deCIFer: Crystal Structure Prediction from Powder Diffraction Data using Autoregressive Language Models
Authors: Frederik Lizak Johansen
Ulrik Friis-Jensen
Erik B Dam
Kirsten M. Ø. Jensen
Rocío Mercado
Raghavendra Selvan
Venue: Accepted by TMLR ()

Abstract: Novel materials drive advancements in fields ranging from energy storage to electronics, with crystal structure characterization forming a crucial yet challenging step in materials discovery. In this work, we introduce \emph{deCIFer}, an autoregressive language model designed for powder X-ray diffraction (PXRD)-conditioned crystal structure prediction (PXRD-CSP). Unlike traditional CSP methods that rely primarily on composition or symmetry constraints, deCIFer explicitly incorporates PXRD data, directly generating crystal structures in the widely adopted Crystallographic Information File (CIF) format. The model is trained on nearly 2.3 million crystal structures, with PXRD conditioning augmented by basic forms of synthetic experimental artifacts, specifically Gaussian noise and instrumental peak broadening, to reflect fundamental real-world conditions. Validated across diverse synthetic datasets representative of challenging inorganic materials, deCIFer achieves a 94\% structural match rate. The evaluation is based on metrics such as the residual weighted profile ($R_{wp}$) and structural match rate (MR), chosen explicitly for their practical relevance in this inherently underdetermined problem. deCIFer establishes a robust baseline for future expansion toward more complex experimental scenarios, bridging the gap between computational predictions and experimental crystal structure determination.

Published in Transactions on Machine Learning Research (04/2026)
Crystal Structure Prediction from Powder Diffraction Data using Autoregressive Language Models
Frederik Lizak Johansen
frjo@di. ku, dk
Deportment of Computer Science, University of Copenhagen, Denmark
Ulrik Friis-Jensen Department of Chemistry & Nano-Science Center, University of Copenhagen, Denmark
uff@chem. ku, dk
Erik Bjørnager Dam
erikdam@di. krs dk
Department of Computer Science, University of Copenhagen, Denmark
Kirsten Marie Ørnsbjerg Jensen
kirsten@chem.kuu dk
Department of Chemistry Nano-Science Center, University of Copenhagen, Denmark
Rocío Mercado
rocio@ailab.bb
Deportment of Computer Science Engineering, Chalmers University of Technology, Sweden
Raghavendra Selvan
raghav@di, ku. dk
Department of Computer Science, University of Copenhagen, Denmark
Reviewed on OpenReview: https: // openreview. net/ forum? L=LFF5033747
Abstract
Novel materials drive advancements in fields ranging from energy storage to electronies, with crystal structure characterization forming crucial yet challenging step in materials discovery. In this work, we introduce deCIFer, autoregressive language model designed for powder X-ray diffraction (PXRD))-conditooned crystal structure prediction (PXRD-CSP). Unlike traditional CSP methods that rely primarily on composition or symmetry constraints, deCIFer explicitly incorporates PXRD data, directly generating crystal structures in the widely adopted Crystallographic Information File (CIF) format. The model trained on nearly 2.3 million crystal structures, with PXRD conditioning augmented by basic forms of synthetic experimental artifacts, specifically Gaussian noise and instrumental peak broaden- ing, to reflect fundamental real-world conditions. Validated across diverse synthetic datasets representative of challenging inorganic materials, deClFeer achieves a 94% structural match rate. The evaluation based on metrics such as the residual weighted profile (Rmnp) and structural match rate (MR), chosen explicitly for their practical relevance in this inherently underdetermined problem. dcCIFer establishes a robust bascline for future expansion toward more complex experimental scenarios, bridging the gap between computational predictions and experimental crystal structure determination.
1 Introduction
Characterizing the atomic structure of functional materials is essential for enabling progress in energy stor- age, electronics, and other emerging technologies. Powder X-ray diffraction (PXRD) a widely employed experimental technique for this purpose: it measures a one-dimensional intensity profile whose peaks reflect the periodic arrangement of atoms a crystalline solid. This makes structure determination an inverse problem: three-dimensional periodic structure is mapped one-dimensional signal by a (largely) known forward process, and the inverse often underdeternined,, so multiple structures match similar PXRD

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profiles. In experimental crystallography, structure solution from PXRD is typically carried out through multi-stage workflow: preprocessing and peak finding, proposing an initial structural hypothesis, and then Rietveld refinement, which is a nonlinear least-squares fit of a simulated PXRD profile to the measured profile. The initial hypothesis is often obtained by identifying representative candidate structures from crys- tallographic databases, and using these as starting points for refinement. A key bottleneck oblaining a good initial candidate, especially when peaks overlap, the pattern is noisy, or the correct structure type is not well represented in available databases.
Crystal structure prediction (CSP) refers to the computational task of inferring these same structures given set of constraints or observations. In traditional settings, these constraints are limited to high-level de- scriptors such as chemical composition or symmelry. While recent work has explored integrating experimen- tal data into generative models, direct PXRD-conditioned CSP remains underexplored. Public structure databasos predominantly archive refined structures, but do not routinely provide standardized, model-ready paired PXRD patterns, since obtained data scans depend on instrument settings, sample preparation, and preprocessing choices. As a. result, large aligned (structure, PXRD) corpora are uncommon, which has limited end-to-end PXRD conditioning in generative models.
In this work, we present deCIFer, an autoregressive transformer based model designed explicitly for PXRD- conditioned crystal utructure prediction (PXRD-CSP) (Figure 1a). To study PXRD conditioning despite the limited availability of paired experimental data, we construct a controlled paired setting: for each reference crystal structure we generate its corresponding PXRD profile using a defined forward simulator, and we use these paired examples for large-scale training and reproducible evaluation. This provides a controlled setting for large-scale training and evaluation, enabling our study of PXRD-conditionel generation. deCIFer can then be extended richer experimental structure-PXRD datasets become available.
Given a target PXRD profile, deCIFer generates a complete crystallographic structure description. We rep- resent this description using the Crystallographic Information File (CIF) format, a standard structured rext-reppesentationn used to exchange crystal structures and to interface with common crystallography tools, including refinement, pipelines and structure databases. At the same time, this motivates a decoder-only autoregressive design: CIF's are variable-length structured text with strict syntax, and autoregressive de- coding both supports fixing known CIF descriptors (such as chemical composition) during generation and enables sampling multiple PXRDDcconsstent hypotheses that can be ranked by PXRDD-consistency. This enables controlled comparisons (PXRD-only vs. PxeDD-decrrppoos). deCIFer is intended to complement traditional workflows as a hypothesis generator, proposing PXRDD-onsissent candidate structures which can then be filtered, ranked by FXRD-consistency, and refined using standard tools.
To establish a practical bascline, we incorporate basic forms of synthetic experimental artifacts into our training and validation datasets, specifically Gaussian noise and instrumental peak broadening. These ba- sic synthetic artefacts represent fundamental yet simplified aspects of real-world PXRD variability, chosen intentionally to provide a controlled, reproducible starting point for evaluation and for future extensions of the method. They act as minimal simulation of mcasurement noise and resolution limits, analogous to data augmentation strategies in vision or speech domains. They do not capture more complex elfects such as peak asymmetry, background drift, or preferred orientation, which we leave for future studies.
The performance of deCIFer is demonstrated on diverse PXRD patterns from large-scale datasets represen- falive of challenging inorganic materials. Our evaluations confirm the robustness of the approach and its ability to produce syntactically correct and structurally meaningful CIFs that accurately reproduce target diffraction patterns. With this, dcCIFer serves as foundational step toward bridging the gap between computational CSP and experimental crystal structure determination workflows.
Our key contributions in this work are:
Integration of PXRD-based experimental conditioning into an autoregressive transformer model, cnabling direct CSP in CIF format; a capability not demonstrated previously in transformer-basod generative models.
Implementation of an effective conditioning mechanism to handle variable-length CIF sequences in autoregressive modelling.
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Reference
Sample
FXRD Comparison
Crystal Descriptors
deCIFer
Crystal (CIF) Output
Refermnce
ceciter Sample
"data CdC12*
Crystal Takenizer
SrBr
Composiion
Conditional
Space Group
Autorearessive Multi-Head Attention
ReNiPb,
Conditioning
Simulation
YGaCu,
Q (A-2)
(a) Overview of the deCIIer model.
(b) Example generations using deCIFer.
Figure 1: (a) Overview of the deCIFer model, which performs autoregressive crystal structure prediction (CSP) from PXRD data, optionally guided by standard crystallographic descriptors (e.g., composition and space group) encoded as CIF fields, which can be provided to constrain generation or omitted for exploratory sampling. PXRD embeddings are prepended to the CIF loken sequence, enabling the generation of struc- turally consistent CIFs directly from diffraction data. (b) Three examples from the NOMA test set showing dcCIFer generations, each illustrating a reference structure, the generated structure and their corresponding PXRD profiles.
3. Simulation of fundamental PXRD experimental artefact, Gaussian noise and peak broadening, practical baseline for real-world scenarios.
4. Comprehensive evaluation two large-scale datasets: NOMA and CHILI-100K (Friis-Jensen al., 2024), including comparison to state-of-the-art CSP models and analysis of sampling consistency under varying conditions.
These contributions aim to establish a reproducible foundation for integrating computational CSP with experimental workflows.
2 Background and Related Work
CSP has traditionally relied on high-level descriptors, such as chemical composition or symmetry constraints, to guide predictions. Recently, approaches termed data-informed CSP have begun intograting explicit ex- perimental data (particularly diffraction data) into their generative processes (Kjær et al., 2023; Guo el al., 2025; Riesel et al., 2024; Lai et al., 2025), marking significant shift away from purely desiriptor-driven CSP. Among the many experimental modalities that could inform such models, PXRD is especially rele- vant because it directly encodes crystallographic information in a widely accessible format. This makes it a natural focus for the present work.
PXRD: Powder X-ray diffraction (PXRD) among the most widely accessible and routinely employed structural characterization techniques solid-state chemistry. Modern benchtop diffractometers, available in most research and industrial laboratories, can produce high-quality diffraction patterns in minutes. PXRD patterns consist of diffraction peaks whose positions and intensities directly encode essential information about a material's crystal structure; specifically atomic arrangements and symmetry. The forward simu- lation of PXRD patterns from known crystal structures in the standard Crystallographic Information File (CIF) format well-ostablished through scattering theory (West, 2014), facilitating realistic computational modelling.
Quantitative PXRD analysis typically involves structural refinement methods, such as Rietveld refine- ment (Young, 1995), wherein parameters of structural model are iteratively adjusted against experimental
NOMA stands for NOMAD (Draxl & Scheffler, 2019), OQMD (Kirklin et al., 2015), MP (Jain al., 2013h) Aggregation.
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data. Such refinements depend heavily on the accuracy of an initial structural model, whose identification (often termed fingerprinling) can be particularly challenging. Fingerprinting typically requires extensive chemical intuition and exhaustive database searches. Nevertheless, structural model identification often remains ambignous, significantly hindering matcrials discovery and optimization.
