arxiv: 2603.06082 · v4 · submitted 2026-03-06 · 💻 cs.AI · cs.CE

Recognition: 2 theorem links

· Lean Theorem

Offline Materials Optimization with CliqueFlowmer

Jakub Grudzien Kuba , Benjamin Kurt Miller , Sergey Levine , Pieter Abbeel

Authors on Pith no claims yet

Pith reviewed 2026-05-15 15:33 UTC · model grok-4.3

classification 💻 cs.AI cs.CE

keywords computational materials discoverymodel-based optimizationgenerative modelstransformersflow modelsoffline optimizationclique-based MBOmaterials design

0 comments

The pith

CliqueFlowmer fuses clique-based optimization into transformer and flow generation to produce materials with superior target properties.

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

The paper presents CliqueFlowmer as an alternative to standard generative models for computational materials discovery. Generative approaches rely on maximum likelihood training, which restricts their ability to explore regions that strongly optimize a chosen material property. CliqueFlowmer instead embeds direct offline model-based optimization into the generation process itself. This produces materials that outperform those from generative baselines on the target property. The work releases code and weights to enable further use in materials applications.

Core claim

CliqueFlowmer is a domain-specific model that incorporates recent advances of clique-based MBO into transformer and flow generation, thereby fusing direct optimization of a target material property into the generation process and yielding materials that strongly outperform those from generative baselines.

What carries the argument

CliqueFlowmer, a transformer and flow generation model that integrates clique-based model-based optimization to perform direct property optimization during generation.

If this is right

Materials produced by CliqueFlowmer achieve higher values on the chosen target property than materials from generative baselines.
The approach supports offline optimization using existing datasets without requiring online interactions or simulations.
Direct fusion of property optimization removes the exploration restrictions imposed by maximum likelihood objectives.
Released code, weights, and resources enable specialized applications in materials discovery and related fields.

Where Pith is reading between the lines

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

The same fusion technique could be tested on property optimization tasks in other domains such as molecular design or catalyst discovery.
Future comparisons against online reinforcement learning or active learning baselines would clarify efficiency trade-offs.
Scaling the architecture to larger material spaces could reveal whether the clique-based component maintains its advantage at higher complexity.

Load-bearing premise

Integrating clique-based MBO directly into transformer and flow generation enables effective direct optimization of material properties without the limits of maximum likelihood training.

What would settle it

A controlled comparison on a standard materials benchmark dataset in which CliqueFlowmer outputs show no statistically significant gain in target property values over generative baselines.

Figures

Figures reproduced from arXiv: 2603.06082 by Benjamin Kurt Miller, Jakub Grudzien Kuba, Pieter Abbeel, Sergey Levine.

**Figure 1.** Figure 1: The unit cell of a hypothetical material. The cell has a shape of a parallelepiped determined by three axes, ⃗a, ⃗b, and ⃗c. The angles between the axes are ang( ⃗b,⃗c) = α, ang(⃗c,⃗a) = β, ang(⃗a, ⃗b) = γ. In this cell, there are five atoms, whose type sequence is a = [N, Cl, C, O, S]. This section provides the necessary background on the key notions discussed by our work. First, we lay down foundations … view at source ↗

**Figure 2.** Figure 2: Computational materials discovery through MBO with CliqueFlowmer. Known materials [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Examples of materials optimized by CliqueFlowmer for band gap minimization. Each [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: The distribution of the property value (formation energy) among discovered materials. We [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Latent interpolation between two materials. We linearly interpolate z (t) = (1 − t)z (0) + tz(1) between As3Rh and MgInBr3 and decode each z (t) . The unit cells evolve smoothly in the cell shape, atom positions, and atom count. More interpolation visualizations in Appendix A.5. gap task, we do not observe this effect because the band gap is lower-bounded by zero, and thus the ordering of the top materials… view at source ↗

