pith. sign in

arxiv: 2606.05849 · v1 · pith:SF5NNFVNnew · submitted 2026-06-04 · ⚛️ physics.optics · cs.CV

Inverse Design of Realizable Metasurface based Absorbers using Improved Conditioning and Diversity Enhanced Progressively Growing GANs

Vineetha Joy , Mohammad Abdullah , Pramit Pal , Anshuman Kumar , Amit Sethi , Hema Singh This is my paper

Pith reviewed 2026-06-28 00:08 UTC · model grok-4.3

classification ⚛️ physics.optics cs.CV
keywords inverse designmetasurface absorbersgenerative adversarial networkselectromagnetic consistencydiversity regularizationprogressive GANspectral constraintsfabrication realizability
0
0 comments X

The pith

A GAN with spectral conditioning and diversity regularization generates accurate and realizable metasurface absorber designs.

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

This paper presents a generative framework for the inverse design of metasurface absorbers using an enhanced progressively growing GAN. The method embeds electromagnetic consistency through a surrogate loss and promotes geometric diversity for the same target response. It aims to overcome the computational cost of traditional optimization by directly generating valid designs from spectral targets. If the approach holds, it allows rapid production of multiple fabricable configurations for applications in stealth and sensing within 2 to 18 GHz.

Core claim

The paper claims that the proposed framework, which integrates feature-wise linear modulation conditioning into a progressively growing Wasserstein GAN with gradient penalty, along with a surrogate-assisted spectral alignment loss and determinantal point process diversity regularization, generates metasurface absorber designs that are highly accurate, diverse, electromagnetically consistent, and fabrication realizable, as shown by average mean squared error of 0.0052, diversity score of 0.8730, band alignment accuracy of 0.8533, and 89.57 percent valid designs validated by EM simulations.

What carries the argument

Progressively growing WGAN-GP with FiLM conditioning, surrogate spectral alignment loss, and DPP-based diversity regularization that enforces physical consistency and variety during generation.

If this is right

  • The designs match target spectra with high accuracy as measured by low mean squared error.
  • Multiple diverse geometries are produced for identical spectral targets.
  • The generated structures are electromagnetically consistent and fabrication realizable.
  • Band alignment accuracy reaches 0.8533 for the absorber responses in 2-18 GHz.
  • Valid electromagnetic design generation rate is 89.57 percent.

Where Pith is reading between the lines

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

  • This method could shorten design times for metasurfaces by avoiding repeated full-wave optimizations.
  • Similar conditioning and loss strategies might apply to inverse design of other wave-manipulating structures.
  • Selecting from the diverse outputs based on additional criteria like material cost could enhance practicality.
  • Extending the frequency range or adding more fabrication constraints in training would test broader applicability.

Load-bearing premise

The surrogate model used in the spectral alignment loss correctly approximates the electromagnetic behavior of the generated metasurfaces.

What would settle it

Full-wave simulations revealing that many generated designs have reflection spectra far from the targets or geometries that cannot be fabricated would disprove the framework's effectiveness.

Figures

Figures reproduced from arXiv: 2606.05849 by Amit Sethi, Anshuman Kumar, Hema Singh, Mohammad Abdullah, Pramit Pal, Vineetha Joy.

Figure 1
Figure 1. Figure 1: EM wave incident on a metasurface [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Encoding scheme used to represent meta-atoms [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Architecture of the proposed model (a) Overall block diagram (b) FiLM conditioned convolution block (c) Generator block (d) Generator (e) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Configuration of metasurface based RAS models included [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between input spectrum and spectra obtained on simulation of generated design. (a) Case-1 (Material: AD1000 ( [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Geometrically diverse metasurface designs generated by the proposed model for [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

Metasurfaces enable precise manipulation of electromagnetic waves for applications such as beam steering, sensing, and stealth technology. However, inverse design of metasurfaces with targeted EM responses remains challenging due to the computational expense of iterative full wave simulation driven optimization and the limited conditioning fidelity and diversity of existing generative approaches. To address these challenges, this paper presents a generative inverse design framework for controllable and physically consistent metasurface synthesis under continuous spectral constraints. The proposed approach employs a progressively growing Wasserstein generative adversarial network with gradient penalty integrated with feature wise linear modulation based conditioning for stable propagation of continuous spectral and fabrication constraints. EM consistency is embedded directly into the generative learning process through a surrogate assisted spectral alignment loss, enabling physics constrained generation during training. Further, a determinantal point process based diversity regularization strategy is incorporated to generate geometrically diverse yet spectrally consistent realizations for the same target response. The effectiveness of the proposed framework is demonstrated through the generation of practically realizable metasurface absorbers exhibiting diverse reflection characteristics in the frequency range of 2 to 18 GHz. EM simulations validate that the generated designs meet the target specifications with high accuracy. The final proposed framework achieved an average mean squared error of 0.0052, diversity score of 0.8730, band alignment accuracy of 0.8533, and a valid EM design generation percentage of 89.57, clearly demonstrating its capability to generate highly accurate, diverse, electromagnetically consistent and fabrication realizable metasurface configurations.