CSP with LLMs: Large language models (LLMs)) based on transformer architectures (Vaswani et al., 2017) have recently been leveraged for automation tasks in chemistry, including synthesis planning (Hocky & White, 2022; Szymanski
al., 2023; M. Bran et al., 2024), chemical data extraction (Gupta et al., 2022; Dagdelen et al., 2024; Polak & Morgan, 2024; Schilling- Wilhelmi et al., 2025), and property predic- tion (Zhang et al., 2024; Rubungo et al., 2024; Jablonka et al., 2024). Despite their growing popularity, these LLMs have yet to become widely utilized in materials design workflows. Recent work has started adapting these models specifically for crystal structure prediction (CSP). For instance, Gruver et al. (2024) fine-tuned Llama-2 models (Touvron et al., 2023) on text-based representations of atomistic data, enabling tasks such as the unconditional generation of stable crystalline matorials. Similarly, Mohanty al. (2024) finc-tuned LLaMA-3.1-3 (Dubey et. al., 2024) using QLoRA (Dettmers al., 2023) to efficiently generate CIFs condi- tioned compositional and symmetry constraints, Another recent approach, CrystaLLM (Antunes et al., 2024), utilizes extensive pre-training on millions of inorganic crystal structures and likewise targets CIF generation using only high-level descriptors like composition and symmetry, without explicitly incorporating experimental constraints. While these methods represent significant advancements in generative CSP, they remain disconnected from direct experimental observations, which are often critical for accurate and practical structure determination.
CSP with diffusion models: In parallel to transformer-based LLM approaches, diffusion- and flow-based generative models have emerged as complementary methods for CSP (Jiao et al., 2023; Miller et al., 2024; Zeni et al., 2025; Xie et al., 2022). These frameworks typically utilize compositional constraints or partial structural information to guide structure generation and have shown promise in reliably predicting stable crystalline configurations. However, like many transformer-based CSP methods, diffusion-based models predominantly rely on purely computational constraints. The recent framework MatterGen (Zeni et al., 2025) has made notable strides by enabling generative modeling conditioned on a variety of property-base based constraints, improving predictions for structures likely to be synthesizable. Nevertheless, direct conditioning experimental data, such as PXRD patterns, remains underexplored in diffusion-based CSP, underscoring the necessity for methods that bridge computational generation with explicit experimental data conditioning.
3 Methods
Consider a crystal structure represented in the CTF format, tokenized into a sequence of length Tj: xf (z), 2e1.r2...,,.7] (see Appendix A.3 for details). The corresponding PXRD pattern, denoted by y", is a collindous-valued vector encoding the intensity prosile of the diffraction pattern. Our dataset thus comprises pairs of CIF sequences and their corresponding PXRD patterns: D = [xx,, y Our objective is to minimize the negative conditional log-likelihood over this training data:
T log Pe (cf))))))))) Σ
((X N
(1)
This is accomplished through the transformer-baser conditional autoregressive model fe(-), termed deCIFer. Given PXRD data, deCIFer generates crystal structures in the CIF format autoregressively.
PXRD Conditioning: PXRD data explicitly encodes structural fingerprints of crystal structures. We leverage PXRD as a direct conditioning input to guide our CSP.
Using standard crystallographic procedures, we generate discrete diffraction peaks from CIF structures, represented as the set P = {(qx, i via pymatgen (Ong al., 2013). These peaks are transformed into continuous PXRD patterns, y, under synthetic experimental conditions. Formally, let T represent set of transformations applied to P.
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To establish a robust baseline model, transformations reflect simplified but fundamental experimental artifacts: each transformation 7 7~ T consists of (1) peak broadening characterized by a full-width-at-hall: maximum (FWHM) sampled uniformly from 0.001 to 0.100, and (2) additive Gaussian noise with variance unise uniformly sampled from 0.001 to 0.050. A new T is sampled for each training sample on every epoch, ensuring diverse exposure lo synthetic experimental variability. For evaluation purposes, we define a fixed transformation, Thxed; with specific parameters governed by the experiments to systematically assess robustness, and clean transformation To (FWHM 0.05, of noise 0) to assess similarity in context of PXRD. Examples from T on PXRD are shown in Figure A3 (in Appendix).
Conditioning Model: PXRD patterns are embedded into a learned vector space via multilayer perceptron (MLP) fa (y), parameterized by Φ. The resulting embedding vector e (y) E RD is prepended to the tokenized CIF sequence, providing a direct conditioning mechanism. Joint optimization of the embedding network fe and the transformer model fe results our final objective: L $).
Sequence Packing and Isolation: To handle variable-length CIF sequences efficiently during training, we employ sequence packing, inspired by recent methods in NLP (Kosec et al., 2021). Tokenized CIF sequences, each of length Tú, are concatenated into fixed-length segments of context size C' = 3076, chosen to optimize GPU usage and throughput. Formally, a packed sequence is represented as S = [e', tt......tt .,,,tt/,, t et, ti...., ff....,tl.. where each e' is the D-dimensional conditioning embedding, and tú are input embeddings. Long CIFs exceoding C' tokens are split between sequences inside batches, but occur infrequently 0=044 of sequences; see Figure A4 in the Appendix). To reduce adverse elfects from splits, data shufllig is performed each epoch.
Isolation between CIFs within a packod sequence is ensured by an attention mask M, where Ma = tokens k and originate from the same CIF, and otherwise, resulting in blckkwiis diagonal attention structures (shown in Figure A2 in the Appendix). Additionally, positional encodings are reset at each CIF boundary, preventing leakage of positional information across CIF sequences.
4 Dataset and Experiments
Dataset: We utilize two large-scale open-source datasets that serve as the foundation for this study. The first, NOMA, is a synthetic dataset comprising crystal structures aggregated in CrystaLLM (Antunes et al., 2024), sourced from the Materials Project (April 2022) (Jain et al., 2013b), OQMD (v. 1.5, October 2023) (Kirklin et al., 2015), and NOMAD (April 2023) (Draxl & Scheffler, 2019). The second, CHILI- 100K (Friis-Jensen et al., 2024), contains experimentally determined structures curated from a filtered subset of the Crystallography Open Database (COD) (Gražulis et al., 2009). NOMA is used for both training and testing, while CHILI-100K is used exclusively for testing. Both datasets are open-source and available for 2ownload.2
These datasets are intentionally chosen to approximate key aspects of real-world PXRD structure determi- nation under controlled setlings. Although synthetic in nature, they represent a practical and reproducible foundation for benchmarking models under basic structural and experimental variability. We note that these datasots are not intended to span the full spectrum of real experimental complexity. Rather, they are used here to establish a robust baseline for future studies that incorporate richer experimental variation and direct measurements.
Preprocessing: We follow the standard CrystaLLM preprocessing pipeline and apply additional steps to ensure consistency between NOMA and CHILI-100K. For NOMA, we select the lowest-volume structure per composition, filter duplicates, and retain only fully occupied CTFs with standardized formatting. The resulting dataset comprises approximately 2.3 million structures containing between 1 10 elements, up to atomic mumber 94 (excluding unstable or radioactive clements). Floating point values are rounded to four decimal places. For CHILI-100K, we retain x 8,200 experimentally derived CIFs with up to 8 elements, including atoms up to atomic number 85. Detailed statistics including space group distributions, token lengths, and composition diversity are provided in Appendix Figures A4 and A5.
NOMA: github. wtt.c///aaattteeerrrraaaaalal (CC-BY 4.0 licence), CHIL.--10K: github. comuub..om/uleeee 11tr:///fr111eeee////HIIIII
(Apache 2.0 licence).
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Due to the known overrepresentation of high-symmetry structures in synthetic databases (Davariashtiyani et al., 2024; Zhang et. al., 2023), we apply stratified sampling during the NOMA vrain/validation// split based on space group labels. This mitigates structural distributional biases and improves evaluation robust- ness. For further details, see Section A.9.
Tokenization: All CTFs are tokenized using a 373-token vocabulary, including space group and element sym- bols, CIF tags, numerics, punctuation, and conditioning tokens. See Sections A.2 and A.3 in the Appendix for full preprocessing details.
Model Hyperparameters: deCIFer consists of two components: the PXRD encoder fa, 2-layer MLP that maps a 1000-dimensional PXRD profile into a 512-dimensional embedding; and the structure generator fe, an 8-layer decoder-only transformer (Vaswani et al., 2017) with 8 attention heads per layer. The token dimension is set to 512 for both components. The model is trained using AdamW (Loshchilov & Hutter, 2017) with a batch size of 32 and a context length of 3076. Learning rate lincarly warmed up over the first 100 steps, followed by a cosine decay over 50,000 steps. Gradient accumulation (40 steps) and training are used on a single NVIDIA A100 GPU. These optimization and scheduling hyperparameters follow CrystaLLM (Antunes et al., 2024), which we adopt previously validated default for autoregressive CIF generation.
The total parameter count is 27.72M: fo has s 0.78M and fe has x 26.94M. All components are im implemented in PyTorch (Paszke et al., 2019). Full architectural and training details are provided Section A.9.
Figure 2 outlines the evaluation procedure. A reference CIF from the test set is first converted into discrete set of diffraction peaks, p ((ge, (=)= which then transformed into continuous PXRD pattern y = Tixeed (P), where Trixed simulates a predefined experimental setting. This PXRD signal, together with any known descriptors (e.g., composition or space group) when available, is passed to deCIFer to generate new CIF structure, CIF". All evaluations are based on clean transformation with FWHM = 0.05 and no added noise.
Evaluation:
We evaluate the generated structures using three complementary metrics:
deCIFer Generation Pipeline
Simulate peeks P 1igh-13)....
Simulate PXRD Tam???
Encode PXRC fely)
(1) Residual Weighted Profile (Rwp) quantifies
Test Dataset
the difference between the reference and gener- It is computed as Rwp =
CIF
Extract descriptors
Toienize descriptors
Model Inference ful))
CIF
ated PXRD profiles.
(m (m--1)) where all weights w; = 1, following E
convention.
Simulate P and y - (P))
Evaluate performance
Simulate P and y Tp(P")
(2) Match Rale (MR) measures geometric similar- ity using StructureMatcher (Ong et al., 2013). Two CIFs are considered a match if their lattice, atomic positions, and symmetry match within toler- ance thresholds. MR is the fraction of matches over the total number of test structures. Full details are given in Appendix Section A.7.
Figure 2: Evaluation pipeline: A test set CIF gener- ates a PXRD profile, tokenized for deCIFer to produce a new CIF, compared to the reference using a clean transformation.
(3) Validily ( (Val.) assesses whether the generated CIF is internally consistent. A structure is considered valid only if it passes all four checks: formula balance, site multiplicity, realistic bond lengths, and symmetry agreement. See Appendix Section A.6 for criteria.
These metrics were chosen for their practical relevance in evaluating structure predictions from PXRD data. While each carries limitations, they jointly capture fidelity to both diffraction signals and erystallographic constraints.
Experiments: We designed four controlled experiments to assess deClFer's ability to perform PXRD conditioned CSP across a range of settings:

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(1) Comparison with State-of-the-Art: We benchmark deCIFer against three recent CSP models that rely solely on composition symmetry constraints, evaluating the benefit of PXRD-based conditioning. We report match rate (MR) under the standard composition-only protocol to enable a like-for-like comparison.
(2) Ablation of PXRD Conditioning: We compare deCIFer with an unconditioned variant, U-deCIFer, to isolate the contribution of PXRD data to the quality of generated structures. Here, diffraction-pran profill agreement (Rwp) is the primary measure of the contribution of conditioning, with MR and validity reported complementary checks.
(3) Robustness to Perfurbations: We apply deCIFer to PXRD data with varying levels of synthetic noise and peak broadening, simulating more challenging, experimentally relevant condition.
(4) Generalization to CHILI-10OK: We evaluate deCIFer (trained on NOMA) on the CHILI-100K dataset to assess generalization to more chemically and structurally diverse experimental data.
In all experiments, we generale one structure per PXRD input. We also vary which information is provided at inference time. We use three descriptor settings: 'none' (no fixed descriptors), "comp." (composition fixed), and "comp.+s.g." (composition and space group fixed), implemented by fixing the corresponding CIF fields during generation (see Section A.3). In the special case U-deCIFer + 'none", the model receives no fixed descriptors and is initialized only from the CIF start token, and therefore samples unconditionally from its learned prior over CIFs, For this case, a near-zero match rate is to be expected, and we interpret it primarily via validity and Rwp.