**Figure 6.** Figure 6: Comparison of gradient estimators— back-propagation (BP) vs. evolution strategies (ES), and weight decay. We plot the average change of the target property due to optimization, over 100 materials. Each algorithm performed 1000 steps, which was sufficient to reject back-propagation as divergent. The architecture of our model learns reparameterizations z of materials M that are meant to navigate the tran… view at source ↗

**Figure 7.** Figure 7: Average f(M) (we used formation energy) with standard error of the mean (SEM) over the course of linear interpolation. The curve was smoothed out with the Gaussian kernel. The value tends to be higher along the interpolation trajectory. Since the latent space of CliqueFlowmer was trained to follow a clique decomposition, we study how individual pieces of this structure impact the represented materials. … view at source ↗

**Figure 8.** Figure 8: Latent interpolation of cliques between As3Rh and MgInBr3—2D visualization of primitive cells. Top: The studied clique does not significantly affect composition or the unit cell shape, but it does affect atom position and atom count slightly. In particular, it affects positions of two of the four Rh atoms that, eventually, from the bottom of the cell move to its top. Bottom: The clique does not alter the m… view at source ↗

**Figure 9.** Figure 9: The distribution of the property value (band gap) among discovered materials. We compare [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗

**Figure 10.** Figure 10: Full version of Figure (4). Our method puts significant weight on ∆band = 0 materials. 100 500 1000 Number of structures 10 2 10 3 Wall-clock time (s) MBO (ES) Decoding (Beam + Flow) [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗

**Figure 11.** Figure 11: Wall clock time of material optimization with CliqueFlowmer. The optimization (MBO) [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗

**Figure 12.** Figure 12: Latent interpolation of materials. The materials change smoothly by modifying their unit cell shapes, positions of atoms, as well as atom composition. The majority of the composition changes (removal and arrival of new atom types) happens mainly around the midpoint of the interpolation, between timestep t = 0.25 and t = 0.75. A.5 Latent Interpolation of Materials In this section, we provide more visualiza… view at source ↗

**Figure 13.** Figure 13: Intuition behind performance discrepancy between BP and ES. The function approximator [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗

**Figure 14.** Figure 14: Ablation of the weight decay strength λ in the latent-space optimization algorithm. Weight decay λ = 0.4 delivers the strongest compromise between target property values and stability [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗

**Figure 15.** Figure 15: Impact of clique decomposition on the target property (formation energy) optimization [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗

**Figure 16.** Figure 16: Two ways to model the distribution of lattice lengths, demonstrated on variable [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗

**Figure 17.** Figure 17: The density plot of the lifted logit-normal distribution ( [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗

read the original abstract

Recent advances in deep learning inspired neural network-based approaches to computational materials discovery (CMD). A plethora of problems in this field involve finding materials that optimize a target property. Nevertheless, the increasingly popular generative modeling methods are ineffective at boldly exploring attractive regions of the materials space due to their maximum likelihood training. In this work, we offer an alternative CMD technique based on offline model-based optimization (MBO) that fuses direct optimization of a target material property into generation. To that end, we introduce a domain-specific model, dubbed CliqueFlowmer, that incorporates recent advances of clique-based MBO into transformer and flow generation. We validate this model's optimization abilities and show that materials it produces strongly outperform those from generative baselines. To support specialized materials discovery applications and broader interdisciplinary research, we release our code, model weights, and additional project resources at https://github.com/znowu/CliqueFlowmer, https://colab.research.google.com/drive/1usUg7zezFkcYHlm2MdYwZUNJXf_YkWnY?usp=sharing, and https://x.com/kuba_AI/status/2033382617442345321.

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.

