. InAdvances in Neural Information Processing Systems, volume 30, pp. 5998–6008,

    2024

  10. [2025]

    Siddharth Betala, Samuel P

    doi: 10.1063/5.0297006. Siddharth Betala, Samuel P. Gleason, Ali Ramlaoui, Andy Xu, Georgia Channing, Daniel Levy, Clémentine Fourrier, Nikita Kazeev, Chaitanya K. Joshi, Sékou-Oumar Kaba, Félix Therrien, Alex Hernandez-Garcia, Rocío Mercado, N. M. Anoop Krishnan, and Alexandr...

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