5 Results
Baseline Comparisons with State-of-the-art: We compare deCIFer with three state-of-the-art CSP models that generates structures solely from the composition descriptor: CDVAE (Xie et al., 2022), Dif- fCSP (Jiao et al., 2023), and CrystaLLM (Antunes et al., 2024).
To compare these models within a shared evaluation setup, we follow the protocol used in prior work (Antunes et al., 2024): for each test composition, a single structure is generated and evaluated using match rate and atomic root-mean-square error (RMSE). Table shows the results. For deCIFer and U-deCIFer, we report mean + standard deviation over three independent training runs (different random seeds); other methods are shown reported in prior work.
The baseline models are provided only the composition. Nevertheless, they achieve high match rates. This can happen when a composition is strongly associated with one common structure type in the training data, so returning the most frequent structure often matches the tost reference. However, the same composition can also have multiple different crystal structures (polymorphs) with the same elements but different alomic arrangements. In those cases, composition alone is not enough to select the structure that would be observed in particular experiment.
deCIFer, by contrast, can only partially rely on compositional priors and is explicitly constrained by the PXRD signal, which defines a more structurally constrained and underdeternined prediction task. As shown in Table 1, deCIFer achieves substantially higher match rates on Perov-5 and Carbon-24, where the PXRD patterns offer strong structural signals. On MP-20 and MPTS-52, however, the match rate drops significantly. This performance drop may stem from the fact that the PXRD signal, when weak or ambiguous, does not sufficiently narrow the space of plausible structures; or worse, it may mislcad the model away from the correct solution. In such cases, deCIFeer appears unable to resolve the true structure from the PXRD input, suggesting that conditioning does not always help, and in some cases might even interfere with the model's brsor-based predictions.
Still, this failure is instructive. It highlights the genuine difficulty of structure determination in the presence of polymorphism and non-disermminative PXRD data. This is a problem that naturally includes failure modes, ambiguity, and uncertainty, all of which are essential elements real-world structure determination. Unlike traditional CSP models, which confidently return the most likely structure according to their priors, deClFer conditions generation on observed measurement.
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Table I: Performance comparison on four public CSP benchmarks: Perov-5 (Castelli et al., 2012a;b), Carbon- 24 (Pickard, 2020), MP-20 (Jain et al., 2013a), and MPTS-52 (Baird, 2023). Following the singlo-sample evaluation protocol used in prior work (Antunes et al., 2024), one structure generated per test composition. We report the match rate (%) based on structural equivalence under StructureMatcher and the atomic root-mean-square error (RMSE in Á) after aligmment. For deCIFeer and U-deCIFeer we report mean + 1 standard deviation over three independent seeds; other baselines are single-run values taken from the original references.
Perov-3
Carbon-24
MP-20
MPTS-52
Model
Match (56)
RMSE]
Match (Kir
RMSE
Match (%)1
RMSEL
Match (%)
RMSE1
CDVAE
45.31
0.2138
17.09
0.2989
$3.90
0.1045
5.34
0.2106
DiACSP
$2.02
0,0780
17.84
0.2759
51.49
0.0631
12.19
0.1786
97:95
0. 0.0965
91.13
D-1687
55. 65
0.0437
17:47
0.1113
46. 10
0.09933
20:25
D-1761
58.
0,0408
19 21
0.1130
U-deCIFFr
61.65=#0.99
0,1113=0..00 0004
17.60++0.27
0,15824-0 0000
44.75
0.0777
11.70=0.10
0.1647++0.001
deCIFer
83.39220338
0.01802000000
37.9610.62
0.2028110
44.85:21:40
0.07092000033
11.6020.13
0.14442000070
Overall, Table 1 shows that run-to-run variability in match rate narrow across random soeds. However, as we will see later, repeating the inference step multiple times for the same PXRD input reveals different kind of variability: when the PXRD conditioning signal is inconclusive, samples drawn from that single imput do not collapse to one answer, but instead exhibit increased sample-to-sample diversity. This effect is most pronounced in more ambiguous regimes, such as lower-symmetry systems, where the PXRD profile is less discriminative and multiple structural solutions are plausible.
Importance of PXRD Conditioning: Having established the challenges of PXRD-CSP in ambiguous cases, we now examine the effect of PXRD conditioning within controlled synthetic setting. Specifically, we compare deCIFer with its unconditioned variant (U-deCIFer) the NOMA test set, using simulated PXRD profiles with controlled noise and broadening. This ablation isolates the impact of PXRD input by evaluating both models under identical architectural conditions, varying only in the inclusion of structural conditioning.
We consider three descriptor settings: (i) no additional input ("none"), (ii) composition only ('comp.'), and (fii) composition plus space group ('comp. + s.g.'). Figure 3 shows that deCIFer consistently outperforms U-deCIFer across all settings in terms of Rep: indicating a closer match between the generated and reference PXRD profiles. While U-deCIFer benefits from access to composition and symmetry descriptors, it never reaches the fidelity achieved by PXRD-cooditioned generation.
The improvement is particularly pronounced in the absence of any crystal descriptors, where deCIFer sig- nificantly outperforms U-deCIFor. This demonstrates that PXRD alone provides a strong structural signal, whereas unconditioned generation collapses without access to priors. The gains persist when descriptors are included, with PXRD further narrowing the solution space toward structures that reproduce the target pattern.
Figure further supports this, showing that performance is best for common, high-symmetry crystal systems, while rare or low-symmetry systems remain more difficult. The three test examples illustrate the spectrum of outcomes: from precise structural matches to clear mismatches, reflecting the varying information content in the PXRD input.
Robustness to Perturbations in PXRD Conditioning: To establish a reproducible baseline for PXRD- conditioned generation, we probe robustness under two simple, parameterized perturbation families applied to simulated PXRD patterns: additive Gaussian noise and instrumental peak broadening. These are the same perturbation families used during training, and use them here as interpretable proxies for degraded signal-to-noise ratio and finite resolution. We evaluate performance across fixed parameter settings that are explicitly defined relative to the training perturbation ranges: in-distribution (ID) settings use noise and broadening values that lie within the ranges sampled during training, whereas out-of distiiiibiiitii (OOD) settings use values outside those training ranges to test extrapolation to more severe corruption. We do this within the bounds of the assumed forward sinulator to isolate the model's robustness to these perturbations when trained with them. We leave it to future work to extend the forward simulation to incorporate
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none
comp.
comp.+5.g.
U-deCIFer
deCIFer
Desc.
Model
Rup
(M
Val. (%)
MR (%)
U-deCIFor
1.24 4:026
93.49
0.00
U-deCIFer
none
deCIFer
0.32 #0.34
92.06
5.01
U-deCIFer
0.82 #:041
93.78
49.30
deCIFer
comp.
deCIFer
0:25 1:0.99
93.73
91.50
U-deCIFer
0.65 #0.36
93.72
87.07
U-deCIFer
comp,
deCIFer
0.24 1:0.9
deCIFer
0.0
1.0
2.0
3.0
Rwp
Figure 3: Left: Distribution of Rep for deCIFer and U-deCIFer on the NOMA test set with boxplots. Performance for 20K NOMA test samples using dcCIFer
Lower Rwp indicates better CIF alignment. Right: and U-deCIFer with different descriptors: (no descriptors), comp. (composition), and comp.+ s.g. (composition space group). Metries include validity (Val.) and match rate (MR).
Reference
Sample
PXRD Comparison
deOife
Cubic
V,CuTe, Hr,MOSs
Lower Symmetry
Hexagonal
Trigonal
1879
91
Tetragonal
3441
1558 1566
Orthorhombic
2-25
Monoclinic
ZiPt
Triclinic
1129
0.0
0.5
1.0
5000
Rup
Count
Q [A-2]
Figure 4: Left: Average Rwp by crystal system for deCIFer on the NOMA test set shows better performance for common high symmetry systems and higher Rwp for rare low symmetry systems. Right: Examples from the NOMA test set highlight. this trend with predicted structures from PXRD and composition maintaining reasonable matches even for low symmetry systems with higher Rwp.
additional experimental effects, such as background and fluorescence, preferred orientation, absorption and microstrain, peak asymmetry, multi-phase mixtures, and instrument- and wreprocessing-specif artifacts.
As summarized in Figure 5, deCIFer remains remarkably stable under ID noise and broadening. Even as the PXRD signal becomes progressively degraded, the model maintains strong alignment with target profiles (Rwp) and structure validity. Only under extreme OOD conditions does performance degrade more noticeably. Importantly, this degradation is gradual and consistent with the level of distortion, indicating that the model is not overfitting to narrow PXRD conditions but has learned robust mapping from signal to structure.
Unsurprisingly as shown in Appendix Figure A9, lower-symmetry crystal systems remain more difficult to recover under perturbation. But crucially, this behaviour consistent across conditions, reaffirming that structural ambiguity core challenge and a side effect of noise sensitivity. This supports the view that deCIFer robust to experimental imperfections the level of simulation, critical prerequisite for real-world deployment.
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NOMA
ID: 00.00,0.05 0.05)
Dataset (comp.)
Sotting
Rup (w:d:: m) 4
Val. (%)
f
(%6 f
CHILI-10OK
U-deCIFer
0.8210041
93.78
49.30
NOMA
NOMA
ID: (0.00, 0.05)
0.25:10.20
93.73
91.50
ID: (0.05, 0.10)
ID: (0.05, 0.10)
0.31
93.77
89.28
CHILI-100K
OOD: (0. 10, 0.20)
0.65
91.66
77.06
U-deCIFer
0.96.10.32
43.26
25.92
NOMA
CHILI-100K
ID: (0.00, 0.05)
0.70:1..37
41.83
37.34
(0.10, 0.20)
ID: (0.05, 0.10)
0.73#0.300
40.95
35.97
CHILI-10OK
OOD: (0.10, 0.20)
0.8740.33
33.62
26.09
0.0
1.0
2.0
3.0
Rwp
Figure 5: Left: Distribution of Rwp for deCIFer on NOMA and CHILI-100K when conditioned on PXRD and composition across three PXRD corruption settings (ID and OOD defined by the noise and FWHM parameters shown). Right: Corresponding summary of Rwp: validity (Val.), and match rate (MR). We additionally include U-deCTFer as a PXRD-free bascline for each datasct.
OOD Evaluation on CHILI-100K: To test whether this robustness extends beyond synthetic bound- aries, we evaluate deCIFer on the CHILI-10OK dataset: a curated set of experimentally determined crystal structures with significantly greater structural complexity and lower symmetry than NOMA, CHILI-100K contains no overlap with dcCIFer's training data, and thus serves as a structurally out-of-distribution bench- mark. Importantly, while the underlying crystal structures in CHILI-100K are experimentally determined, the PXRD patterns used for conditioning tion Trxxdd defined in Section 3. Consequently, this experiment primarily probes structural out-of-distribution generalization (different chemistry, symmetry, and geometric complexity).
still synthetically generated using the same fixed transforma-
The results are summarized in Figure 5, which also includes U-deCTFer as a PXRD-free baseline for com- parison. Despite the increased difficulty, deClFer maintains a reasonable Rup and match rate, with only a modest performance drop under in-distribution noise and broadening. As expected, validity decreases mainly due to bond length violations (see Appendix Table A4) but remains interpretable. This highlights the greater geometric complexity of experimental structures. The performance gap relatíve to NOMA reflects the real structural diversity in CHILI-10OK, not failure of conditioning. This is made apparent by comparing this to the unconditioned baseline, where PXRD conditioning leads to a clear improvement in match rate (from 25.9% to 37.3%) and reduction in Rwp: confirming that the gain is not due to memorized compositional priors but driven by alignment with PXRD.