Desk Editor's Note private letter to a colleague

CliqueFlowmer combines clique MBO with transformer-flow generation for offline materials optimization and claims stronger property targeting than pure generative baselines, but the abstract supplies no numbers or setup details to back it up.

read the letter

The main thing here is a new model called CliqueFlowmer that tries to fix the exploration problem in generative models for materials by baking direct offline optimization into the generation step. It pulls in clique-based model-based optimization and mixes it with transformers and flows, then releases the code and weights. That release is useful on its own for anyone working in computational materials discovery who wants to try an optimization-focused alternative to standard maximum-likelihood generators. The core idea makes sense on paper: generative models trained only on likelihood often stay too close to the data distribution and miss better regions for a target property, so adding surrogate-guided clique selection and flow sampling could help push further. The authors position this as domain-specific for CMD and say the outputs beat generative baselines. What is actually new is the specific fusion for this offline setting; prior MBO work exists, but the integration with flows and transformers for materials looks fresh. The release of Colab notebook and GitHub repo is a clear positive for reproducibility. The soft spot is the lack of any concrete evidence in the abstract. No metrics, no property names, no baseline descriptions, no error bars, and no discussion of how they avoided dataset leakage or surrogate bias. Without those, the outperformance claim is impossible to assess, and the stress-test note about unspecified controls is on target. The paper is for people already in materials optimization who are looking for new generative tricks; a general ML reader would get little from it. It deserves a serious referee because the idea is coherent and the resources are there, but the experiments will need heavy scrutiny on implementation details and statistical reliability before it can be taken as a solid advance.

Referee Report

2 major / 2 minor

Summary. The paper introduces CliqueFlowmer, a domain-specific model that fuses clique-based model-based optimization (MBO) with transformer and flow-based generative architectures for offline optimization of target material properties in computational materials discovery (CMD). It argues that standard generative models are limited by maximum-likelihood training and cannot boldly explore attractive regions of materials space, whereas the proposed offline MBO approach directly optimizes the target property during generation. The central empirical claim is that materials generated by CliqueFlowmer strongly outperform those produced by generative baselines, with code, weights, and resources released to support further research.

Significance. If the outperformance claims are substantiated with rigorous controls, this work could meaningfully advance offline optimization methods in CMD by integrating direct property optimization into generative pipelines, sidestepping some MLE limitations. The public release of code, model weights, and Colab resources is a clear strength that supports reproducibility and broader adoption.

major comments (2)

[Abstract and §4] Abstract and §4 (Experiments): The manuscript asserts that 'materials it produces strongly outperform those from generative baselines' and that the model 'validates this model's optimization abilities,' yet supplies no quantitative metrics (e.g., property improvement deltas, MAE/RMSE values), no description of the target properties optimized, no baseline implementations or hyperparameter details, no error bars or statistical significance tests, and no discussion of controls for dataset leakage or surrogate bias. This empirical support is load-bearing for the central claim and cannot be assessed from the provided text.
[§3] §3 (Model Architecture): The description of how clique-based MBO is fused into the transformer and flow components lacks concrete equations or pseudocode showing the surrogate guidance mechanism, the clique selection procedure, or how the flow sampling is conditioned on the offline optimization objective. Without these details, it is impossible to verify whether the approach concretely sidesteps the stated MLE limitations or reduces to a standard conditional generative model.

minor comments (2)

[Abstract] The abstract and introduction use the term 'CliqueFlowmer' without an initial definition or expansion; a brief parenthetical expansion on first use would improve readability.
[Abstract] The GitHub and Colab links are provided, but the manuscript does not include a brief summary of what the released resources contain (e.g., training scripts, evaluation notebooks, or dataset splits).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address the major comments point by point below and will revise the manuscript to strengthen the presentation of empirical results and technical details.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (Experiments): The manuscript asserts that 'materials it produces strongly outperform those from generative baselines' and that the model 'validates this model's optimization abilities,' yet supplies no quantitative metrics (e.g., property improvement deltas, MAE/RMSE values), no description of the target properties optimized, no baseline implementations or hyperparameter details, no error bars or statistical significance tests, and no discussion of controls for dataset leakage or surrogate bias. This empirical support is load-bearing for the central claim and cannot be assessed from the provided text.

