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arxiv: 2606.00126 · v1 · pith:K5V7EO2Anew · submitted 2026-05-28 · 📡 eess.IV

Bounding Global and Local Compression Error of Signal Parameterizations

Quang Luong Nhat Nguyen , Sara Fridovich-Keil This is my paper

Pith reviewed 2026-06-29 00:18 UTC · model grok-4.3

classification 📡 eess.IV
keywords compression error boundsignal parameterizationimplicit neural representationreconstruction errorwithout ground truthglobal and local errorinverse problems
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The pith

When a signal parameterization meets certain natural properties, its reconstruction error at any compression level is bounded by a scaled difference between its predictions at two different compression levels.

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 to predict reconstruction error for compressive signal parameterizations such as implicit neural representations without ground truth access. It proves that under natural properties satisfied by the parameterization, the error is bounded by a scaled difference between model outputs at different compression levels. The properties are verified to hold for interpolated grids, Fourier feature networks, multi-resolution hash encodings, and tensor factorizations. The resulting bounds produce signal-specific global error curves and local error heatmaps that closely track actual errors in direct fitting and inverse problems including radiance fields and MRI reconstruction.

Core claim

When parameterization-based compression satisfies certain natural properties, the compression error at any compression level is bounded by a simple scaled difference between model predictions at different compression levels.

What carries the argument

The error bound formed by a scaled difference between a parameterization's predictions at two compression levels, which serves as a computable proxy for reconstruction error.

If this is right

  • The bound holds for interpolated grids, Fourier feature networks, multi-resolution hash encodings, and tensor factorizations.
  • It produces tight, generalizable, signal-specific error predictors that are efficiently computable.
  • The method yields both global error curves and local error heatmaps without ground truth.
  • It applies to direct signal fitting and to inverse problems such as radiance field and MRI reconstruction.

Where Pith is reading between the lines

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

  • The bound could support choosing compression levels during training by tracking the difference in real time.
  • Similar difference-based bounds might be derivable for other parameterization families not yet verified.
  • Local error heatmaps could guide spatially adaptive compression or refinement in imaging pipelines.

Load-bearing premise

The parameterization must satisfy certain natural properties for the error bound to apply.

What would settle it

Finding a parameterization that satisfies the natural properties yet has actual reconstruction error larger than the scaled prediction difference at some compression level.

Figures

Figures reproduced from arXiv: 2606.00126 by Quang Luong Nhat Nguyen, Sara Fridovich-Keil.

Figure 1
Figure 1. Figure 1: Global error curves for direct fitting of signals. We fit Grid, FFN, Instant-NGP, and GA-Planes directly to a 2D natural image from DIV2K [48] and the 3D Stanford Dragon surface volume [49]. The actual error (blue, left axis) is the ℓ2 distance between reconstruction and ground truth, the optimization-gap-adjusted theoretical bound (green, right axis) follows from Theorem 2 as a function of compression lev… view at source ↗
Figure 2
Figure 2. Figure 2: Global error curves for inverse problems. We evaluate Grid, FFN, Instant-NGP, and GA-Planes on three imaging tasks across two settings: (a) on 2D and 3D MRI reconstruction, and (b) radiance field reconstruction. MRI results are plotted against compression level d/n while NeRF results are plotted against model size, as the ground-truth signal dimension is not well￾defined for radiance fields. For MRI, the a… view at source ↗
Figure 3
Figure 3. Figure 3: Local error heatmaps for direct fitting of a DIV2K [48] natural image. Each row corresponds to a different architecture, with small and large models at compression levels d/n ≈ 0.2 and 0.4, respectively. Across all four representations, the predicted error heatmap c|g˜small − g˜large| captures the spatial structure of the actual error heatmap |g˜small −x|, showing that local compression artifacts can be es… view at source ↗
Figure 4
Figure 4. Figure 4: Local error heatmaps for 3D MRI volume reconstruction. Each row corresponds to a different architecture, with small and large models at compression levels d/n ≈ 0.2 and 0.4, respectively. Each model maps 3D coordinates to signal values and is supervised indirectly through a k-space loss on a 3D volume from the ATLAS dataset [50]. A single axial slice is shown for visualization. Across all four representati… view at source ↗
Figure 5
Figure 5. Figure 5: Local error heatmaps for 3D radiance field reconstruction. Each row corresponds to a different architecture, with small and large models having 2.5 × 105 and 1.6 × 106 parameters, respectively. Each model represents a 3D radiance field supervised through a photometric loss on training views from the Lego scene in NeRF-Blender [51]; a single test viewpoint is shown. Across all four representations, the pred… view at source ↗
Figure 6
Figure 6. Figure 6: Global error curves for direct fitting of synthetic signals. We fit Grid, FFN, Instant￾NGP, and GA-Planes directly to 2D and 3D synthetic signals, including bandlimited and sphere targets. The actual error (blue, left axis) is the ℓ2 distance between reconstruction and ground truth, the optimization-gap-adjusted theoretical bound (green, right axis) follows from Theorem 2 as a function of compression level… view at source ↗
Figure 7
Figure 7. Figure 7: Local error heatmaps for 2D MRI slice reconstruction. Each row corresponds to a different architecture, with small and large models at compression levels d/n ≈ 0.2 and 0.4, respectively. Each model maps 2D pixel coordinates to signal values and is supervised indirectly through a k-space loss on a single axial slice from the ATLAS dataset [50]. Across all four representations, the predicted error heatmap c|… view at source ↗
Figure 8
Figure 8. Figure 8: Local error heatmaps for direct fitting of 3D Stanford Dragon surface volume [49]. Each row corresponds to a different architecture, with small and large models at compression levels d/n ≈ 0.2 and 0.4, respectively. Across all four representations, the predicted error heatmap c|g˜small − g˜large| captures the spatial structure of the actual error heatmap |g˜small − x|, showing that local compression artifa… view at source ↗
read the original abstract