These findings reaffirm that deCTFer's design enables to generalize beyond synthetic structure datasets and that its failures reflect genuine difficulty rather than collapse. PXRD conditioning proves beneficial not only in idcalized simulations but also in settings that approximate real-world structure determination. We reiterate that this evaluation focuses on structural diversity, while real-world PXRD data may contain additional experimental artifacts that could further challenge deClFer's robustness.
Consistency and Variability in CIF Generation: Building on these robustness results, we next ex- amine deCTFer's generative behaviour under repeated sampling from the same PXRD input. Specifically, we investigate the consistency and variability of generated structures when the model is conditioned on a fixed PXRD pattern but with different levels of descriptor constraint. Using a monoclinie structure from the NOMA test set CdzSee,, we generate 16,000 CIFs under the three previously established settings: no descriptors ('none"), composition only ('comp."), and composition plus space group ('comp. + +sg."") ").
Figure 6 illustrates the results. When no crystal descriptors are provided, deCIFer produces a wide variety of cell parameters, compositions, and space groups, reflecting the model's ability to explore the broader space of PXRD-consistent structures. Interestingly, even this unconstrained mode, the Rwp values are relatively stable, clustering around a narrow range. This suggest that many structurally distinct outputs can yield similar diffraction patterns.
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a)
Reference
b)
none
comp.1s.g.
none
comp.
comp. + s.g.
40
Best
#
10
In,Mo,Br C21
Sr, C2/m Rup = 0.039
Sr,cd, C2/m Rap 0.029
0
Rep = 0.061
Sr,co,se, C2/m
0.0
0.2
0.4
0.6
0.8
d)
Rgy
Median
Hexagunal
Trigonal
Tetragonal
Orthorhombli
Monaclinc
Ricinic
e)
Cd,n,Ge, Cmmm Rep 0.504
Sr,Cd,Se, C2/m Rap 0.367
Sr. Sr.Cd,Se, C2/m Rap 0.345
13.0
20.0
11
120
OP
Figure 6: deClIeer-sampedd structures for monoclinic Sde PXRD profile (16K samples). a) Reference structure. b) Distribution of Rwp for generated CIFs. c) Examples of generated structures showing best, median, and diverse samples. d) Distribution of sampled crystal systems. e) Histograms of cell lengths (a, b, c) and angles (a,3,7) with reference values as dotted lines.
In contrast, adding composition and space group constraints narrows the distribution of generated structural parameters, as expected, but leads to broader Rwp distributions. This highlights the sensitivity of the Rwp metric to subtle geometric differences, and highlights the importance of complementing it with other validity or matching criteria. Notably, across all settings, the match rate to the reference structure remains high, indicating that deCIFer can recover accurate solutions both in exploratory and constrained modes.
These findings support a flexible view of deCIFer: when crystal descriptors are known with confidence, adding them improves convergence toward a precise structural solution; when exploring structural hypotheses or navigating ambiguous PXRD signals, descriptor-free generation enables broader sampling of plausible configurations without sacrificing physical fidelity.
6 Discussion and Outlook
PXRD-driven Structure Generation: The experiments in Section 5 demonstrate that incorporating PXRD as a conditioning signal significantly improves the quality and relevance of generated structures, especially when clear and informative diffraction patterns are available. On the NOMA test set, deCIFer consistently produces structures that align closely with the PXRD larget, outperfrninng unconditioned or composition-only models. This supports a central claim of this work: conditioning on PXRD allows generative models move beyond compositional priors and dircetly engage with structural data.
At the same time, these results highlight that PXRD-CSP is inherently more challenging than traditional CSP. When the diffraction signal is ambiguous or when multiple structural solutions (e.g., polymorphs) produce similar PXRD patterns, deCIFer's task becomes fundamentally underdetermined. In such cases deCIFer's performance declines.
Furthermore, our experiments show that deCIFer adapts flexibly both constrained and unconstrained inference scenarios. When provided with composition space group descriptors, the model converges to tighter solution distributions. When these are omitted, it samples broader space of physically plausible structures. This adaptability suggests that PXRD-CSP is not just harder task, but also a more expressive one, capable of supporting exploratory or targeted workflows depending on available information.
Extensibility through Conditioning: By embedding the PXRD signal y into a learnable conditioning vector fy) deCIFer establishes general and extensible mechanism for incorporating physical mea- surements into generative modeling. This approach naturally generalizes: if additional data sources are available (e.g., thermodynamic, spectroscopic, electronic properties), they be incorporated using sep-
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arate conditioning networks. Formally, for P properties (y.....,pp) the conditional generation objective becomes L.. yp; O p)). This opens the door to multi-modal structure generation aligned with experimental realities.
Limitations and Challenges: While the NOMA and CHILI-100K datasets are stratified and indepen- dently curated, data leakage remains a nuanced concern in materials science, where structural or composi- tional similarity can introduce implicit bias (Cheetham & Seshadri, 2024). However, rigorous preprocessing, deduplication, and independent dataset design significantly reduce this risk.
Another key limitation lies in the nature of PXRD itself. Due to the phenomenon of homometry, where different atomic arrangements produce indistinguishable diffraction patterns, PXRDD-infommed models can- not always resolve structural degeneracy (Pallerson, 1944; Schneider et al., 2010). Metrics like Rwp reflect diffraction fit, not atomic uniqueness. Nonetheless, our results show that even partial inclusion of com- plementary data (o.g., composition) can help disambiguate near-degenerate structures, particularly when combined with fine-grained conditioning mechanisms (Shen et. al., 2022).
Finally, while our perturbation and OOD experiments simulate realistic noise and broadening, they do not yet capture the full complexity of experimental PXRD, such as peak asymmetry, background drift, or instrumental artifacts. Addressing these effects will require further refinement of both data simulation and conditioning mechanisms.
Outlook: deCIFer and the PXRD-CSP paradigm mark a step toward generative models that do not merely recall statistically likely materials, but actively interpret physical measurements. This makes them fun- damentally more aligned with the goals of structure determination in experimental settings. While this approach introduces greater complexity and structural uncertainty, it also makes the generative process more transparent, testable, and useful. Future work can expand on this foundation with richer experimental conditioning, active-learning loops, and downstream applications in materials discovery and verification.
7 Conclusion
We introduced deCIFer, PXRD-conditioned autoregressive language model for crystal structure predic- tion. Unlike traditional CSP approaches that rely solely on compositional or symmetry priors, deCIFer directly incorporates simulated PXRD profiles conditioning input, enabling generation of CIFs that are structurally consistent with diffraction measurements. The model is trained on large-scale synthetic datasets and developed with lab-scale compute resources, yet demonstrates robust performance across varying noise levels, peak broadening, and structural complexity, including out-of-distribution generalization.
deCIFer represents a foundational step toward PXRD-informed CSP: a formulation of structure prediction that embraces physical constraints and explicitly addresses the ambiguity inherent in real-world data. While this makes the problem harder, it also makes the model's outputs more interpretable and testable. Our results show that diffraction guidedd conditioning substantially improves alignment with structural targets, even when uncertainty or degeneracy is present.
In our comparison to existing state-of-the-art CSP models, we observed that composition-basse methods achiove high match rates on benchmark datasets; in large by relying on learned priors that align with frequent structures in the training data. While these models perform well terms of matching reference structures, they operate under a simpler formulation that does not incorporate experimental constraints. The comparison therefore currently limited.
In practical terms, deCIFer is best viewed not an end-to-end solution, but powerful structural hypothesis generator. It is particularly effective when the PXRD signal is informative and we suspect that it will be most elfectively used in landem with expert evaluation or downstream refinement. By shifting generative modelling closer to experimental reality, deCIFer lays the groundwork for more integrated and data-aware materials discovery pipelines.
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Acknowledgments: The authors thank Richard Michael and Adam F. Sapnik for useful feedback.
This work is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement No. 804066). We are grateful for funding from University of Copenhagen through the Data+ program. RM acknowledges funding provided by the Wallenberg AI, Autonomous Systems, and Software Program (WASP), supported by the Knut and Alice Wallenberg Foundation.
References
Luis M. Antunes, Keith T. Butler, and Ricardo Srau-Crespo Crystal structure generation with autore- gressive large language modeling. Nature Communications, 15(1):10570, 2024. ISSN 2041-1723. doi:
Sterling Baird. mp-timo-split. accessod in 2024. 2023.
Tvano F. Castelli, David D. Landis, Kristian Thygesen, Søren Dahl, Tb Chorkendorff, Thomas F. Jaramillo, and Karsten W. Jacobsen. New cubic perovskites for one- and two-photon water splitting using the computational materials repository. Energy Environ. Sci., 5:9034-9043, 2012a. doi: 10.1039//2EE0 CCEE22341D.
Ivano E. Castelli, Thomas Olsen, Soumendu Datta, David D. Landis, Soren Dahl, Kristian S. Thygesen, and Karsten W. Jacobsen. Computational screening of perovskite metal oxides for optimal solar light capture. Energy Environ. Sci., 5:5814 5819, 2012b. doi: 10.1039 (0039/CC11022111
Anthony K. Cheetham and Ram Seshadri. Artificial intelligence driving materials discovery? perspective on the article: Scaling deep learning for materials discovery. Chemistry of Materials, 36(8):3440-34)) 3349,, 2024.
doi: wtt.///ac..ceemater...
John Dagdelen, Alexander Dunn, Sanghoon Lee, Nicholas Walker, Andrew S Rosen, Gerbrand Ceder, Kristin A Persson, and Amubhav Jain. Structured information extraction from scientific text with large language models. Nature Communications, 15(1):1418, 2024.
Ali Davariashtiyani, Busheng Wang, Samad Hajinazar, Fva Zurek, and Sara Kadkhodaei. Impact of data bias machine learning for crystal compound synthesizability predictions. Machine Learning: Science and Technology, 5(4):040501, nov 2024. doi: 10.1088/ 20082/2222-222 215322153399992
Tim Dettmers, Artidoro Pagnoni, Ari Holtzman, and Luke Zettlemoyer. QLORA: efficient finetuning of quantized LLMs. In Proceedings of the 37th International Conference on Neural Information Processing Systems, NIPS '23, Red Hook, NY, USA, 2023. Curran Associates Inc.
Claudia Draxl and Matthias Schefllr. The NOMAD laboratory: from data sharing to artificial intelligence. 233)0036011, may 2019. doi: 10.
Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. The llama 3 herd of models. arXiv preprint 27X.v2247..21783, 2024.
Ulrik Friis-Jensen, Frederik L. Johansen, Andy S. Anker, Erik B. Dam, Kirsten M. Ø. Jensen, and Raghaven- dra Selvan. Chili: Chemically
largo-scale inorganic nanomaterials datasct for advancing graph machine learning, In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD '24 pp. 4962-4973, New York, NY, USA, 2024. Association for Computing Machinery. ISBN 97984400044901. doi:
Elena Gazzarrini, Rose K. Cersonsky, Marnik Berex, Carl Adorf, and Nicola Marzari. The rule of four: anomalous distributions in the stoichiometries of inorganic compounds. npj Computational Materials, 10 (1):73, Apr 2024. ISSN 2057-3960. doi: 10.1038//41152240244-02242
13

---

Published in Transactions on Machine Learning Research (04/2026)
Saulius Gražulis, Daniel Chateigner, Robert T. Downs, A. F. T. Yokochi, Miguel Quirós, Luca Lutterotti, Flena Manakova, Justas Butkus, Peter Moeck, and Armel Le Bail. Crystallography Open Database an open-access collection of crystal structures. Journal of Applied Crystallogruphy, 42(4))726 729, Aug 2009.
doi:
Nate Gruver, Amuroop Sriram, Andrea Madotto, Andrew Gordon Wilson, C. Lawrence Zitnick, and Zachary Ward Ulissi. Fine-tuned language models generale stable inorganic materials as text. In The Twelfth International Conference on Learning Representations (ICLR), 2024.