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

3 major / 0 minor

Summary. The paper proposes a progressively growing Wasserstein GAN with gradient penalty, FiLM-based conditioning for continuous spectral and fabrication constraints, a surrogate-assisted spectral alignment loss to embed EM consistency during training, and DPP-based diversity regularization. It claims generation of realizable metasurface absorbers (2-18 GHz) with average MSE 0.0052, diversity score 0.8730, band alignment accuracy 0.8533, and 89.57% valid designs, with EM simulations validating that generated designs meet target specifications.

Significance. If the surrogate generalizes accurately to generated geometries, the framework could advance inverse metasurface design by enabling physics-constrained generation without full-wave simulation in the training loop while promoting diversity. The integration of progressive growing, conditioning, surrogate loss, and diversity regularization addresses multiple known challenges in the area.

major comments (3)
  1. [Abstract] Abstract: The reported aggregate metrics (MSE of 0.0052, 89.57% valid EM designs) supply no details on the number of designs evaluated, the exact validation protocol (including how many full-wave simulations were run post-generation), error bars, baseline comparisons, or post-hoc selection criteria, rendering the central performance claims difficult to evaluate.
  2. [Abstract] Abstract (surrogate-assisted spectral alignment loss): The claim that the surrogate loss produces electromagnetically consistent designs (MSE 0.0052, 89.57% valid) without full-wave simulation during training rests on the unverified assumption that the surrogate generalizes to novel geometries produced by the GAN. No quantitative surrogate-vs-full-wave spectral comparison on held-out generated samples, no information on whether the surrogate was trained on the same distribution as the generated designs, and no ablation removing the surrogate loss are provided.
  3. [Abstract] Abstract / framework description: No ablation studies are reported to quantify the individual contributions of the surrogate loss versus the diversity regularization (or the progressive growing and FiLM conditioning) to the final metrics, leaving the load-bearing role of each component untested.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment point-by-point below, indicating where revisions will be made to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The reported aggregate metrics (MSE of 0.0052, 89.57% valid EM designs) supply no details on the number of designs evaluated, the exact validation protocol (including how many full-wave simulations were run post-generation), error bars, baseline comparisons, or post-hoc selection criteria, rendering the central performance claims difficult to evaluate.

    Authors: We agree that the abstract would benefit from greater specificity on the evaluation setup. In the revised manuscript we will expand the abstract to report the number of designs evaluated, the validation protocol including the number of post-generation full-wave simulations performed, error bars from repeated runs, baseline comparisons, and confirmation that no post-hoc selection was applied beyond the validity criteria defined in the methods. revision: yes

  2. Referee: [Abstract] Abstract (surrogate-assisted spectral alignment loss): The claim that the surrogate loss produces electromagnetically consistent designs (MSE 0.0052, 89.57% valid) without full-wave simulation during training rests on the unverified assumption that the surrogate generalizes to novel geometries produced by the GAN. No quantitative surrogate-vs-full-wave spectral comparison on held-out generated samples, no information on whether the surrogate was trained on the same distribution as the generated designs, and no ablation removing the surrogate loss are provided.

    Authors: The surrogate was trained on geometries drawn from the same parameter ranges used for GAN training and generation. We will revise the manuscript to include a quantitative surrogate-versus-full-wave comparison on held-out generated samples and an ablation that removes the surrogate-assisted loss, thereby directly addressing the generalization concern. revision: yes

  3. Referee: [Abstract] Abstract / framework description: No ablation studies are reported to quantify the individual contributions of the surrogate loss versus the diversity regularization (or the progressive growing and FiLM conditioning) to the final metrics, leaving the load-bearing role of each component untested.