Differentiable signal parameterizations such as implicit neural representations (INRs) and hybrid models are increasingly central to computational imaging, yet principled tools for evaluating reconstruction fidelity at finite model size remain limited when ground truth is unavailable. We introduce a framework for predicting the reconstruction error of compressive signal parameterizations, yielding non-asymptotic, signal-specific bounds that are both theoretically sound and efficiently computable without access to the ground truth signal. Specifically, we prove that when parameterization-based compression satisfies certain natural properties, the compression error at any compression level is bounded by a simple scaled difference between model predictions at different compression levels. We verify these properties for representative model families including interpolated grids, Fourier feature networks, multi-resolution hash encodings, and tensor factorizations, and show empirically that the resulting worst-case guarantees can be efficiently adapted into signal-specific error predictors that are tight and generalizable. Across direct fitting of synthetic and natural signals, and inverse problems including radiance field and MRI reconstruction, our method closely tracks global error curves and yields informative local error heatmaps without ground-truth access. Code is available at https://github.com/voilalab/global_error_bound.

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 / 2 minor

Summary. The paper claims to introduce a framework for non-asymptotic, ground-truth-free bounds on global and local reconstruction error for compressive differentiable signal parameterizations (INRs, grids, Fourier networks, hash encodings, tensor factorizations). The central result is a proof that, when the parameterization satisfies certain natural properties, the compression error at any level is bounded by a scaled difference between predictions at two different compression levels; these properties are verified for the listed families, and the bounds are empirically adapted into tight, generalizable error predictors demonstrated on direct fitting and inverse problems (radiance fields, MRI).

Significance. If the properties are correctly identified and the bound holds without reducing to a fitted quantity, the result supplies a practical, signal-specific tool for assessing finite-model reconstruction fidelity in settings where ground truth is unavailable. The empirical adaptation to global error curves and local heatmaps, plus code release, strengthens applicability in computational imaging.

major comments (3)
  1. [Proof of the bound] The central theorem (proof section): the bound is stated to hold under 'certain natural properties,' but the manuscript must explicitly enumerate these properties (e.g., any requirements on monotonicity, interpolation behavior, or continuity) and prove they are necessary and sufficient; without this, it is impossible to verify whether the guarantee applies to standard INR variants or contains hidden restrictions that would make the non-asymptotic claim inapplicable.
  2. [Verification for model families] Verification subsection for model families: the claim that the properties hold for multi-resolution hash encodings and tensor factorizations must include explicit checks against common implementation choices (e.g., hash collisions, rank choices); any counter-example in these families would render the headline guarantee inapplicable to the very models highlighted in the abstract and experiments.
  3. [Empirical adaptation into predictors] Empirical adaptation section: the post-hoc conversion of the bound into a signal-specific predictor must be shown not to introduce fitting parameters that make the 'ground-truth-free' guarantee circular; if the scaling factor or predictor coefficients are estimated from data, the independence from ground truth claimed in the abstract is undermined.
minor comments (2)
  1. [Abstract] Abstract and introduction: the phrase 'post-hoc adaptation into predictors' is mentioned but not expanded; a one-sentence clarification of the adaptation procedure would improve readability.
  2. [Figures] Figure captions for local error heatmaps: ensure axis labels and color scales are defined so that readers can directly compare predicted vs. actual local error without referring to the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the presentation of our theoretical framework. We address each major comment point by point below, providing clarifications and indicating where the manuscript will be revised.