Gabe Guo, Tristan Luca Saidi, Maxwell W. Terban, Michele Valseochi, Simon J. L. Billinge, and Hod Lipson. Ab initio structure solutions from nanocrystalline powder diffraction data via diffusion models, Nov 2025. ISSN 1476-4660.
Tanishq Gupta, Mohd Zaki, NM Anoop Krishnan, and Mausam. Matscibert: A materials domain language model for text mining and information extraction. ngj Computational Materials, 8(1):102, 2022.
Glen M Hocky and Andrew D White. Natural language processing models that automate programming will transform chemistry rescarch and tcaching. Digital discovery, 1(2):79-83, 2022.
Kevin Maik Jablonka, Philippe Schwaller, Andres Ortega-Gueerrer, and Berend Smit. Leveraging large language models for predictive chemistry. Nature Machine Intelligence, 6(2):161 169, 2024.
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 innovation. APL Materials, 1 (1):011002, 07 2013 3a. ISSN 2166-532X. doi: 10.1063/1.444 1.482233..
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 innovation. APL Materials, 1 (1):011002, 07 2013b. ISSN 2166-532X. doi: 10.1063 101///1481223
Rui Jiao, Wenbing Huang, Peijia Lin, Jiaqi Han, Pin Chen, Yutong Lu, and Yang Liu. Crystal structure prediction by joint equivariant. diffusion. Advances in Neural Information Processing Systems, 36:17464- 17497, 2023.
Scott Kirklin, James E Saal, Bryce Meredig, Adam Thompson, Jeff W Doak, Muratahan Aykol, Stephan Rühl, and Chris Wolverton. The open quantum materials database (oqmd): assessing the accuracy of dft formation energies. ngj Compulational Materials, 1(1):1 15, 2015.
Emil T. S. Kjær, Andy S. Anker, Marcus N. Weng, Simon J. L. Billinge, Raghavendra. Selvan, and Kirsten M. Ø. Jensen. Deepstruc: towards structure solution from pair distribution function data using deep generative models. Digital Discovery, 2:69-80) 2023. doi:
Matej Kosec, Sheng Fu, and Mario Michael Krell. Packing: Towards 2x NLP BERT acceleration. CoRR, 0os/2107.02027 2021.
Qingsi Lai, Panjie Xu, Lin Yao, Zhifeng Gao, Siyuan Liu, Hongshuai Wang, Shuqi Lu, Di He, Liwei Wang, Linfeng Zhang, Cheng Wang, and Guolin Ke. End-to-end crystal structure prediction from powder x-ray diffraction. Advanced Science, pp. 2410722, 2025.
Tya Loshchilov and Frank Hutter. Fixing weight decay regularization in adam. CoRR, abs/ 17100111.,5101, 2017.
Andres M. Bran, Sam Cox, Oliver Schilter, Carlo Baldassari, Andrew D White, and Philippe Schwaller, Augmenting large language models with chemistry tools. Nature Machine Intelligence, pp. 11, 2024.
Benjamin Kurt Miller, Ricky TQ Chen, Amuroop Sriram, and Brandon M Wood. Flowmm: Generating materials with riemannian flow matching. In Forty-first International Conference on Machine Learning, 2024.
14

---

Published in Transactions on Machine Learning Research (04/2026)
T. Mohanty, M. Mchta, H. M. Sayeed, V. Srikumar, and T. D. Sparks. Crystext: A generative ai ap- proach for text-conditioned crystal structure generation using llm. ChemRriv, 2024. doi: 10.26434/ chemrxiv-2024-gihee gjbpqq. This content is a preprint and has not been peer-reviewed.
Koichi Momma and Fujio Izumi. VESTA: three-dimensional visualization system for electronic and
structural analysis. Journal of Applied Crystallography, 41(3):653-66 658, Jun 2008. doi: 10.1107/
S0021889808012016.
Shyue Ping Ong, William Davidson Richards, Anubhav Jain, Geoffroy Hautier, Michael Kocher, Shreyas Cholia, Dan Gunter, Vincent Chevrier, Kristin A. Persson, and Gerbrand Ceder. Python materials ge- nomics (pymatgen): A robust, open-source python library for materials analysis. Compulational Materials Science, 68:314-319 319, 2013. doi:
201.0.00mmcc2222210.02.... 10.2..
Robert Palgrave. An explanation for the rulc of four in inorganic materials, 2024. Preprint, not pecr-reviewed.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep lcarning library. In H. Wal- lach, H. Larochelle, A. Beygelzimer, F. d' Alché-Buc, E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
A. L. Patterson. Ambiguitics the x-ray analysis of crystal structures. Phys. Rev., 65:195-201, Mar 1944. doi: 10.1108/PhysSRex.65.119 19..
Chris J. Pickard. AIRSS Data for Carbon at 10GPa and the C+N+H+O System at 1GPa. https:// archive mwteriallclood.. wrw/recorrd/2/0.oooooooooo 0026/v1, 2020.
Maciej P Polak and Dane Morgan. Extracting accurate materials data from rescarch papers with conversa- tional language models and prompt engineering. Nature Communicaations, 15(1):1569, 2024.
Eric A. Riesel, Tsach Mackey, Hamed Nilforoshan, Minkai Xu, Catherine K. Badding, Alison B. Altman, Jure Leskovec, and Danna E. Freedman. Crystal structure determination from powder diffraction patterns with generative machine learning. Journal of the American Chemical Society, 146(44)330340 30348, 2024.
doi: 20.1021/jacsAAc12244 PMID: 39298266.
Andre Niyongabo Rubungo, Kangming Li, Jason Hattrick- Sentrick-Simpers, and Adji Bousso Dieng. LLM4mat- bench: Benchmarking large language models for materials property prediction. In AT for Accelerated Materials Design NewrIPS 2024, 2024.
Mara Schilling- Wilhelmi, Martiño Ríos- García, Sherjeel Shabih, María Victoria Gil, Santiago Miret, Christoph T Koch, José A Márquez, and Kevin Maik Jablonka. From text to insight: large language models for chemical data extraction. Chemical Society Reviews, 2025.
Matthias N. Schneider, Markus Seibald, Patrick Lagally, and Oliver Oeckler. Ambiguities in the structure de- termination of antimony tellurides arising from almost homometric structure models and stacking disorder. Journal of Applied Crystallography, 43(5 Part 1):1012-100 10200, Oct 2010. doi: (0.1107/S002/ 1LL1177/$00228888800006666
Yihan Shen, Yibin Jiang, Jianhua Lin, Cheng Wang, and Junliang Sun. A general method for search- ing for homometric structures. Acta Crystallographica Section B, 78(1):44-19, Feb 2022. doi: 10.1107/ $2052520621011856
Nathan J Szymanski, Bernardus Rendy, Yuxing Fei, Rishi E. Kumar, Tanjin He, David Milsted, Matthew J McDermott, Max Gallant, Ekin Dogus Cubuk, Amil Merchant, et al. An autonomous laboratory for the accelerated synthesis of novel materials. Nature, (7990)90) 91, 2023.
Atsushi Togo and Isao Tanaka. Spglib: software library for erystal symmetry search, 2018.
15

---

Published in Transactions on Machine Learning Research (04/2026)
Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaci, Nikolay Bash- lykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arxic preprint orXiu:2307.09950 2023.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, L. ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In 1. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (eds.), Advances in Newral Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
Anthony R. West. Solid Slate Chemistry and ils Applications. Wiley, 2nd edition, 2014.
Tian Xie, Xiang Fu, Octavian-Eugen Ganea, Regina Barzilay, and Tommi Jaakkola. Crystal diffusion variational autoencoder for periodic material generation, 2022.
R.A. Young. The Rietveld Method. IUCr monographs on crystallography. Oxford University Press, 1995.
ISBN 9780198588 98559122.
Claudio Zeni, Robert Pinsler, Daniel Zügner, Andrew Fowler, Matthew Horton, Xiang Fu, Zilong Wang, Aliaksandra Shysheya, Jonathan Crabbé, Shoko Ueda, et al. A generative model for inorganic materials design. Nature, pp. 1-3, 2025.
Duo Zhang, Xinzijian Liu, Xiangyu Zhang, Chengqian Zhang, Chun Cai, Hangrui Bi, Yiming Du, Xuejian Qin, Anyang Peng, Jiameng Huang, Bowen Li, Yifan Shan, Jinzhe Zeng, Yuzhi Zhang, Siyuan Liu, Yifan Li, Junhan Chang, Xinyan Wang, Shuo Zhou, Jianchuan Liu, Xiaoshan Luo, Zhenyu Wang, Wanrun Jiang, Jing Wu, Yudi Yang, Jiyuan Yang, Manyi Yang, Fu-Qiang Gong, Linshuang Zhang, Mengchao Shi, Fu-Zhi Dai, Darrin M. York, Shi Liu, Tong Zhu, Zhicheng Zhong, Jian Lv, Jun Cheng, Weile Jia, Mohan Chen, Guolin Ke, Weinan E, Linfeng Zhang, and Han Wang. DPA-2: a large atomic model as a multi-task learner. npj Computational Materials, 10(1):293, December 2024. ISSN 2057-3960. doi:
10.1035/s411224-02--0112
Hengrui Zhang, Wei (Wayne) Chen, James M. Rondinelli, and Wei Chen. Et-al: Entropy-targeted active learning for bias mitigation in materials data. Applied Physics Reviews, 10(2):021403, 04 2023. ISSN 1931-9401. doi: 10. 10.1063/5.00 55038393.
Daniel M Ziegler, Nisan Stiennon, Jeffrey Wu, Tom B Brown, Alec Radford, Dario Amodei, Paul Chris- tiano, and Geoffrey Irving. Fine-tuning language models from human preferences. arXiv preprint 1rXiv:1909. 08593, 2019.
A Appendix
A.1
Code and Data Availability
The code for training and using the deCIFer model is open source and released under the MIT License. Official source code and model checkpoints are available here: httpps///ggttbb...c////errrriiie deCIFer.
A.2 CIF Syntax Standardization
To enhance the transformer model to process CIF's effectively, we standardized all CIF's in the dataset. In- spired by CrystaLLM (Antunes et al., 2024), employed similar pre-proccssing and tokenization strategies, incorporating additional steps to ensure that CHILL-100K (Friis-Jensen et al., 2024) was aligned to the stan- dardized format of NOMA, by the removal certain details such as oxidation states and partial occupancies. We employ the following steps:
Uniform Structure Conversion: CIFs were converted to wwwatgen.Struutuuueee Structure (Ong et al., 2013) objects to provide consistent base representation.
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2. Standardized CIF Regeneration: Using pymatgen. CifWriter (Ong et al., 2013), CIFs were regenerated to ensure uniform formatting, eliminate customs headers, etc.
3. Data Tag Normalization: The reduced formula, following the data_ tag was replaced with the full cell composition, sorted by atomic number for consistency.
4. Symmetry Operator Removal: Symmetry operators were excluded during pre-processing to simplify the data, but reintroduced during evaluation for validating structural matches, This can casily be done bocause the reintroduction process uses the space group information retained in the pre-processed files, ensuring compatibility and accuracy.