    Authors: We acknowledge that explicit ablation studies would strengthen the claims. The revised manuscript will add ablation experiments that isolate the surrogate loss, DPP diversity regularization, progressive growing, and FiLM conditioning to quantify their individual effects on the reported metrics. revision: yes

Circularity Check

0 steps flagged

No circularity: framework uses independent surrogate training and external EM validation

full rationale

The paper trains a progressively growing WGAN with a surrogate-assisted spectral alignment loss to enforce EM consistency during generation, then reports final performance metrics (MSE 0.0052, 89.57% valid) after explicit full-wave EM simulations on the generated designs. No equation or step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing claim rest solely on self-citation of an unverified uniqueness result. The surrogate is presented as a separate model whose outputs are cross-checked by independent EM simulation; the diversity regularization and conditioning are standard architectural choices whose effectiveness is measured against held-out targets. This keeps the central claims externally falsifiable and self-contained against the reported validation protocol.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework rests on standard deep-learning assumptions plus one domain-specific surrogate model; no new physical entities are postulated. Hyperparameters for the GAN, loss weights, and surrogate training are free parameters whose values are not reported.

free parameters (2)
  • GAN training hyperparameters and loss weights
    Learning rates, progressive growth schedule, surrogate loss coefficient, and DPP regularization strength are chosen or fitted to achieve the reported metrics.
  • Surrogate model architecture and training data
    The surrogate that supplies the spectral alignment loss is itself a learned model whose capacity and data are not specified.
axioms (1)
  • domain assumption The surrogate model provides sufficiently accurate electromagnetic response predictions to guide generation
    Invoked to embed physics constraints directly into the generative training loop.

pith-pipeline@v0.9.1-grok · 5819 in / 1518 out tokens · 30516 ms · 2026-06-28T00:08:33.969010+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

43 extracted references · 15 canonical work pages

  1. [1]

    An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,

    C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O'Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag., vol. 54, no. 2, pp. 10–35, Apr. 2012

    2012

  2. [2]

    A review of metasurfaces: physics and applications,

    H.-T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys., vol. 79, no. 7, p. 076401, 2016

    2016

  3. [3]

    Negative refraction makes a perfect lens,

    J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., vol. 85, no. 18, pp. 3966–3969, Oct. 2000

    2000

  4. [4]

    Composite medium with simultaneously negative permeability and permittivity,

    D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., vol. 84, no. 18, pp. 4184–4187, May 2000

    2000

  5. [5]

    Metasurfaces: From microwaves to visible,

    S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Physics Reports, vol. 634, pp. 1–72, 2016

    2016

  6. [6]

    Kats, Francesco Aieta, Jean-Philippe Tetienne, Fed- erico Capasso, and Zeno Gaburro

    N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science, vol. 334, no. 6054, pp. 333–337, Oct. 2011, doi: 10.1126/science.1210713

    work page doi:10.1126/science.1210713 2011

  7. [7]

    Planar photonics with metasurfaces,

    A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science, vol. 339, no. 6125, p. 1232009, Mar. 2013, doi: 10.1126/science.1232009

    work page doi:10.1126/science.1232009 2013

  8. [8]

    Flat optics with designer metasurfaces,

    N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials, vol. 13, no. 2, pp. 139–150, Feb. 2014, doi: 10.1038/nmat3839

    work page doi:10.1038/nmat3839 2014

  9. [9]

    Metasurface holograms for visible light,

    X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nature Communications, vol. 4, p. 2807, Dec. 2013, doi: 10.1038/ncomms3807

    work page doi:10.1038/ncomms3807 2013

  10. [10]

    Devlin, Jaewon Oh, Alexander Y

    M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction- limited focusing and subwavelength resolution imaging,” Science, vol. 352, no. 6290, pp. 1190–1194, Jun. 2016, doi: 10.1126/science.aaf6644

    work page doi:10.1126/science.aaf6644 2016

  11. [11]

    Metalenses: Versatile multifunctional photonic components,

    M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science, vol. 358, no. 6367, p. eaam8100, Nov. 2017, doi: 10.1126/science.aam8100

    work page doi:10.1126/science.aam8100 2017

  12. [12]

    Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,

    C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Physical Review Letters, vol. 110, no. 19, p. 197401, May 2013, doi: 10.1103/PhysRevLett.110.197401

    work page doi:10.1103/physrevlett.110.197401 2013

  13. [13]

    Sinha and S

    F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: A review of fundamentals and applications,” Reports on Progress in Physics, vol. 81, no. 2, p. 026401, Feb. 2018, doi: 10.1088/1361- 6633/aa8732

    work page doi:10.1088/1361- 2018

  14. [14]

    All-dielectric metamaterials,

    S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nature Nanotechnology, vol. 11, no. 1, pp. 23–36, Jan. 2016, doi: 10.1038/nnano.2015.304

    work page doi:10.1038/nnano.2015.304 2016

  15. [15]

    Inverse designed plasmonic metasurface with parts per billion optical hydrogen detection,