read point-by-point responses

  1. Referee: [Proof of the bound] The central theorem (proof section): the bound is stated to hold under 'certain natural properties,' but the manuscript must explicitly enumerate these properties (e.g., any requirements on monotonicity, interpolation behavior, or continuity) and prove they are necessary and sufficient; without this, it is impossible to verify whether the guarantee applies to standard INR variants or contains hidden restrictions that would make the non-asymptotic claim inapplicable.

    Authors: We will revise the proof section to explicitly enumerate the properties in a dedicated lemma (P1: monotonic decrease in prediction difference with increasing compression; P2: bounded Lipschitz constant of the parameterization map; P3: continuity of the compression operator). The central theorem shows these are sufficient for the non-asymptotic bound to hold via a direct application of the triangle inequality and the parameterization assumptions. We do not claim necessity, as the result is an implication (properties imply bound), and proving necessity would require constructing counterexamples outside the stated families, which is not required for the contribution but can be briefly discussed as future work. revision: partial

  2. Referee: [Verification for model families] Verification subsection for model families: the claim that the properties hold for multi-resolution hash encodings and tensor factorizations must include explicit checks against common implementation choices (e.g., hash collisions, rank choices); any counter-example in these families would render the headline guarantee inapplicable to the very models highlighted in the abstract and experiments.

    Authors: We agree this strengthens the verification. In the revised subsection, we will add explicit analysis: for hash encodings, the properties depend only on the differentiability and interpolation scheme, which hold independently of hash collisions (collisions affect the stored values but preserve monotonicity and continuity of the overall map); for tensor factorizations, we verify across rank choices by showing the low-rank constraint maintains the required properties as long as the factorization remains differentiable. No counterexamples arise under standard implementations. revision: yes

  3. Referee: [Empirical adaptation into predictors] Empirical adaptation section: the post-hoc conversion of the bound into a signal-specific predictor must be shown not to introduce fitting parameters that make the 'ground-truth-free' guarantee circular; if the scaling factor or predictor coefficients are estimated from data, the independence from ground truth claimed in the abstract is undermined.

    Authors: The adaptation computes the scaling factor and predictor coefficients exclusively from the model's own predictions at multiple compression levels, using only the theoretical bound expression; no ground-truth signal is involved at any stage. This preserves the ground-truth-free property. We will add a clarifying paragraph in the empirical section to explicitly state that all estimation steps operate solely on model outputs. revision: partial

Circularity Check

0 steps flagged

No circularity; bound is a conditional mathematical result under independently verified properties

full rationale

The paper states a theorem that compression error is bounded by a scaled difference of model predictions at different levels, conditional on the parameterization satisfying certain natural properties. It then verifies those properties hold for the listed families (grids, Fourier networks, hash encodings, tensor factorizations) and demonstrates empirical tightness. No equations reduce the bound to a fitted quantity by construction, no load-bearing self-citations are invoked for the core result, and the derivation does not rename known empirical patterns. The central claim remains independent of ground truth and is not forced by its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the existence of 'certain natural properties' that the parameterizations must satisfy for the bound to hold; these are not enumerated in the abstract and therefore cannot be classified further.

axioms (1)
  • domain assumption Parameterization-based compression satisfies certain natural properties (invoked as prerequisite for the error bound).
    Stated in the abstract as the condition under which the proof applies.

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discussion (0)

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Works this paper leans on

64 extracted references · 21 canonical work pages · 1 internal anchor

  1. [1]

    Extreme MRI: Large-scale volumetric dynamic imaging from continuous non-gated acquisitions.Magnetic Resonance in Medicine, 84(4):1763–1780, 2020

    Frank Ong, Xucheng Zhu, Joseph Y Cheng, Kevin M Johnson, Peder EZ Larson, Shreyas S Vasanawala, and Michael Lustig. Extreme MRI: Large-scale volumetric dynamic imaging from continuous non-gated acquisitions.Magnetic Resonance in Medicine, 84(4):1763–1780, 2020

    2020

  2. [2]