Incorporation of Extra Information: Custom properties that easily derived from the com- position of each CIF, such electronegativity, atomic radius, and covalent radius, were appended to each CTF to maximize the readily available information within each CTF.
6. Oxidation State and Occupancy Filtering: Oxidation stale refers to the charge of an atom within a compound, which can vary depending on chemical bonding. Occupancy indicates the fraction of particular atomic site that occupied in the crystal structure (c.g., a value of 1.0 represents a fully occupied site, while 0.5 indicates partial occupancy). states were removed, and only crystal structures with full occupancy were retained. This ensures consistency by aligning CHILI-100K (Friis-Jensen al., 2024) with the standardized format of NOMA (Antunes et al., 2024).
traces of oxidation
7. Numerical Value Normalization. Numerical values were rounded to four decimal places.
Figure A1 shows a pre-processed and standardized CIF from the NOMA dataset alongside its corresponding unit coll representation and a realisation of its corresponding PXRD profile, as could be input into deCIFer.
leop.
Jaom byp siectronsgabbily
aeam hyp losz raduo
Mo L.520 14330 6603
3,4000 5:5000 3500
238 Jonglrr 5.7500
2 13.0404
_osil engs, zima
50 cose
.enl anga, garma
Synmeiry Tacles emurtua
Cremical Jsmmata
18 Mit Dop
(ed valume
Sanp.
10sg.
.a5mL be. Mbel
.nom km Fart
JKom Fac
1/ LIT & 6 EONOE 02337 0.7651 1,0000
E.20de 8a:5t cass1 1000
04 0849
0.748
G1A-13
31893 0:1130
0.8155 1,0020
Figure A1: Illustration of a CIF after applying the pre-procossing and standardization steps described. Also shown are the corresponding unit cell representation using VESTA (Momma & Izumi, 2008) for visualiza- tion and the simulated PXRD profile (with a² = 0.00 and FWHM=0.01). The red highlight in the CIF indicates where the original symmetry operators were replaced during pre-processing and would be restored for evaluation.
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A.3 CIF Tokenization
To process CIF files effectively, we tokenized each file into a sequence of tokens using custom vocabulary tailored to crystallographic data in the CIF format. Each CIF was parsed to extract key structural and chemical information, such as lattice paramcters, atomic positions, and space group symbols. Numerical values were tokenized digit-by-digit, including decimal points and special characlers as separate Lokens. Table Al shows all supported tokens.
Table Al: Supported atoms, CIF tags, space groups, numbers, and special tokens.
Category
Num.
Tokens
Atoms
89
Si Pb Br CI Eu O Pe Sb In N Mn Lu Se TI Hf Ir Ca Ta Cr K Pm Mg Za Tb
Cu Su
Pd
Zr Cd Se Ge Pt Ga Li Os F Ba Te Mo Gd Pr Bi Se Ag Rb Dy
Np Hg
Rh Th Na. Ra La Re Y
Rr
Kr He Ne Ar
CIP Tags
31
data
loop
symmetry group name H-M
symmetry_ Int Int___ant_______________________ TTalls__number
-cell _cel__length length_
cell length
ccll length_
_cell _oell_angle _lpha
_cell celll_nngee_bet
cell augle gamma
_oell _oell_volume
_atom_sste site frrc__rac____
atom site fract
_atom_site_fract
attom_sit__oocuppae
symmetry _ewileeeuvvvv.. pos_ xyz chemical formula structural cell formula untks__nt______ Z systematic chemical formula sum sesstt__smmmrry__meee
chemical
Lattt site aitom_sst__Attachedd attacche___aatt.ee shydroge_n atom site label
atom site type_ symbol atom B iso or eeuuvv
symmetry equiv pos site id
atom aatom_type_st_ wwwptttppp____eeeeee
_attm atttm__tpe_eleettonngatvve
attat selom__tpe_rradlle radius
atom type atom typeeye_eee _oe__dxtiiioon number
Space
230
P6/mmm Imma P4 12 P4 2/mnnu Fd-3m P3ml P-3 P4mm P4 332 P4/anc
Groups
12_ 12 Pan2 Pbon P4 2/1 Cm R3m Cice Aea2 P-42 1m P-42m P2 13 R-
Fm-3 Cmm2 Pu-3a P6/mce
P-3ml P3
123
P1
Pma2 Pmmna 1-42m P-31c Pa-3 Pmmmn Pmmmu P4 2/ucm 14/incm 1-4m2 P3
Cmem 1222
P6
P6
Pm-3
Ia-3d Pm-3m P2_1/e C222 Pe P4/n Pba2 Ama2 Pbem P31m Peca P222 P-
43a Peem P6 422 F23 P42 C222
Pnnn P6 3cm P1 12. 12 P6/m Fmm2
1/a P4/mbm Pmu22 1 P4 2bc P4 22 12 1-43d 14/m P4bm Fdd2 P3 P6 122
Pnc2 P4 2/mcm P4 122 Cmc2 P-6c2 R32 P1 P1 232 Pana P/122 Pban Ce
3/m P6
1/amd P4 2 Pmnna P4/m Fm-3m P4/mmm
1mm2 P4/nce P-62c Ima2 P6 P2/c P4/nbmm Ibam P6 522 P6 3/mmc 14/ 14/mmm
Fmmm P2/m P-4h2 C2/m P4 2/4_2/me 3/mme P4
P4_3
1/m
P-42c
F4_132 Pm Peen P-1n2 P4_ 13____2____11 P23 Iemm R3c Amm2 Immm Iba2 14 Fd-3 P1
Pbam P4 2/ube 1m-3 P4 2/amm Pmn22 1 P-31m R-3m la-3 P622 F222 P2 P-1
Pmm12 P-4 Aem2 P6 222 P-3cl P4 322 1422 Pama P6 3 P3cl Pn-3 P4nc P-6
P4/mce 12 12 12 P4 2/mbc P31c Ccc2 P4 2/amc P6 3/mom C2 Pbea F-
P222 1-42d I-4c2 P6cc P6 P6__ 2 P3 221 P321 Pea2 14 //aod 14_ 132 F432 Pna2 1 Cooe Thea
P2
Pn-3m C2/c
P4/mne Imd P2 12 P2_12____ 12_ 1 R-3e
P-4m2 Pmn-3n 14mm F-43m Pnom
42 1e Caumm P6mm P1 2cm P4 2/m Im-3m Fm-3c 11 Pice Came
Numbers
10
1234667
Special
x xyx. () (space) (newline) (unk) (pad) (cond)
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.
Attention to PXRD embedding e²
Attention to token embedding
positions
le
1......
M
[e 1.
cell parameters
le te .e........
space group
I composition
(c',
Token embedding index
Figure A2: Visualization of the attention masking strategy, showing the log-mean attention weights (averaged over all heads) for an example sequence and highlighting how CIFs are isolated using the attention mask. The figure also illustrates how the embeddings of the second CIF attend to the conditioning PXRD embedding. Lighter shades indicate stronger attention.
A.4 Attention Masking Strategy
Figure A2 provides detailed visualization of the attention masking strategy employed in our model. It illustrates the log-mean attention weights (averaged over all heads) for a sample sequence, highlighting the isolation of CIFs through attention masking. The figure also demonstrates how the embeddings of the socond CIF attend to the conditioning PXRD embedding. Lighter shades the figure correspond to stronger allention values.
A.5 PXRD Simulation
What do the axes in PXRD mean? In typical PXRD experiment, the x-axis corresponds to the magnitude of the scattering vector, commonly denoted by Q (in units of À Á-1), or sometimes the diffraction angle 20, In this work, we use Q sine where À is the radiation wavelength and the scattering angle, The y-axis represents the scattered intensity observed each Q-value, sometimes normalized to have maximum intensity of 1.
Peak data and transformations. Following the methods section, we start with the discrete diffraction peak data: p = (4k,4) ix) where each 9k is the center a reflection peak, and is is the associated peak intensity. To simulate experimental effects, we apply transformation T, which includes peak broadening and additive noise.
Peak broadening. For each peak k centered at gs, convolve idealized delta function peak with pscudo-Voigg profile. At the continuous variable Q, the psuedo-Voot profile is the mixture of a Lorentzian L and a Gaussian G, such that
PV g+) nl(Q qx) + (1-1))(( qk),
where 0 5n S fixed at 17 = 0.5 in this work.
Let FWHM denote the full width half maximum. The Lorentzian half-width is then 7
FWHM
making
2
1
L(Q - 9x)
+
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Peak Broadening
Additive Noise
Norm. Intensity
nosse 0.001 FWHM: 0.010
Coose 0.001 FWHM: 0.100
11011 III DIRI H10
IHIEI BB IN HIMMI IIII
Norm. Intensity
noise 0.050
naise : 0.050
FWHM: 0.010
FWHM: 0.100
1IT1 UHI DIGGO DIDG0
THEET WEE BIERER II
1
Q 1
Figure A3: Simulated PXRD profiles with fixed transformation FWHM and moise as indicated. Discrete peaks, {(k. ==) are shown in red, while the convolved PXRD profiles, y, are shown in blue. Examples with minimal and maximal noise and broadening levels are shown for a compound with composition CdRhBra and space group R3m.
The Gaussian standard deviation is
FWHM 2/2
making
G(Q qb) exp (- (-1(2(e))
(4)
Convolved PXRD. Given the peak centers gk: itensities in. and a choice of FWHM, we obtain the convolved PXRD profile
Lconv (Q)
in PV - (k).
(5)
Afterwards, normalize Loonv (Q) so that its maximum intensity is 1.
Noise addition. Let e(Q) be drawn from zero-mean Gaussian distribution with variance hosse This yields the final transformed intensity PXRD profile:
((Q) (Q) cQQ).
(6)
Implementation details. In practice, we use the XRDCal from the pymatgen library (Ong et al., 2013) for generating the initial discrete peak data P. For training, we sample Q-values in [Qmins Quax] at increments of Qstep- We then apply random transformations т during model training. Specific parameters for FWHM and nolse are listed in Table A2.
A.6 Validity Metrics
To evaluate consistency and chemical sensibility of the generated CIFs, we conduct a scries of validation checks. The methodology is described below.
Formula Consistency
We check for consistency in the chemical formula printed in different locations within the CIF. Specifically, ensure that:
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Table A2: Training configuration for deCIFer and U-deCIFer.
PXRD Transformation Training Parameters
Value
Wavelength (A)
Cu-Ka (1.5406 A)
Q-grid (Qming Qmax: Qstep)
(0.0, 10.0, 0.01)
FWHM
u (0.001, 0.10)
Mixing Factor (1)
0.5
Noise Magnitude
u ~ (0.001, 0.05)
Model / Training Parameters
Value
Optimizer
AdamW
Learning Rate
x 10-3
Warmup Steps
100
Docay Steps
50,000
Minimum Learning Rate
1 10-6
Weight Decay
0.1
Batch Size
32
Gradient Accumulation Steps
40
Maximum Iterations
50,000
Embedding Dimension (Nemba)
512
Layers (Mayer)
Atlention Heads (Thead)
Conditioning Model Layers (Ne-layers)
2
Conditioning Model Hidden Size
512
Sequence Length (block_sste _ize)
3076
Precision
16
Dropout
0.0
The chemical formula. in the _chemical_formmlaaaappo tag matches the reduced chemical formula derived from the atomic sites.
The chemical formula in the wtw.cccccl_foommmiii ftt.uualttastuuuurrallllll derived from the CIF file.
structural tag is consistent with the composition
Site Multiplicity Consistency
We validate that the total multiplicity of atomic sites is consistent with the stoichiometry derived from the composition. Specifically, ensure:
The atom types are specified under the _atom__aa site_ site_type type_symbol tag.
