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arxiv: 2605.14769 · v2 · pith:HHH5LJUQnew · submitted 2026-05-14 · 💻 cs.LG

Composable Crystals: Controllable Materials Discovery via Concept Learning

Nian Liu , Yuwei Zeng , Ryoji Kubo , Nikita Kazeev , Stephen Gregory Dale , Artem Maevskiy , Pengru Huang , Thomas Laurent
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Kostya S. Novoselov Xavier Bresson
This is my paper

Pith reviewed 2026-06-30 21:50 UTC · model grok-4.3

classification 💻 cs.LG
keywords crystal generationconcept learningVQ-VAEmaterials discoverycompositional modelsde novo designgenerative models
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The pith

Recombining concepts discovered by a VQ-VAE allows controllable generation of novel crystals outside the training distribution.

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

The paper establishes a framework in which a vector-quantized variational autoencoder automatically finds a shared set of reusable concepts from crystal structures. These concepts act as building blocks that can be recombined to guide the creation of new crystals. This approach aims to move beyond black-box random sampling by providing control over how generated crystals differ from known ones. Experiments demonstrate that using these compositions improves performance on validity, stability, uniqueness, and novelty metrics, particularly boosting novelty.

Core claim

The central claim is that training a VQ-VAE on crystal data reveals interpretable concepts based on local atomic environments and global symmetry patterns, which generalize across distributions and can be recombined using a composition generator to produce valid, stable, unique, and novel crystals beyond the training set.

What carries the argument

The vector-quantized variational autoencoder that discovers a shared set of reusable crystal concepts serving as building blocks for guided generation.

If this is right

  • Controllable exploration of novel crystals rather than unconstrained random sampling.
  • Up to 53.2% and 51.7% improvement on the V.S.U.N metric on MP-20 and Alex-MP-20 datasets.
  • Particular gains in novelty of generated crystals.
  • Concepts exhibit interpretability from local and global patterns and generalize to different crystal distributions.

Where Pith is reading between the lines

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

  • The iterative refinement of the composition generator using the model's own high-quality samples could create a feedback loop for continuous improvement in generation quality.
  • If the concepts are generalizable, the method might reduce reliance on massive training datasets for materials discovery tasks.
  • The shared concepts could enable transfer between different crystal datasets without full retraining.

Load-bearing premise

The learned concepts from the VQ-VAE can be recombined into valid and stable crystals that do not require additional post-processing or retraining to achieve the claimed controllability.

What would settle it

A test where many concept-recombined crystals turn out to be invalid or unstable, or where the novelty gains disappear when compared to an improved base model without concepts.

Figures

Figures reproduced from arXiv: 2605.14769 by Artem Maevskiy, Kostya S. Novoselov, Nian Liu, Nikita Kazeev, Pengru Huang, Ryoji Kubo, Stephen Gregory Dale, Thomas Laurent, Xavier Bresson, Yuwei Zeng.

Figure 1
Figure 1. Figure 1: Pipelines for (a) learning a VQ-VAE to extract crystal concepts, and (b) training and refining [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Transformer architectures used in (a) the encoder and (b) the decoder of the VQ-VAE, as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustrations of two learned concepts represented by VQ-VAE codes. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cosine similarities of concept selection [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustrations of two generated crystals together with their supporting concepts. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The whole pipeline of training VQ-VAE. Directly training a VQ-VAE on crystal structures led to limited reconstruction performance in our preliminary experiments. Therefore, we adopt a three-stage training strategy. We first train a variational autoencoder (VAE) to learn a continuous latent space for local atomic environments. We then apply K-Means clustering to the learned latent embeddings to obtain discr… view at source ↗
read the original abstract