    F. A. A. Nugroho, G. W. Castellanos, P. Bai, I. Darmadi, J. Fritzsche, J. Gómez Rivas, and A. Baldi, “Inverse designed plasmonic metasurface with parts per billion optical hydrogen detection,” Nature Materials, vol. 18, no. 5, pp. 489–495, May 2019, doi: 10.1038/s41563-019-0296-9

    work page doi:10.1038/s41563-019-0296-9 2019

  16. [16]

    Metasurfaces for stealth applications: A comprehensive review,

    V. Joy, A. Dileep, P. V. Abhilash, R. U. Nair, H. Singh, “Metasurfaces for stealth applications: A comprehensive review,” Journal of Electronics Materials, vol. 50, no. 6, pp. 3129–3148, Jun. 2021

    2021

  17. [17]

    Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters,

    M. Khorasaninejad and F. Capasso, “Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters,” Nano Letters, vol. 15, no. 10, pp. 6709–6715, Oct. 2015

    2015

  18. [18]

    Structured transparent low emissivity coatings with high microwave transmission,

    O. Bouvard, M. Lanini, and L. Burnier, “Structured transparent low emissivity coatings with high microwave transmission,” Applied Physics A, vol. 123, no. 1, Art. no. 66, 2017

    2017

  19. [19]

    Empowering metasurfaces with inverse design: Principles and applications,

    Z. Li, R. Pestourie, Z. Lin, S. G. Johnson, and F. Capasso, “Empowering metasurfaces with inverse design: Principles and applications,” ACS Photonics, vol. 9, no. 7, pp. 2178–2192, Jul. 2022, doi: 10.1021/acsphotonics.1c01850

    work page doi:10.1021/acsphotonics.1c01850 2022

  20. [20]

    Global optimization of metasurface designs using statistical learning methods,

    M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed & P. Genevet, “Global optimization of metasurface designs using statistical learning methods,” Scientific Reports, vol. 9, p. 17918, 2019, doi: 10.1038/s41598-019-53878-9

    work page doi:10.1038/s41598-019-53878-9 2019

  21. [21]

    Large-scale photonic inverse design: Computational challenges and breakthroughs,

    C. Kang, C. Park, M. Lee, J. Kang, M. S. Jang, and H. Chung, “Large-scale photonic inverse design: Computational challenges and breakthroughs,” Nanophotonics, vol. 13, no. 20, pp. 3765– 3792, Jun. 2024, doi: 10.1515/nanoph-2024-0127

    work page doi:10.1515/nanoph-2024-0127 2024

  22. [22]

    Deep learning enabled inverse design in nanophotonics,

    S. So, T. Badloe, J. Noh, J. Bravo-Abad, and J. Rho, “Deep learning enabled inverse design in nanophotonics,” Nanophotonics, vol. 9, no. 5, pp. 1041–1057, 2020

    2020

  23. [23]

    Training deep neural networks for the inverse design of nanophotonic structures,

    D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photonics, vol. 5, no. 4, pp. 1365–1369, 2018

    2018

  24. [24]

    Generative model for the inverse design of metasurfaces,

    Z. Liu, D. Zhu, K. Lee, A. S. Kim, and J. R. W. Mark, “Generative model for the inverse design of metasurfaces,” ACS Nano, vol. 12, no. 7, pp. 7073–7083, 2018

    2018

  25. [25]

    Prediction of multi-layer metasurface design using conditional deep convolutional generative adversarial networks,

    A. Nezaratizadeh, S. M. Hashemi, and M. Bod., “Prediction of multi-layer metasurface design using conditional deep convolutional generative adversarial networks,” International Journal for Light and Electron Optics, vol. 313, p. 172005, 2024

    2024

  26. [26]

    Single-layer metasurface design with symmetrical free-form patterns using generative adversarial networks,

    G. Dai, H. Li, X. Zhang, and Y. Liu, “Single-layer metasurface design with symmetrical free-form patterns using generative adversarial networks,” Applied Soft Computing, vol. 127, Art. no. 109353, 2022

    2022

  27. [27]

    A cyclical deep learning based framework for simultaneous inverse and forward design of nanophotonic metasurfaces,

    A. Mall, A. Patil, A. Sethi & A. Kumar, “A cyclical deep learning based framework for simultaneous inverse and forward design of nanophotonic metasurfaces,” Scientific Reports, Article number: 19427, 2020

    2020

  28. [28]

    Fast design of plasmonic metasurfaces enabled by deep learning,

    A. Mall, A. Patil, D. Tamboli, A. Sethi and A. Kumar, “Fast design of plasmonic metasurfaces enabled by deep learning,” Journal of Physics D: Applied Physics, vol. 53, no. 49, October 2020