The multiplicity of each atom provided in the aatomssite the__ttossiiee_smmettt.mttt symmetrry.mlliiplicctyy tag.
The lotal number of atoms derived from these tags matches the stoichiometry derived from the _chemicallformula_appooaaa formula_ssseeeee sum tag.
Bond Length Reasonability
To check the reasonableness of bond lengths:
We Voronoi-based nearest-ncighbour algorithm implemented in the CrystalNN module of pymatgen (Ong el. al., 2013) to identify bonded atoms.
For each bond, the expected bond length calculated based on the atomic radii and the electroneg- ativity difference between the bonded atoms:
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If the electronegativity difference is greater than equal to 1.7, the bond is treated as ionic, and the bond length is based on the cationic and anionic radii Otherwise, the bond is treated as covalent, and the bond length is based on the atomic radii.
A bond length reasonableness score B is computed the fraction of bonds whose lengths are within +30% of the expected lengths.
structure passes this test. if 2 Chond, where Cbond = 1.0.
Space Group Consistency
We validate the space group by:
Extracting the stated space group from the
htw.rgggoouuu_______ee _aMMe_HMM tag.
Analyzing the space group symmetry using the Spacegrouphnalyyzrr class in pymatgen (Ong et al., 2013), which employs the spglib (Togo & Tanaka, 2018) library.
Comparing the stated space group with the one determined by the symmetry analysis.
Overall Validity
A CIF file is deemed valid if all the above checks are satisfied:
Formula consistency (FM).
Site multiplicity consistency (SM).
Bond length reasonableness B 2 Cbond: where Chond = 1.0 (BL).
Space group consistency (SG).
A.7
Match Rate
The Match Rate (MR) quantifies how many generated structures successfully match their corresponding reference structures, as determined by StructureMatcher from the pymatgen library (Ong et al., 2013). Two structures are considered match if their compositions, lattice parameters, atomic coordinates, and symmetry are sufficiently similar, according to the tolerances set StructureMatcher. For the implementation of deCIFer, we follow the example set by CrystaLLM (Antunes et al., 2024), using the parameter values:
stol 0.5: site tolerance, defined fraction of the average free length per atom.
angle_tol sol = 10": maximum angular deviation tolerance.
ltol 0.3: fractional length tolerance, meaning the lattice parameters can differ by up to 30%
relative to the reference lattice.
StructureMatcher compares two structures by:
Optionally reducing them to primitive (Niggli) cells.
Verilying that the lattice parameters are within the fractional length tolerance (1tol).
Checking that the angles are within the angle tolerance Langle_tol).
Ensuring that atomic coordinates align within the site tolerance (stol), normalized by the average free length per atom.
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Dataset OQMD
MP
NOMAD
CIF Count
107
81
101
121
141
161
201
221
Spacegroup Number
CF Count
8
Number of Elements in Unit Cells
Occumences
202
Element
Occurences
10a
0.03
Hinl Iilmmll filia aal
Ball
1000
2000
3000
4000
5000
6000
7000
length
Figure A4: Statistical overview the NOMA (Antuncs et al., 2024) dataset (2,283,345 346 total samples), show- ing the distribution of space group frequencies, the number of elements per unit cell, elemental occurrences and CIF token lengths (indicating the percentage of CIFs with larger token sequences than the context length of 3076)
With these parameters, each generated CIF is compared against its reference CIF*. If the two structures are deemed structurally equivalent, we count that as successful match. MR computed as the fraction of structures in the dataset for which match is found:
MR = N Σ (match(CIIF (CIF,
where N is the total number of structures and 1(-) is an indicator function that returns 1 if two structures match (according to StructureMatcher) and 0 otherwise.
A.8
Datasets Statistics
Figure A4 illustrates the NOMA dataset. Figure A5 illustrates the statistics of the curated CHILL- 100K (Friis-Jensen et al., 2024) dataset.
A.9 Model Architecture- and Training Details
Table A2 provides concise overview of all hyperparameters and data augmentation settings used for training deCIFFer (and its variant U-deCIFer). Below, we describe additional implementation details.
Data-stratification We extract the space group number from each CIF (ranging from 230) and group these into bins of size ten (c.g., 1-10, 11-20, etc.). This heuristic aims to preserve the overall symmetry distribution across splits while reducing the risk of data leakage from structurally similar entries appearing in
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Dataset
CHILI-10O
10a
10a
61
121
Spacegroup Number
10a
CiF
101
2
Number of Elements in Unit Cells
Occurences
-02
1o3
101
488 2 2
20
Element
Occurences
103
10a
10a
1000
2000
3000
4000
length
Figure A5: Statistical overview of the curated CHILI-100K (Friis-Jensen al., 2024) dataset. (8201 total samples), showing the distribution of space group frequencies, the mumber of elements per unit cell, elemental occurrences, and CIF token lengths (indicating the percentage of CIFs with larger token sequences than the context length of 3076).
multiple subsets. While this does ensures coverage across symmetry classes and even representation crystal systems across the splits, it does not reflect the most intuitive or principled grouping scheme. In particular, it does not account for fner-grained biases that may be embedded in crystal symmetry or composition distri- butions. This points broader issue in materials datasets: statistical artefacts, such the 'Rule of Four" symmetry clustering (Gazzarrini et al., 2024), generalisation and interpretability (Palgrave, 2024). Future work should explore alternative stratification strategies (e.g,, stratified sampling based on structural descriptors) to better assess generalisation.
introduce shorteuts that models may learn, reducing
Hardware Setup All experiments were conducted on GPUs with sufficient memory to accommodate a batch size of 32 tokenized sequences, each truncated or padded to context length of 3076. We employed half-precision (float.66 lo reduce memory usage and improve throughput, ensuring that gradient updates remain numerically stable via built-in automatic mixed -xecissre
Optimizer and Learning Rate Schedule. We adopt AdamW with a base learning rate of x 10-3 which is warmed up for 100 steps and then gradually decayed to x 10 over 50,000 steps (Table A2). Weight decay is set to 0.1 to regularize model parameters, and we employ gradient accumulation (40 steps) effectively increase the total number of tokens processed per update.
Transformer Architectural Notes. The final transformer stack has 8 layers, each with 8 attention heads, and a model dimension 512 (embedding dimension). The food-forward blocks inside cach layer use dimension of 512, and dropout is to 0.0 minimize underfitting. We continue observe stable convergence in practice despite using dropout.
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0.30
U-deCIfer [Train]
Cross-Entropy Loss
U-deCIFer [Validation] deCIFer [Train]
0.25
deCIFer [Validation]
0.20
0.1717
0.15
0.1360
0
10000
20000
30000
40000
50000
Epoch
Figure A6: Cross-entropy loss curves for U-deCTFer and deCIFer over 50,000 training iterations, showing progressive reduction in the training and validation losses.
Maximum Iterations and Convergence. We train for 50,000 iterations, at which point the model's cross-entropy loss stabilizes, as illustrated Figure A6. Beyond this range, no significant improvements were observed on validation metrics.
A.10 PXRD Embedding Space
For completeness, we examined the learned embeddings for 50K random training-set PXRD profiles and applied principle component analysis (PCA) for visualization. As shown Figure A7, the emboddings form distinct gradients when colored by crystal system, cell-volumes, and constituent atomic numbers Z, indicating that the model's PXRD embedding captures relevant structural characteristics, such symmetry, scale, and elemental composition. These patterns highlight the effectiveness of the conditioning mechanism in encoding mcaningful structural information directly from the PXRD input.
A.11 Baseline Comparison with and without PXRD
With regards to the baseline comparison in Table 1, deCIFer is explicitly conditioned on PXRD data, while the baseline models are conditioned only on composition or latent priors. This distinction means that the comparisons are not direct but instead reveal the relative value of PXRD conditioning. particular, PXRD conditioning can improve structure prediction when the diffraction signal is rich in structural information, but may introduce ambiguily or conflict with the model's learned priors cases where the PXRD pattern is noisy or minimally informative. Perov-5 and Carbon-24 provide strong tests of PXRD conditioning due to their polyhedral complexity and carbon-based structural diversity, where diffraction features directly inform the model. In rast, MP-20 is drawn from the Materials Project, dataset where composition-only models may benefit from learned priors due to the high representation of standard chemistries. MPTS-52 further challenges models with low-symmetry structures, where the PXRD signal can become ambiguous, making it difficult for a model to resolve atomic positions purely from the diffraction pattern.
A.12 Additional Results
Figures A8, A9, and A10 provide additional insights into deCIFer's performance. Table A3 shows a detailsed breakdown the validity metrics for the NOMA test set corresponding to the results in Figure Table A4 shows a detailed breakdown of validity metrics for the NOMA test set and CHILI-10OK test evaluated two in-distribution (ID) scenarios and one out-of-distribution (OOD) scenario for the PXRD input.
A.13 Future Work
One promising area for improvement lies in exploring more advanced decoding strategies, such beam search, to enhance the generative model's capabilities in downstream tasks. By maintaining multiple hy-
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Log Cell Volume (LogA?]
Average Z
40
80
35
30
00
PC2
10
-0.5-
-35
-10
-10
1.0
-1.5
15
PC1
PC1
Crystal System
Crystal System
Unknown
0.5
Triclinic
Monoclinic
0.0-
Orthorhombic
Tetragonal
-0.
Trigonal
Hexegonel
-10-
Cubic
-23 -2.0
-1.5
-1.0
-05
0.0
0.5
PC1
Figure A7: 2D PCA projection of learned PXRD embeddings for 500K training-set samples from NOMA. The three subplots are colored by crystal system, log(cell volume), and average atomic number Z, illustrating clear gradients that correspond to structural and compositional features as indicated by the arrows.
potheses during decoding, beam search could produce diverse candidate CIFs for a given PXRD profile, improving structure determination accuracy by ranking outputs based on metrics like Rwp- This method could also support optimization strategies that prioritize structural validity and relevance.
Another direction could be to integrate reinforcement learning from human feedback (RLHF) to guide the model more directly toward generating accurate and chemically valid structures (Ziegler et al., 2019). By defining a reward function tailored to properties such as low Rwp values, structural integrity, and adherence to chemical constraints, and interaction with a human expert, RLHF could further refine the model's outputs.
A complementary direction for future improvement lies in increasing the diversity of the training data. While NOMA offers excellent scale, its distribution is skewed toward high-symmetry and well-sampled structures, which limits model generalisation to more uncommon systems. CHILI-100K, with its broader structural com- plexity and greater representation of low-symmelry crystals, could serve as valuable training supplement. Mixing synthetic and experimental data, or applying curriculum learning strategies that gradually expose the model to under-represented symmetry groups, could improve generalisation and robustness, particularly for monoclinic and triclinic systems, which remain challenging as seen Figure
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Table A3: Validity of generated CIFs for the NOMA test set using deCIFer and U-deCIFer. Abbreviations: Form = formula validity, SG = space group validity, BL = bond length validity, SM = site multiplicity validity. Overall validity (Val.) is calculated as the percentage of CIFs that satisfy all four validity metrics simultancously. Match rate (MR) represents the percentage of generated CIFs that replicate the reference
CIF.
Desc.