    FFEINR: Flow Feature-Enhanced Implicit Neural Representation for Spatiotemporal Super-Resolution.Journal of Visualization, 27(2):273–289, 2024

    Chenyue Jiao, Chongke Bi, and Lu Yang. FFEINR: Flow Feature-Enhanced Implicit Neural Representation for Spatiotemporal Super-Resolution.Journal of Visualization, 27(2):273–289, 2024

    2024

  3. [3]

    D-NeRF: Neural Radiance Fields for Dynamic Scenes

    Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francesc Moreno-Noguer. D-NeRF: Neural Radiance Fields for Dynamic Scenes. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10318–10327, 2021

    2021

  4. [4]

    Plenoxels: Radiance Fields without Neural Networks

    Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance Fields without Neural Networks. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5501–5510, 2022

    2022

  5. [5]

    Morgan Kaufmann, 1995

    Richard H Bartels, John C Beatty, and Brian A Barsky.An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann, 1995

    1995

  6. [6]

    John Wiley & Sons, 2018

    S Allen Broughton and Kurt Bryan.Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing. John Wiley & Sons, 2018

    2018

  7. [7]

    Learning Continuous Image Representation with Local Implicit Image Function

    Yinbo Chen, Sifei Liu, and Xiaolong Wang. Learning Continuous Image Representation with Local Implicit Image Function. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8628–8638, 2021

    2021

  8. [8]

    Lindell, Dave Van Veen, Jeong Joon Park, and Gordon Wetzstein

    David B. Lindell, Dave Van Veen, Jeong Joon Park, and Gordon Wetzstein. BACON: Band- limited Coordinate Networks for Multiscale Scene Representation. In2022 IEEE/CVF Con- ference on Computer Vision and Pattern Recognition (CVPR), pages 16231–16241, 2022. doi: 10.1109/CVPR52688.2022.01577

    work page doi:10.1109/cvpr52688.2022.01577 2022

  9. [9]

    WIRE: Wavelet Implicit Neural Representations

    Vishwanath Saragadam, Daniel LeJeune, Jasper Tan, Guha Balakrishnan, Ashok Veeraraghavan, and Richard G Baraniuk. WIRE: Wavelet Implicit Neural Representations. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18507–18516, 2023

    2023

  10. [10]

    Martel, Alexander W

    Vincent Sitzmann, Julien N.P. Martel, Alexander W. Bergman, David B. Lindell, and Gordon Wetzstein. Implicit Neural Representations with Periodic Activation Functions. InAdvances in Neural Information Processing Systems (NeurIPS), 2020

    2020

  11. [11]

    Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains.Advances in Neural Information Processing Systems (NeurIPS), 33:7537–7547, 2020

    Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains.Advances in Neural Information Processing Systems (NeurIPS), 33:7537–7547, 2020. 10

    2020

  12. [12]

    Implicit Neural Representations for Image Compression

    Yannick Strümpler, Janis Postels, Ren Yang, Luc Van Gool, and Federico Tombari. Implicit Neural Representations for Image Compression. InEuropean Conference on Computer Vision, pages 74–91. Springer, 2022

    2022

  13. [13]

    Instant Neural Graphics Primitives with a Multiresolution Hash Encoding.ACM Transactions on Graphics (TOG), 41 (4):1–15, 2022

    Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant Neural Graphics Primitives with a Multiresolution Hash Encoding.ACM Transactions on Graphics (TOG), 41 (4):1–15, 2022

    2022

  14. [14]

    3D Gaussian Splatting for Real-Time Radiance Field Rendering.ACM Transactions on Graphics, 42(4), July

    Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3D Gaussian Splatting for Real-Time Radiance Field Rendering.ACM Transactions on Graphics, 42(4), July

  15. [15]

    URLhttps://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/

  16. [16]

    MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers.arXiv preprint arXiv:2311.15475, 2023

    Yawar Siddiqui, Antonio Alliegro, Alexey Artemov, Tatiana Tommasi, Daniele Sirigatti, Vladislav Rosov, Angela Dai, and Matthias Nießner. MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers.arXiv preprint arXiv:2311.15475, 2023

    work page arXiv 2023

  17. [17]

    Continuous PDE Dynamics Forecasting with Implicit Neural Representations

    Yuan Yin, Matthieu Kirchmeyer, Jean-Yves Franceschi, Alain Rakotomamonjy, and patrick gallinari. Continuous PDE Dynamics Forecasting with Implicit Neural Representations. In NeurIPS 2022 AI for Science: Progress and Promises, 2022. URL https://openreview. net/forum?id=iB3KkHR4gc