Authors: We agree that the current manuscript version does not provide sufficient quantitative detail to fully substantiate the central empirical claims. In the revised version we will expand the abstract and §4 to report concrete property improvement deltas, MAE/RMSE values on the target properties, explicit descriptions of the optimized properties, baseline implementation and hyperparameter details, error bars across multiple runs, statistical significance tests, and explicit discussion of controls for dataset leakage and surrogate bias. revision: yes
Referee: [§3] §3 (Model Architecture): The description of how clique-based MBO is fused into the transformer and flow components lacks concrete equations or pseudocode showing the surrogate guidance mechanism, the clique selection procedure, or how the flow sampling is conditioned on the offline optimization objective. Without these details, it is impossible to verify whether the approach concretely sidesteps the stated MLE limitations or reduces to a standard conditional generative model.

Authors: We accept that §3 currently lacks the level of formal detail needed for independent verification. We will add the missing concrete equations for the surrogate guidance term, pseudocode for the clique selection and conditioning steps, and a precise description of how flow sampling is guided by the offline optimization objective. These additions will make explicit how the clique-based MBO component enables direct property optimization rather than reducing to standard conditional generation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical validation against baselines

full rationale

The paper introduces CliqueFlowmer as a fusion of clique-based MBO with transformer and flow generation for offline materials optimization. No equations, derivations, or self-definitional reductions appear in the provided text. The central claim of outperformance is supported by reported validation experiments rather than any fitted parameter renamed as prediction or load-bearing self-citation chain. The approach is self-contained against external generative baselines with no evident reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Central claim depends on the effectiveness of the newly introduced CliqueFlowmer model as an invented entity; no free parameters or axioms are detailed in the abstract.

invented entities (1)

CliqueFlowmer no independent evidence
purpose: Domain-specific model that incorporates clique-based MBO into transformer and flow generation for materials optimization
Newly proposed model whose performance is the basis for the outperformance claim

pith-pipeline@v0.9.0 · 5502 in / 1011 out tokens · 48169 ms · 2026-05-15T15:33:08.116883+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation (J-cost uniqueness) and Foundation modules on structured optimization washburn_uniqueness_aczel; reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we use tools from offline model-based optimization (MBO) to model the target property f(M) and search for candidate minimizers ... clique-based MBO paradigm

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages · 10 internal anchors

[1]

GPT-4 Technical Report

Achiam, J., Adler, S., Agarwal, S., Ahmad, L., Akkaya, I., Aleman, F. L., Almeida, D., Altenschmidt, J., Altman, S., Anadkat, S., et al. Gpt-4 technical report.arXiv preprint arXiv:2303.08774,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

D4RL: Datasets for Deep Data-Driven Reinforcement Learning

Fu, J., Kumar, A., Nachum, O., Tucker, G., and Levine, S. D4rl: Datasets for deep data-driven reinforcement learning.arXiv preprint arXiv:2004.07219,

work page internal anchor Pith review Pith/arXiv arXiv 2004
[3]

K., Yan, B., Domingo-Enrich, C., Sriram, A., Wood, B., Levine, D., Hu, B., Amos, B., Karrer, B., et al

Havens, A., Miller, B. K., Yan, B., Domingo-Enrich, C., Sriram, A., Wood, B., Levine, D., Hu, B., Amos, B., Karrer, B., et al. Adjoint sampling: Highly scalable diffusion samplers via adjoint matching.arXiv preprint arXiv:2504.11713,

work page arXiv
[4]

Gaussian Error Linear Units (GELUs)

Hendrycks, D. and Gimpel, K. Gaussian error linear units (gelus).arXiv preprint arXiv:1606.08415,

work page internal anchor Pith review Pith/arXiv arXiv
[5]

doi: 10.1063/1.1564060. Ho, J. and Salimans, T. Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598,

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1063/1.1564060
[6]