Model
Form (%) t SG (%) t BL (%)
SM (%)
Val. (%)
MR (%) t
U-deCIFer
99.82
98.87
94.30
99.47
93.49
0.00
none
deC1Fer
99.42
98.85
93.69
99.46
92.66
5.01
U-deCIFer
99.87
99.09
94.40
99.46
93.78
49.30
comp.
deCIFer
99.68
99.21
94.37
99.55
93.73
91.50
U-deCIFerr
99.85
98.88
94.51
99.17
93.72
87.07
comp.ts.g. deCIFer
99.74
99.26
94.38
99.58
93.90
94.53
Table A4: Validity of generated CIFs for the CHIL1-100K test set using deCIFer. Abbreviations: Form formula validity, SG = space group validity, BI. bond length validity, SM = site multiplicity validity. Over- validity (Val.) is calculated as the percentage of CIFs that satisfy all four validity metrics simultaneously. Match rate (MR) represents the percentage of generated CIFs that replicate the reference CIF.
Dataset
nooieer FWHM)
FORM (%) f
SG (%t
(%)
SM (%)
Val. (%)
MR (%)
ID: (0.00, 0.05)
99.68
99.21
94.37
99.55
93.73
91.50
NOMA
ID: (0.05, 0.10)
99.64
99.18
94.39
99.55
93.77
89.28
OOD: (0.10, 0.20)
99.60
92.60
91.66
77.66
ID: (0.00, 0.05)
95.98
97.88
42.61
94.58
41.83
37.34
CHILL-100K
ID: (0.05, 0.10)
97.17
98.22
41.50
94.47
40.95
35.97
OOD: (0.10, 0.20)
95.80
98.42
34.11
93.91
33.62
26.09
NOMA
ID: (0.00, 0.05)
CHILI-100K
NOMA ID: 10.05, 0.05)
CHILI-100K
NOMA ID: 10.00, 0.10)
CHILI-100K
NOMA CHILI-100K
NOMA (0.10, 0.05)
CHILI-100K
NOMA
0OD: (0.00 10.00, 0. 20)
CHILI-100K
NOMA
OOD: (0.1 0.20)
CHILI-100K
0.0
1.0
2.0
3.0
Rwp
Figure A8: Distribution of Rwp for deCIFer on the NOMA- and CHILI-100K test set, presented violin plots with overlain boxplots; the median is shown for each distribution. Presented four in-distribution transformations of the input PXRD profiles and three out-of-distribution transformations.
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(0.00, 0.05")
(0.05, 0.10")
(0.10, 0.20*)
Lower Symmetry
Cubic
6079
6071
811
Hexagonal
Trigonal
1687
3841
Tetragonal
3843
38
4567
Orthorhombic
4563
Monoclinic
2846
2843
129
Triclinic
0.0
0.5
1.0 0
5000
Rwp
Sample
Distribution
Figure A9: Average metric values by crystal systems for deCIFer on the NOMA test set under two in- distribution transformations the imput PXRD profiles and one out-of-distribution transformation. deCIFer shows better performance for well-represented systems, while rarer, low-symmetry systems lead to worse performance. The right-most plot shows crystal system distribution of the NOMA test set.
(0.00, 0.05%)
(0.05, 0.10")
(0.10, 0.20)
Lower Symmetry
Cubic
2182
2174
1184
Hexagonal
1188
Trigonal
1110
1111
1692
Tetragonal
1694
1694
3253
Orthorhombic
3266
44981
Monoclinic
4976
4983
5296
Triclinic
5289
0.0
0.5 Rwp
1.0 0
5000
Sample
Distribution
Figure A10: Average metric values by crystal systems for deCIFer on the CHILI-10OK test show better performance for well-represented systems in the training data (NOMA), while low-symmetry systems lead to worse performance. The right-most plot shows crystal system distribution of the CHILI-100K test set, highlighting that CHILI-100K contains significantly higher proportion of lower-symmetry structures com- pared to synthetic datasets like NOMA.
28


Reviews:
[{"review_id": "CVJp2sLzzw", "reviewer": "Reviewer_oxhp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this paper, the authors adress the task of Crystal Structure Prediction (CSP). Unlike previous methods, which mostly relied on high-level descriptors such as symmetry constraints, they introduce a generative model that is also conditioned on powder X-ray Diffraction (PXRD), a continuous-valued vector that contains diffraction peaks (up to some experimental noise). They report significantly improved results, perform various ablation studies, and discuss some limitations of their method, mostly due to the increased difficulty of the PXRD-conditioned task itself, sometimes subjected to underdetermined ambiguities.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The proposed architecture is clever but pretty straightforward, experiments are well-designed, and results are plausible.", "audience_yn": "Yes", "audience_explanation": "While the topic can seem a bit niche, it is definitely an important topic in its own rights (part of the so-called \"AI for science\" trend), and results are definitely improved compared to the state-of-the-art.", "requested_changes": "The paper is well-written and clear.\n\nJust a small question; in the \"U-Decifer + none\" architecture used in the ablation study, what is the input used at inference exactly? If PXRD conditioning is removed and descriptors are \"none\", what is left?", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "njHpAEZle9", "reviewer": "Reviewer_4DJb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces deCIFer, an autoregressive language model for PXRD-conditioned crystal structure prediction. Unlike prior CSP approaches that rely primarily on compositional or symmetry-based priors, deCIFer conditions directly on synthetic PXRD patterns to generate crystal structure. While the use of PXRD signals to help condition crystal generation appears to be an underexplored area, the poor performance on multiple benchmarks raise critical concerns about the utility of the approach. Currently, it is not clear when or why the method helps or hurts performance and a more thorough analysis is needed.", "claims_and_evidence_yn": "Yes", "claims_explanation": "While the results are promising, several claims are insufficiently supported or contextualized.\n\n- On multiple datasets, decipher does worse than other models that don't use conditioning. While the authors explain that even when this is true, it can be helpful. However, the analysis of where conditioning helps, where it hurts, or why is lacking. An ablation comparing: conditioned vs. unconditioned models on datasets where classical baselines outperform deCIFer would provide evidence for when PXRD conditioning is genuinely beneficial. \n\n- The introduction does not situate the contribution relative to prior PXRD-based structure determination pipelines and prior work in structure generation. Why do other methods not use this signal? Is it costly to acquire? Do you always get the PXRD signal?\n\n- The ablations focus on synthetic datasets and does not thoroughly explore realistic experimental conditions. The limited augmentations (Gaussian noise, peak broadening) do not reflect the full complexity of PXRD artifacts.\n\n- The method’s robustness to PXRD preprocessing (e.g., peak detection errors) and instrument variability is not studied. Is this a reason why some datasets don't benefit from the conditioning?\n\n- The architectural choice of autoregressive modeling is stated but not well justified or compared to alternative ways to incorporate PXRD information. Some simpler baselines that use PXRD would be useful.", "audience_yn": "Yes", "audience_explanation": "There is likely interest among subsets of the TMLR community. However, the broader ML audience may find the contribution somewhat narrow without more conceptual framing, stronger empirical grounding, or clearer methodological insights beyond “apply a language model to CIF prediction conditioned on PXRD.” Interest is therefore moderate, not broad.", "requested_changes": "1. Substantially strengthen the introduction and related work. Provide clear references to: prior PXRD CSP pipelines, learning-based approaches for structure inference, and better insights into how the PXRD can be related to structure prediction problem.\n\n2. Provide deeper evaluation of when PXRD conditioning helps vs. hurts.\n\n3. Include ablations against unconditioned models on datasets where other baselines outperform deCIFer.\n\n4. Clarify how one could predict whether conditioning is beneficial a priori.\n\n5. Analyze dependence on peak detection accuracy. \n\n6. Justify architectural choice. Why autoregressive? Could alternative conditioning strategies or architectures be superior?\n\n7. Discuss practicality: when is PXRD collection feasible, expensive, or unnecessary relative to model gains?", "broader_impact_concerns": "None noted", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "JI9fcqRUeZ", "reviewer": "Reviewer_hb8D", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "## Summary:\nThis paper proposes a novel method, deCIFER, for the generation of crystal structures in the crystallographic information file format. The key contribution of this method is that the generative process is conditioned upon powder X-ray diffraction (PXRD) data. This allows the method, once trained, to accept unseen PXRD data and subsequently generate plausible crystal structures which correspond to the atomic scale structure embedded in this data. To build this model, the paper introduces a novel simulation process for generating noisy PXRD data for training and a conditioning mechanism for handling various input lengths. The method is evaluated on the NOMA and CHILI-100K datasets and the performance was compared to several baselines (CDVAE, DiffCSP and Crystal LLM). The proposed deCIFer approach achieved a higher match rate on two out of the four benchmarks. Additionally, several experiments were done to investigate the effect of the PXRD-conditioning by comparing the performance of deCIFer to its unconditioned variant. Lastly, the paper also tested the effect of varying the gaussian noise that was added to simulate the real-world variation of PXRD data and showed robustness to in-distribution variation of the noise.\n\n## Strengths:\n- Applying autogressive models for crystal structure generation is novel and the results in Table 1 suggest that this approach has some potential. \n- The paper clearly discusses the limitations of their approach such as the limitations of PXRD data and the use of synthetic datasets. \n\n\n## Weaknesses:\n- The main weakness of the paper is that it is very hard to read for researchers with limited knowledge of material science. I am listing a few of the things that were unclear as a result of this:\n    -  it is unclear what is the significance of having direct CSP in CIF format.\n    -  It is unclear whether the Gaussian noise and the instrumental peak broadening are actually mimicking real-world data or not. And How is the use of synthetic PXRD data transfer to real-world data?\n    - The structurally out of distribution benchmark metrics are challenging to judge without the context of how other methods would perform on this setup.  The results for deCIFer showcase impressive robustness results, but it is not evident how impressive they are without comparison to other methods. For instance, the drop from 35% to a 26% match rate on CHILI-100k would serve from additional contextualization. \n - It’s unclear whether the Gaussian noise is used to mimic noise in the real-world or as a data augmentation method to generate additional training data. These two uses are different but the paper seems to imply that they are the same in the introduction section. \n- The paper didn’t mention how the hyperparameters were chosen. Were they chosen based on prior work or based on some sort of search? For example, I find the choice of doing both warm-up and cosine annealing for the learning rate to be an odd combination. \n- The deCIFer’s performance degrades with out-of-distribution noise. How would that affect its applicability to real-world data since the noise in those data would be out-of-distribution? \n- The performance metrics are presented without any indication of the variance or statistical significance of the results, and the out of distribution experiments are presented without sufficient context.\n  - The main results in Table 1, 2 and Figures 3, and 5 are challenging to judge without the inclusion of either standard errors or confidence intervals across random seeds. The highly stochastic nature of the autoregressive language model and the results in Figure 6, would suggest the possibility for variability in the generated results. The impressive results, on for instance RMSE, would be more convincing if they were shown to be non-overlapping in terms of standard error with the baselines. This could be addressed by producing standard errors for these metrics. \n- On page 7, the paper claims “When that data is inconclusive, the model’s uncertainty is reflected in its predictions”. It is not clear how the model does this, other than by producing worse test metrics. How would one know based on the generated output of the model, if the model is uncertain? \n- What does optional descriptions, as mentioned on page 5, mean in the context of this data? Are these features of the dataset, since they are “natively encoded in CIFs”?", "claims_and_evidence_yn": "Yes", "claims_explanation": "- The performance comparisons to recent methods in Table1 was thorough and included several recent algorithms. \n- The authors provided several ablations highlighting the importance of the components presented in their approach. Such as varying the Gaussian noise and investigating the effect of PXRD-conditioning.", "audience_yn": "Yes", "audience_explanation": "Applying autoregressive models to crystal structure predictions is an interesting application that would be of interest to  the general ML audience.", "requested_changes": "- Some rewriting is required to make the paper approachable to the ML audience (See main points in the weaknesses above). \n- Clarifications of other questions in the weaknesses section above are highly needed.", "broader_impact_concerns": "No concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)