    2022

  18. [18]

    TensoRF: Tensorial Radiance Fields

    Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. TensoRF: Tensorial Radiance Fields. InComputer Vision – ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXXII, page 333–350, Berlin, Heidelberg,

    2022

  19. [19]

    ISBN 978-3-031-19823-6

    Springer-Verlag. ISBN 978-3-031-19823-6. doi: 10.1007/978-3-031-19824-3_20. URL https://doi.org/10.1007/978-3-031-19824-3_20

    work page doi:10.1007/978-3-031-19824-3_20

  20. [20]

    K-Planes: Explicit Radiance Fields in Space, Time, and Appearance

    Sara Fridovich-Keil, Giacomo Meanti, Frederik Warburg, Benjamin Recht, and Angjoo Kanazawa. K-Planes: Explicit Radiance Fields in Space, Time, and Appearance. InComputer Vision and Pattern Recognition (CVPR), 2023

    2023

  21. [21]

    Geometric Algebra Planes: Convex Implicit Neural V olumes

    Irmak Sivgin, Sara Fridovich-Keil, Gordon Wetzstein, and Mert Pilanci. Geometric Algebra Planes: Convex Implicit Neural V olumes. InForty-second International Conference on Machine Learning, 2025. URLhttps://openreview.net/forum?id=yHpWI6a2xT

    2025

  22. [22]

    Dictionary Fields: Learning a Neural Basis Decomposition.ACM Trans

    Anpei Chen, Zexiang Xu, Xinyue Wei, Siyu Tang, Hao Su, and Andreas Geiger. Dictionary Fields: Learning a Neural Basis Decomposition.ACM Trans. Graph., 42(4), July 2023. ISSN 0730-0301. doi: 10.1145/3592135. URLhttps://doi.org/10.1145/3592135

    work page doi:10.1145/3592135 2023

  23. [23]

    Mixture of V olumetric Primitives for Efficient Neural Rendering.ACM Trans

    Stephen Lombardi, Tomas Simon, Gabriel Schwartz, Michael Zollhoefer, Yaser Sheikh, and Jason Saragih. Mixture of V olumetric Primitives for Efficient Neural Rendering.ACM Trans. Graph., 40(4), 2021. ISSN 0730-0301. doi: 10.1145/3450626.3459863. URL https://doi. org/10.1145/3450626.3459863

    work page doi:10.1145/3450626.3459863 2021

  24. [24]

    Deep Learning for Accelerated and Robust MRI Reconstruction: a Review, 2024

    Reinhard Heckel, Mathews Jacob, Akshay Chaudhari, Or Perlman, and Efrat Shimron. Deep Learning for Accelerated and Robust MRI Reconstruction: a Review, 2024. URL https: //arxiv.org/abs/2404.15692

    work page arXiv 2024

  25. [25]

    Michael Lustig, David Donoho, and John M. Pauly. Sparse MRI: The application of compressed sensing for rapid MR imaging.Magnetic Resonance in Medicine, 58(6):1182–1195, 2007. doi: https://doi.org/10.1002/mrm.21391. URL https://onlinelibrary.wiley.com/doi/abs/ 10.1002/mrm.21391

    work page doi:10.1002/mrm.21391 2007

  26. [26]

    Implicit Neural Representation in Medical Imaging: A Comparative Survey, 2023

    Amirali Molaei, Amirhossein Aminimehr, Armin Tavakoli, Amirhossein Kazerouni, Bobby Azad, Reza Azad, and Dorit Merhof. Implicit Neural Representation in Medical Imaging: A Comparative Survey, 2023. URLhttps://arxiv.org/abs/2307.16142

    work page arXiv 2023

  27. [27]

    NeRFs in Robotics: A Survey, 2025

    Guangming Wang, Lei Pan, Songyou Peng, Shaohui Liu, Chenfeng Xu, Yanzi Miao, Wei Zhan, Masayoshi Tomizuka, Marc Pollefeys, and Hesheng Wang. NeRFs in Robotics: A Survey, 2025. URLhttps://arxiv.org/abs/2405.01333. 11

    work page arXiv 2025

  28. [28]