R., and Hoang, T

Hoang, M., Fadhel, A., Deshwal, A., Doppa, J. R., and Hoang, T. N. Learning surrogates for offline black-box optimization via gradient matching.arXiv preprint arXiv:2503.01883,

work page arXiv
[7]

Space group constrained crystal generation.arXiv preprint arXiv:2402.03992,

Jiao, R., Huang, W., Liu, Y ., Zhao, D., and Liu, Y . Space group constrained crystal generation.arXiv preprint arXiv:2402.03992,

work page arXiv
[8]

K., Fu, X., Liao, Y .-L., Gharakhanyan, V ., Miller, B

Joshi, C. K., Fu, X., Liao, Y .-L., Gharakhanyan, V ., Miller, B. K., Sriram, A., and Ulissi, Z. W. All-atom diffusion transformers: Unified generative modelling of molecules and materials.arXiv preprint arXiv:2503.03965,

work page arXiv
[9]

Adam: A Method for Stochastic Optimization

URLhttps://doi.org/10.6084/m9.figshare.29145101.v4. Kingma, D. P. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980,

work page internal anchor Pith review Pith/arXiv arXiv doi:10.6084/m9.figshare.29145101.v4
[10]

Kingma, D. P. and Welling, M. Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114,

work page internal anchor Pith review Pith/arXiv arXiv
[11]

G., Abbeel, P., and Levine, S

Kuba, J. G., Abbeel, P., and Levine, S. Cliqueformer: Model-based optimization with structured transformers.arXiv preprint arXiv:2410.13106,

work page arXiv
[12]

Data-driven offline optimization for architecting hardware accelerators.arXiv preprint arXiv:2110.11346,

Kumar, A., Yazdanbakhsh, A., Hashemi, M., Swersky, K., and Levine, S. Data-driven offline optimization for architecting hardware accelerators.arXiv preprint arXiv:2110.11346,

work page arXiv
[13]

Derivative-free guidance in continuous and discrete diffusion models with soft value-based decoding, 2024.URL https://arxiv

Li, X., Zhao, Y ., Wang, C., Scalia, G., Eraslan, G., Nair, S., Biancalani, T., Ji, S., Regev, A., Levine, S., et al. Derivative-free guidance in continuous and discrete diffusion models with soft value-based decoding, 2024.URL https://arxiv. org/abs/2408.08252. Li, Y ., Huang, L., Ding, Z., Wei, X., Wang, C., Yang, H., Wang, Z., Liu, C., Shi, Y ., Jin, P...

work page arXiv 2024
[14]

Flow Matching for Generative Modeling

Lipman, Y ., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling.arXiv preprint arXiv:2210.02747,

work page internal anchor Pith review Pith/arXiv arXiv
[15]

K., and Chen, R

13 Liu, G.-H., Choi, J., Chen, Y ., Miller, B. K., and Chen, R. T. Adjoint schr\” odinger bridge sampler. arXiv preprint arXiv:2506.22565,

work page arXiv
[16]

Decoupled Weight Decay Regularization

Loshchilov, I., Hutter, F., et al. Fixing weight decay regularization in adam.arXiv preprint arXiv:1711.05101, 5,

work page internal anchor Pith review Pith/arXiv arXiv
[17]

K., Chen, R

Miller, B. K., Chen, R. T., Sriram, A., and Wood, B. M. Flowmm: Generating materials with riemannian flow matching.arXiv preprint arXiv:2406.04713,

work page arXiv
[18]

Evolution Strategies as a Scalable Alternative to Reinforcement Learning

Salimans, T., Ho, J., Chen, X., Sidor, S., and Sutskever, I. Evolution strategies as a scalable alternative to reinforcement learning.arXiv preprint arXiv:1703.03864,

work page internal anchor Pith review Pith/arXiv arXiv
[19]

Treatment stitching with schr\” odinger bridge for enhancing offline reinforcement learning in adaptive treatment strategies.arXiv preprint arXiv:2511.12075,