De novo crystal generation, a central task in materials discovery, aims to generate crystals that are simultaneously valid, stable, unique, and novel. Existing methods mainly rely on black-box stochastic sampling, providing limited control over how generated structures move beyond the observed distribution. In this paper, we introduce a concept-based compositional framework for crystal generation. We train a vector-quantized variational autoencoder to automatically discover a shared set of reusable crystal concepts, which serve as building blocks for guided generation. These learned concepts naturally exhibit interpretability from both local atomic environments and global symmetry patterns, and generalize to crystals from different distributions. By recombining such concepts, our framework enables controllable exploration of novel crystals beyond the training distribution, rather than relying solely on unconstrained random sampling. To further improve composition efficiency, we introduce a composition generator and iteratively refine it using high-quality samples generated by the model itself. The resulting concept compositions are then used to condition downstream crystal generation. Numerical experiments on MP-20 and Alex-MP-20 show that compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper introduces a concept-based framework for de novo crystal generation. A VQ-VAE is trained to discover reusable, interpretable concepts from crystal structures that generalize across distributions. These concepts are recombined via a composition generator that is iteratively refined on self-generated high-quality samples; the resulting compositions condition a downstream generator. Experiments on MP-20 and Alex-MP-20 report that concept compositing improves a base model by up to 53.2% and 51.7% on the V.S.U.N. metric, with largest gains in novelty, enabling controllable exploration beyond the training distribution.

Significance. If the central claims hold without hidden selection effects, the work would offer a concrete advance over black-box sampling methods by providing interpretable, reusable building blocks and explicit controllability. The VQ-VAE concept discovery and reported generalization to out-of-distribution crystals are potentially valuable contributions to materials informatics.

major comments (2)
  1. [Abstract / Methods (composition generator)] Abstract (and the description of the composition generator): the iterative refinement step that uses 'high-quality samples generated by the model itself' to train the composition generator is load-bearing for the controllability claim. It is unclear whether any validity/stability/quality filter is applied during this self-supervised loop; if so, the reported V.S.U.N. gains (53.2% / 51.7%) cannot be attributed solely to recombination of the learned VQ-VAE concepts and the weakest assumption (generalizability without post-hoc mechanisms) is not yet supported.
  2. [Abstract / Experiments] Abstract: the claim that 'compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty' requires an ablation that isolates the effect of concept recombination from any curation performed during iterative refinement. Without such a controlled comparison, the numerical results do not yet establish that the framework enables exploration 'rather than relying solely on unconstrained random sampling.'
minor comments (1)
  1. [Abstract] The V.S.U.N. metric is referenced without an explicit definition or citation in the provided abstract; a clear statement of its components and how novelty is measured would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. We address each major comment below and commit to revisions that improve clarity and strengthen the supporting evidence.

read point-by-point responses

  1. Referee: [Abstract / Methods (composition generator)] Abstract (and the description of the composition generator): the iterative refinement step that uses 'high-quality samples generated by the model itself' to train the composition generator is load-bearing for the controllability claim. It is unclear whether any validity/stability/quality filter is applied during this self-supervised loop; if so, the reported V.S.U.N. gains (53.2% / 51.7%) cannot be attributed solely to recombination of the learned VQ-VAE concepts and the weakest assumption (generalizability without post-hoc mechanisms) is not yet supported.

    Authors: We agree that the description of the iterative refinement requires greater precision. The manuscript currently states only that the composition generator is refined on 'high-quality samples generated by the model itself,' without enumerating the exact selection criteria. In the revised version we will expand the Methods section to specify the precise validity, stability, and quality thresholds (if any) applied during self-supervised iteration, thereby clarifying whether post-hoc mechanisms beyond concept recombination are involved. revision: yes

  2. Referee: [Abstract / Experiments] Abstract: the claim that 'compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty' requires an ablation that isolates the effect of concept recombination from any curation performed during iterative refinement. Without such a controlled comparison, the numerical results do not yet establish that the framework enables exploration 'rather than relying solely on unconstrained random sampling.'

    Authors: We acknowledge the value of an explicit ablation that separates the contribution of concept recombination from any curation effects of the iterative loop. We will add this controlled comparison in the revised manuscript, reporting V.S.U.N. metrics for (i) the base generator, (ii) the composition generator without iterative refinement, and (iii) the full pipeline, thereby isolating the impact of learned-concept recombination. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The provided abstract and description contain no equations, parameter-fitting steps, or self-referential reductions where a claimed prediction or result is equivalent to its inputs by construction. The iterative refinement of the composition generator is described at a high level without exhibiting a specific loop that forces outputs from inputs (e.g., no fitted parameter renamed as prediction). No self-citations, uniqueness theorems, or ansatzes are quoted. The framework's claims rest on empirical numerical experiments rather than a closed definitional chain, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Full text unavailable; cannot enumerate free parameters, axioms, or invented entities from abstract alone.

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discussion (0)

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