    Teixeira, Joaquim Fonseca, Ricardo Cerqueira, and Sofia C

    Bernardo Araújo, João F. Teixeira, Joaquim Fonseca, Ricardo Cerqueira, and Sofia C. Beco. The Road to Safety: A Review of Uncertainty and Applications to Autonomous Driving Perception.Entropy, 26(8), 2024. ISSN 1099-4300. doi: 10.3390/e26080634. URL https: //www.mdpi.com/1099-4300/26/8/634

    work page doi:10.3390/e26080634 2024

  29. [29]

    Oswald, and Marc Pollefeys

    Zihan Zhu, Songyou Peng, Viktor Larsson, Weiwei Xu, Hujun Bao, Zhaopeng Cui, Martin R. Oswald, and Marc Pollefeys. NICE-SLAM: Neural Implicit Scalable Encoding for SLAM. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022

    2022

  30. [30]

    iMAP: Implicit Mapping and Positioning in Real-Time

    Edgar Sucar, Shikun Liu, Joseph Ortiz, and Andrew Davison. iMAP: Implicit Mapping and Positioning in Real-Time. InProceedings of the International Conference on Computer Vision (ICCV), 2021

    2021

  31. [31]

    Satellite Image Compression-Detailed Survey of the Algo- rithms

    KS Gunasheela and HS Prasantha. Satellite Image Compression-Detailed Survey of the Algo- rithms. InProceedings of International Conference on Cognition and Recognition: ICCR 2016, pages 187–198. Springer, 2018

    2016

  32. [32]

    Belenguer-Plomer, Kennedy Adriko, Paolo Fraccaro, Romeo Kienzler, Rania Briq, Sabrina Benassou, Michele Lazzarini, and Conrad M

    Carlos Gomes, Isabelle Wittmann, Damien Robert, Johannes Jakubik, Tim Reichelt, Stefano Maurogiovanni, Rikard Vinge, Jonas Hurst, Erik Scheurer, Rocco Sedona, Thomas Brun- schwiler, Stefan Kesselheim, Matej Bati ˇc, Philip Stier, Jan Dirk Wegner, Gabriele Caval- laro, Edzer Pebesma, Michael Marszalek, Miguel A. Belenguer-Plomer, Kennedy Adriko, Paolo Frac...

    work page doi:10.1109/mgrs.2025.3546527 2025

  33. [33]

    Astro- nomical image compression.Astronomy and Astrophysics Supplement Series, 136(3):579–590, 1999

    Mireille Louys, Jean-Luc Starck, Simona Mei, François Bonnarel, and Fionn Murtagh. Astro- nomical image compression.Astronomy and Astrophysics Supplement Series, 136(3):579–590, 1999

    1999

  34. [34]

    Compression of interferometric radio-astronomical data.Astronomy & Astro- physics, 595:A99, 2016

    AR Offringa. Compression of interferometric radio-astronomical data.Astronomy & Astro- physics, 595:A99, 2016

    2016

  35. [35]

    Edge Intelligence: A Review of Deep Neural Network Inference in Resource-Limited Environments.Electronics, 14(12), 2025

    Dat Ngo, Hyun-Cheol Park, and Bongsoon Kang. Edge Intelligence: A Review of Deep Neural Network Inference in Resource-Limited Environments.Electronics, 14(12), 2025. ISSN 2079-9292. doi: 10.3390/electronics14122495. URL https://www.mdpi.com/2079-9292/ 14/12/2495

    work page doi:10.3390/electronics14122495 2025

  36. [36]

    A Comprehensive Survey on Orbital Edge Computing: Systems, Applications, and Algorithms.Chinese Journal of Aeronautics, 38(7):103316, July 2025

    Zengshan YIN, Changhao WU, Chongbin GUO, Yuanchun LI, Mengwei XU, Weiwei GAO, and Chuanxiu CHI. A Comprehensive Survey on Orbital Edge Computing: Systems, Applications, and Algorithms.Chinese Journal of Aeronautics, 38(7):103316, July 2025. ISSN 1000-9361. doi: 10.1016/j.cja.2024.11.026. URL http://dx.doi.org/10.1016/j.cja.2024.11.026

    work page doi:10.1016/j.cja.2024.11.026 2025

  37. [37]

    Del Prete, P

    R. Del Prete, P. K. Thind, A. Mazzeo, M. Whitley, L. Papa, N. Longépé, and G. Meoni. Optimizing deep learning models for on-orbit deployment through neural architecture search. Scientific Reports, 15(1), 2025. doi: 10.1038/s41598-025-21467-8. URL https://doi.org/ 10.1038/s41598-025-21467-8

    work page doi:10.1038/s41598-025-21467-8 2025

  38. [38]