Shin, D.-H., Lee, D.-J., Son, Y .-H., and Kam, T.-E. Treatment stitching with schr\” odinger bridge for enhancing offline reinforcement learning in adaptive treatment strategies.arXiv preprint arXiv:2511.12075,

work page arXiv
[20]

B., Bose, A

Tan, C. B., Bose, A. J., Lin, C., Klein, L., Bronstein, M. M., and Tong, A. Scalable equilibrium sampling with sequential boltzmann generators.arXiv preprint arXiv:2502.18462,

work page arXiv
[21]

Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context

Team, G., Georgiev, P., Lei, V . I., Burnell, R., Bai, L., Gulati, A., Tanzer, G., Vincent, D., Pan, Z., Wang, S., et al. Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context.arXiv preprint arXiv:2403.05530,

work page internal anchor Pith review Pith/arXiv arXiv
[22]

Trabucco, B., Kumar, A., Geng, X., and Levine, S

URL https://economictimes.indiatimes.com/magazines/panache/ paypal-co-founder-peter-thiel-warns-of-tech-stagnation-without-ai-theres-just-nothing-going-on/ articleshow/122141331.cms. Trabucco, B., Kumar, A., Geng, X., and Levine, S. Conservative objective models for effective offline model-based optimization. InInternational Conference on Machine Learning...

work page arXiv
[23]

Bridging model-based optimization and generative modeling via conservative fine-tuning of diffusion models.arXiv preprint arXiv:2405.19673,

Uehara, M., Zhao, Y ., Hajiramezanali, E., Scalia, G., Eraslan, G., Lal, A., Levine, S., and Biancalani, T. Bridging model-based optimization and generative modeling via conservative fine-tuning of diffusion models.arXiv preprint arXiv:2405.19673,

work page arXiv
[24]

V ., Norouzi, M., Macherey, W., Krikun, M., Cao, Y ., Gao, Q., Macherey, K., et al

Wu, Y ., Schuster, M., Chen, Z., Le, Q. V ., Norouzi, M., Macherey, W., Krikun, M., Cao, Y ., Gao, Q., Macherey, K., et al. Google’s neural machine translation system: Bridging the gap between human and machine translation. InProceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (EMNLP),

work page 2016
[25]

Crystal diffusion variational autoencoder for periodic material generation.arXiv preprint arXiv:2110.06197,

Xie, T., Fu, X., Ganea, O.-E., Barzilay, R., and Jaakkola, T. Crystal diffusion variational autoencoder for periodic material generation.arXiv preprint arXiv:2110.06197,

work page arXiv
[26]

L., McMorrow, B., Rezende, D

Yang, S., Batzner, S., Gao, R., Aykol, M., Gaunt, A. L., McMorrow, B., Rezende, D. J., Schuurmans, D., Mordatch, I., and Cubuk, E. D. Generative hierarchical materials search.arXiv preprint arXiv:2409.06762,

work page arXiv
[27]

Mattergen: a generative model for inorganic materials design.arXiv preprint arXiv:2312.03687,

Zeni, C., Pinsler, R., Z¨ugner, D., Fowler, A., Horton, M., Fu, X., Shysheya, S., Crabb´e, J., Sun, L., Smith, J., et al. Mattergen: a generative model for inorganic materials design.arXiv preprint arXiv:2312.03687,

work page arXiv
[28]

To ground these results in rigorous physics, however, we have also conducted density functional theory (Kohn & Sham, 1965, DFT) evaluations of proposed materials

A.2 DFT Evaluations Selective DFT.Due to resource constraints, our full-scale evaluations in Tables 1 & 2 were done with machine learning oracles, such as M3GNet and MEGNet. To ground these results in rigorous physics, however, we have also conducted density functional theory (Kohn & Sham, 1965, DFT) evaluations of proposed materials. Namely, for each met...

work page 1965
[29]