    2020

  29. [29]

    A generative machine learning-based approach for inverse design of multilayer metasurfaces,

    P. Naseri and S. V. Hum, “A generative machine learning-based approach for inverse design of multilayer metasurfaces,” IEEE Transactions on Antennas and Propagation, vol. 69, no. 9, pp. 5725 5739, Sep. 2021

    2021

  30. [30]

    Design of Metamaterials for Absorbers Based on Variational Autoencoder,

    Q. Li, J. Wang, T. Lei, T. Xiang, C. Qin and M. Yang, “Design of Metamaterials for Absorbers Based on Variational Autoencoder,” IEEE Access, vol. 12, pp. 92328-92336, 2024

    2024

  31. [31]

    VAE enhanced tandem neural network for reverse design of metasurface structural-colors with high efficiency and accuracy,

    W. Lin, J. Zhang, Z. Zou, Y. Lin, Y. Peng, W. Yang, Y. Zhang, T. Guo, C. Wu, and X. Zhou, “VAE enhanced tandem neural network for reverse design of metasurface structural-colors with high efficiency and accuracy,” Optics Communications, vol. 601, p. 132760, 2026

    2026

  32. [32]

    Optimizing metamaterial inverse design with 3D conditional diffusion model and data augmentation,

    X. Zheng, J. Shiomi and T. Yamada, “Optimizing metamaterial inverse design with 3D conditional diffusion model and data augmentation,” Advanced Materials Tech., vol. 10, 10p., 2025

    2025

  33. [33]

    PaDGAN: A generative adversarial network for performance augmented diverse designs,

    W. Chen and F. Ahmed, “PaDGAN: A generative adversarial network for performance augmented diverse designs,” arXiv preprint arXiv:2002.11304, 2020

    arXiv 2002

  34. [34]

    Continuous conditional generative adversarial networks: Novel empirical losses and label input mechanisms,

    X. Ding, Y. Wang, Z. Xu, W. J. Welch, and Z. J. Wang, “Continuous conditional generative adversarial networks: Novel empirical losses and label input mechanisms,” IEEE Trans.Pattern Analysis and Machine Intelligence, vol. 45, no. 7, pp. 8143-8158, Jul. 2023

    2023

  35. [35]

    PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network for Inverse Design,

    A. H. Nobari, W. Chen, and F. Ahmed, “PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network for Inverse Design,” in Proc. 27th ACM SIGKDD Conf. Knowl. Discovery Data Mining (KDD '21), Virtual Event, Singapore, Aug. 2021, pp. 1–12. doi: 10.1145/3447548.3467414

    work page doi:10.1145/3447548.3467414 2021

  36. [36]

    Improved training of Wasserstein GANs,

    I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville, “Improved training of Wasserstein GANs,” in Adv. Neural Inf. Process. Syst. (NIPS), vol. 30, pp. 5767–5777, 2017

    2017

  37. [37]

    Kulesza and B

    A. Kulesza and B. Taskar, Determinantal Point Processes for Machine Learning. Hanover, MA, USA: Now Publishers Inc., Nov. 2012, pp. 1–178, ISBN: 978-1-60198-628-3

    2012

  38. [38]

    Kernel methods in machine learning,

    T. Hofmann, B. Schölkopf, and A. J. Smola, “Kernel methods in machine learning,” The Annals of Statistics, vol. 36, no. 3, pp. 1171–1220, 2008

    2008

  39. [39]

    On the Lambert W function

    R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Advances in Computational Mathematics, vol. 5, no. 1, pp. 329–359, 1996, doi: 10.1007/BF02124750

    work page doi:10.1007/bf02124750 1996

  40. [40]

    FiLM: Visual reasoning with a general conditioning layer,

    E. Perez, F. Strub, H. de Vries, V. Dumoulin, and A. Courville, “FiLM: Visual reasoning with a general conditioning layer,” in Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, Article No.: 483, pp. 3942 - 3951, 2018

    2018

  41. [41]

    CST Studio Suite®, CST AG, Germany, www.cst.com

  42. [42]

    C. M. Bishop, Pattern Recognition and Machine Learning. New York, NY, USA: Springer, 2006

    2006

  43. [43]

    Boundary IoU: Improving object-centric image segmentation evaluation,

    B. Cheng, R. Girshick, P. Dollár, A. C. Berg, and A. Kirillov, “Boundary IoU: Improving object-centric image segmentation evaluation,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), Nashville, TN, USA, 2021, pp. 15334–15342

    2021