    Cover and Joy A

    Thomas M. Cover and Joy A. Thomas.Elements of Information Theory. Wiley-Interscience, Hoboken, NJ, 2 edition, 2006

    2006

  39. [39]

    A general approximation lower bound in L p norm, with applications to feed-forward neural networks

    El Mehdi Achour, Armand Foucault, Sébastien Gerchinovitz, and Francois Malgouyres. A general approximation lower bound in L p norm, with applications to feed-forward neural networks. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022. URL https://openreview.net/ forum?id=tfkeJG9yAX

    2022

  40. [40]

    Siegel and Jinchao Xu

    Jonathan W. Siegel and Jinchao Xu. Approximation Rates for Neural Networks with General Activation Functions.Neural Networks, 128:313–321, 2020. ISSN 0893-6080. doi: https:// doi.org/10.1016/j.neunet.2020.05.019. URL https://www.sciencedirect.com/science/ article/pii/S0893608020301891. 12

    work page doi:10.1016/j.neunet.2020.05.019 2020

  41. [41]

    C. E. Shannon. Probability of Error for Optimal Codes in a Gaussian Channel.Bell System Technical Journal, 38:611–656, 1959. doi: 10.1002/j.1538-7305.1959.tb03905.x

    work page doi:10.1002/j.1538-7305.1959.tb03905.x 1959

  42. [42]

    NeRV: Neural Representations for Videos

    Hao Chen, Bo He, Hanyu Wang, Yixuan Ren, Ser-Nam Lim, and Abhinav Shrivastava. NeRV: Neural Representations for Videos. InNeurIPS, 2021

    2021

  43. [43]

    G. Dai, R. Zhang, Q. Wuwu, and et al. Implicit Neural Image Field for Biological Microscopy Image Compression.Nature Computational Science, 5:1041–1050, 2025. doi: 10.1038/ s43588-025-00889-4. URLhttps://doi.org/10.1038/s43588-025-00889-4

    work page doi:10.1038/s43588-025-00889-4 2025

  44. [44]

    Compression with Bayesian Implicit Neural Representations

    Zongyu Guo, Gergely Flamich, Jiajun He, Zhibo Chen, and José Miguel Hernández- Lobato. Compression with Bayesian Implicit Neural Representations. In A. Oh, T. Nau- mann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors,Advances in Neu- ral Information Processing Systems, volume 36, pages 1938–1956. Curran Associates, Inc., 2023. URL https://proce...

    1938

  45. [45]

    Towards Lossless Implicit Neural Representation via Bit Plane Decomposition

    Woo Kyoung Han, Byeonghun Lee, Hyunmin Cho, Sunghoon Im, and Kyong Hwan Jin. Towards Lossless Implicit Neural Representation via Bit Plane Decomposition. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2025

    2025

  46. [46]

    Andrew R. Barron. Universal Approximation Bounds for Superpositions of a Sigmoidal Function.IEEE Transactions on Information Theory, 39(3):930–945, 1993. doi: 10.1109/18. 256500

    work page doi:10.1109/18 1993

  47. [47]

    Multilayer Feedforward Networks are Universal Approximators.Neural Networks, 2(5):359–366, 1989

    Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Multilayer Feedforward Networks are Universal Approximators.Neural Networks, 2(5):359–366, 1989. doi: 10.1016/0893-6080(89) 90020-8

    work page doi:10.1016/0893-6080(89 1989

  48. [48]

    Minimum Width for Universal Approximation

    Sejun Park, Chulhee Yun, Jaeho Lee, and Jinwoo Shin. Minimum Width for Universal Approximation. InInternational Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=O-XJwyoIF-k

    2021

  49. [49]

    Minimum width for universal approximation using ReLU networks on compact domain

    Namjun Kim, Chanho Min, and Sejun Park. Minimum width for universal approximation using ReLU networks on compact domain. InThe Twelfth International Conference on Learning Representations, 2024. URLhttps://openreview.net/forum?id=dpDw5U04SU

    2024

  50. [50]

    NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study

    Eirikur Agustsson and Radu Timofte. NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study. InThe IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, July 2017

    2017

  51. [51]

    A V olumetric Method for Building Complex Models from Range Images

    Brian Curless and Marc Levoy. A V olumetric Method for Building Complex Models from Range Images. InProceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 303–312, 1996

    1996

  52. [52]

    Donnelly, Artemis Zavaliangos-Petropulu, Jessica N

    Sook-Lei Liew, Bethany Lo, Miranda R. Donnelly, Artemis Zavaliangos-Petropulu, Jessica N. Jeong, Giuseppe Barisano, Alexandre Hutton, Julia P. Simon, Julia M. Juliano, Anisha Suri, Tyler Ard, Nerisa Banaj, Michael R. Borich, Lara A. Boyd, Amy Brodtmann, Cathrin M. Buetefisch, Lei Cao, Jessica M. Cassidy, Valentina Ciullo, Adriana B. Conforto, Steven C. Cr...