With enhanced DFT infrastructure for development and higher-quality data, we expect CliqueFlowmer to improve its ability to deliver optimized and stable materials

introduces unphysical bias into their performance in terms of stability, while they are very robust in terms of property optimization—we find this result satisfying since solving the optimization problem is the main purpose of this paper. With enhanced DFT infrastructure for development and higher-quality data, we expect CliqueFlowmer to improve its abili...

work page 2000
[30]

left” ground-truth material, and t= 1 is the “right

but it is out of scope of this paper. To demonstrate this, we conduct the following experiments. We encode and optimize, in the latent space, N={100,500,1000} materials and decode them back into the material form, without relaxation. We measure how much time, in seconds, the MBO and the decoding phases took in each experiment. For sample sizes 100, 500, a...

work page 2017
[31]

Then, they are standardized to have mean zero and unit variance, ultimately taking on values (− √ 1.5,0, √ 1.5)

are (10,−1,5) , then the values are turned into ranks (3,1,2) . Then, they are standardized to have mean zero and unit variance, ultimately taking on values (− √ 1.5,0, √ 1.5). This transformation makes the update invariant to monotone rescalings of the objective, improves robustness to outliers and heavy-tailed noise, and stabilizes optimization when the...

work page 2017
[32]

The corresponding x⋆ 1 and x⋆ 2 can then bestitchedtogether to form a strong solution x⋆ = (x⋆ 1,x ⋆ 2)

are rare in the dataset, it suffices to find favorable values of f1(x1) and f2(x2). The corresponding x⋆ 1 and x⋆ 2 can then bestitchedtogether to form a strong solution x⋆ = (x⋆ 1,x ⋆ 2). This finding was corroborated empirically by Cliqueformer (Kuba et al., 2024), which demonstrated strong empirical gains from incorporating the clique decomposition. Ne...

work page 2024
[33]

sequence

Indeed, while we did not sweep the structure’s configuration (we just chose the latent space size to be a reasonable power of 2), our results indicate that the structured latent space delivers large MBO gains, in particular when paired with weight decay. Thus, in this work, we employ the clique decomposition. C Model Design Details C.1 Flow Conditioning v...

work page 2023
[34]

Notably, the lowest match ratio recorded with cross-attention (71%) is higher than the highest match ratio of flat conditioning (63%)

The results indicate that cross-attention conditioning delivers superior reconstruction quality. Notably, the lowest match ratio recorded with cross-attention (71%) is higher than the highest match ratio of flat conditioning (63%). Furthermore, cross-attention conditioning displayed much lower volatility to CFG strength (the range of results being 80%−71%...

work page 2024
[35]

However, excessive guidance (ω= 4 ) degrades performance, likely 26 Table 7: Effect of classifier-free guidance strength on encode–decode consistency

Discussion.Moderate classifier-free guidance ( ω= 2 ) substantially improves reconstruction fidelity compared to no guidance, indicating that conditioning on the latent representation is underutilized without explicit amplification. However, excessive guidance (ω= 4 ) degrades performance, likely 26 Table 7: Effect of classifier-free guidance strength on ...

work page 2022
[36]

We setϵ= 0.1

and ensure sufficient coverage of the edge timesteps (see Figure 17). We setϵ= 0.1. D Additional Background This section provides additional background that helps understand the contribution of our work. D.1 Computational Materials Discovery Practices Computational materials discovery (CMD) aims to identify materials M whose physical or chem- ical propert...

work page 1965
[37]

28 D.4 Functional Graphical Models and Clique-Based Representations CliqueFlowmer builds on the framework offunctional graphical modelsintroduced by Grudzien et al

This decoding step is used after latent-space optimization to produce a high-likelihood composition consistent with the latent code, before sampling the continuous geometry with the flow-based decoder. 28 D.4 Functional Graphical Models and Clique-Based Representations CliqueFlowmer builds on the framework offunctional graphical modelsintroduced by Grudzi...

work page 2024