  53. [53]

    URL https://www.medrxiv.org/content/ early/2021/12/11/2021.12.09.21267554

    doi: 10.1101/2021.12.09.21267554. URL https://www.medrxiv.org/content/ early/2021/12/11/2021.12.09.21267554. 13

    work page doi:10.1101/2021.12.09.21267554 2021

  54. [54]

    Srinivasan, Matthew Tancik, Jonathan T

    Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors,Computer Vision – ECCV 2020, pages 405–421, Cham, 2020. Springer International Publishing. ISBN 978-3-0...

    2020

  55. [55]

    Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals

    Namhoon Kim and Sara Fridovich-Keil. Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025. URLhttps://openreview.net/forum?id=OZljvntsto

    2025

  56. [56]

    van der Schaaf and J

    A. van der Schaaf and J. H. van Hateren. Modelling the Power Spectra of Natural Images: Statistics and Information.Vision Research, 36(17):2759–2770, 1996

    1996

  57. [57]

    Statistics of natural image categories.Network: Computation in Neural Systems, 14(3):391–412, 2003

    Antonio Torralba and Aude Oliva. Statistics of natural image categories.Network: Computation in Neural Systems, 14(3):391–412, 2003

    2003

  58. [58]

    Xu et al

    Y . Xu et al. Systematic Differences Between Perceptually Relevant Image Statistics of Brain MRI and Natural Images.Frontiers in Neuroinformatics, 13:46, 2019

    2019

  59. [59]

    Bartlett, Nick Harvey, Christopher Liaw, and Abbas Mehrabian

    Peter L. Bartlett, Nick Harvey, Christopher Liaw, and Abbas Mehrabian. Nearly-tight VC- dimension and Pseudodimension Bounds for Piecewise Linear Neural Networks.Journal of Machine Learning Research, 20(63):1–17, 2019. URL http://jmlr.org/papers/v20/ 17-612.html

    2019

  60. [60]

    Introduction to the non-asymptotic analysis of random matrices

    Roman Vershynin. Introduction to the non-asymptotic analysis of random matrices, 2011. URL https://arxiv.org/abs/1011.3027

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  61. [61]

    Optimized Spatial Hashing for Collision Detection of Deformable Objects

    Matthias Teschner, Bruno Heidelberger, Matthias Müller, D Pomerantes, Markus Gross, et al. Optimized Spatial Hashing for Collision Detection of Deformable Objects. InProc. VMV, pages 47–54, 2003

    2003

  62. [62]

    Optical Models for Direct V olume Rendering.IEEE Transactions on Visualization and Computer Graphics, 1(2):99–108, 2002

    Nelson Max. Optical Models for Direct V olume Rendering.IEEE Transactions on Visualization and Computer Graphics, 1(2):99–108, 2002. 14 Appendices Norm notation.Throughout the appendices, we use Lp to denote the function-space norms on continuous domains, consistent with the approximation theory literature [ 37, 38, 44], whereas ℓp denotes the finite-dime...

    2002

  63. [63]

    The appended channel ofW ′ line is zero, so W ′⊤ line(e′ 1 ◦e ′

    = (e1 ◦e 2) 0 . The appended channel ofW ′ line is zero, so W ′⊤ line(e′ 1 ◦e ′

  64. [64]

    low-bandwidth

    +W ′⊤ planee′ 12 +b ′ =W ⊤ line(e1 ◦e 2) +W ⊤ planee12 +b, which equals the output of g∈ G k1. Therefore, Gk1 ⊆ G k1+1 and the optimal reconstruction error is nonincreasing ink 1. Lemma GAP.2(GA-Planes satisfies Assumption A2 for squared error).For allk 1 ≥0, ∥x−g ⋆ k1 ∥2 − ∥x−g ⋆ k1+1∥2 ≥ ∥x−g ⋆ k1+1∥2 − ∥x−g ⋆ k1+2∥2. Proof. By the matrix-completion equ...

    2000