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Information Bottleneck Meets Quantization: Finite Rate Analysis and Optimal Designs

T0 review · 2 major / 2 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Jointly optimizing the Gaussian Information Bottleneck with a finite-rate constraint produces quantization designs that preserve more target information than quantizing the standard solution afterward.

desk verdict The finite-rate reformulation of GIB produces task-oriented quantizers that beat separate designs in the Gaussian MMSE simulations, while the non-Gaussian VAE change stays unquantified. read the letter →

arxiv 2606.10869 v1 pith:XHQUYEWV submitted 2026-06-09 eess.SP

Francesco Binucci , Paolo Banelli This is my paper
classification eess.SP
keywords informationbottleneckGaussianIBquantizationfiniterateMMSEregressionvariationalautoencoderslatentrepresentationmutual
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper establishes that the optimal latent representation from the Gaussian Information Bottleneck must itself be adjusted when only a finite number of bits are available for storage or transmission. It derives the effect of scalar and vector quantization on the mutual information between the quantized latent variables and the target, then reformulates the GIB objective to include the rate constraint directly. Simulations on minimum mean square error regression tasks demonstrate that these joint designs outperform both heuristic quantization of the unconstrained GIB solution and separate rate-distortion optimized quantizers. The same task-oriented approach is applied to non-Gaussian data by altering the training objective of vector-quantized variational autoencoders.

What carries the argument

The jointly reformulated GIB optimization problem that incorporates a finite-rate constraint directly on the latent representation.

What would settle it

An MMSE regression experiment in which the jointly optimized quantizers show no accuracy improvement over separate quantization of the standard GIB latent variables at the same bit rate.

Watch

Extended reading notes

Core claim

Reformulating the Gaussian IB optimization problem under an explicit finite-rate constraint on the latent representation yields task-oriented scalar and vector quantizers whose resulting representations retain higher mutual information with the target variable than post-hoc quantization of the unconstrained GIB solution; the same principle extends to non-Gaussian settings through a modified VAE cost function.

Load-bearing premise

The source and target variables are jointly Gaussian, which supplies the closed-form GIB solution and allows exact analysis of the quantized mutual information.

Editorial extensions

If this is right

  • Scalar and vector quantizers designed under the joint objective reduce the loss of target-relevant information compared with independent quantization steps.
  • The finite-rate analysis supplies explicit expressions for the degradation in mutual information caused by quantization of the GIB representation.
  • Modifying the VAE objective in the same task-oriented manner produces IB-inspired vector quantizers for non-Gaussian data.
  • The gains hold for practical MMSE regression problems where the latent representation must be transmitted or stored at limited bit rates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same joint-optimization logic could be applied to other parametric families beyond the Gaussian case once tractable relaxations are found.
  • Resource-constrained inference pipelines that already use IB-style compression would see direct accuracy benefits from replacing separate quantization stages with the integrated designs.
  • The approach suggests a general template for embedding discrete representation constraints inside any information-theoretic objective that admits a differentiable surrogate.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes the impact of scalar and vector quantization on the Gaussian Information Bottleneck (GIB) latent representation and its effect on target informativeness, proposes task-oriented quantization designs obtained by jointly reformulating the GIB optimization under an explicit finite-rate constraint, reports simulation gains on MMSE regression tasks relative to separate or heuristic quantization of the standard GIB solution, and extends the approach to non-Gaussian data by modifying the cost function of IB-inspired VAEs.

Significance. If the central claims hold, the work supplies a principled route from the closed-form GIB to finite-rate task-oriented quantizers and demonstrates concrete performance improvements in regression settings; the theoretical quantization analysis and the joint-optimization reformulation constitute the primary technical contribution.

major comments (2)
  1. [Non-Gaussian extension] The non-Gaussian extension (final paragraph of the abstract and corresponding section) modifies the VAE cost function without deriving or bounding its deviation from the true IB objective (mutual-information terms); this step is load-bearing for the claim that the task-oriented philosophy extends beyond the joint-Gaussian regime where closed-form solutions exist.
  2. [Simulation results] Simulation results (abstract and results section) are invoked to confirm “significant gains,” yet no details are supplied on error bars, data exclusion criteria, exact optimization procedures, or verification that gains are not due to post-hoc tuning; these omissions undermine the empirical support for the proposed designs.
minor comments (2)
  1. Clarify the precise mathematical statement of the finite-rate constraint that is added to the GIB objective (e.g., which mutual-information term is replaced or bounded).
  2. Specify the exact form of the modified VAE cost function used for the non-Gaussian vector quantizer.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. Below we address each major comment point by point and indicate the revisions to be made in the next version of the manuscript.

read point-by-point responses

  1. Referee: [Non-Gaussian extension] The non-Gaussian extension (final paragraph of the abstract and corresponding section) modifies the VAE cost function without deriving or bounding its deviation from the true IB objective (mutual-information terms); this step is load-bearing for the claim that the task-oriented philosophy extends beyond the joint-Gaussian regime where closed-form solutions exist.

    Authors: We agree that the non-Gaussian extension modifies the VAE cost function without deriving or bounding its deviation from the true IB objective. Since the true mutual information terms are intractable for non-Gaussian data, the modification is a heuristic adaptation inspired by the IB principle. We will revise the manuscript to explicitly state the heuristic nature of this step, discuss its limitations, and temper the claim that the task-oriented philosophy extends beyond the Gaussian regime. revision: partial

  2. Referee: [Simulation results] Simulation results (abstract and results section) are invoked to confirm “significant gains,” yet no details are supplied on error bars, data exclusion criteria, exact optimization procedures, or verification that gains are not due to post-hoc tuning; these omissions undermine the empirical support for the proposed designs.

    Authors: We acknowledge that additional details are required to support the empirical claims. In the revised manuscript we will report error bars from multiple independent runs, specify data handling and exclusion criteria, detail the exact optimization procedures and hyperparameters, and include verification that the reported gains are robust and not attributable to post-hoc tuning. We will also release the simulation code to aid reproducibility. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: independent reformulation of GIB optimization and simulation validation

full rationale

The paper derives a finite-rate constrained reformulation of the GIB problem and analyzes quantization effects via direct theoretical steps on mutual information terms. These steps do not reduce to fitted parameters renamed as predictions or self-definitional loops. Simulations on MMSE regression are presented as external validation rather than inputs to the derivation. The non-Gaussian VAE modification is an explicit extension without claiming it equals the true IB objective by construction. No load-bearing self-citations or uniqueness theorems imported from prior author work appear in the provided text. The derivation chain remains self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities; all fields left empty.

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Cite this review

Pith. "Pith review of Information Bottleneck Meets Quantization: Finite Rate Analysis and Optimal Designs." pith.science (2026). https://pith.science/paper/XHQUYEWV

@misc{pith2026260610869,
  author       = {Pith},
  title        = {Pith review of: Information Bottleneck Meets Quantization: Finite Rate Analysis and Optimal Designs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHQUYEWV}},
  note         = {Machine review of arXiv:2606.10869}
}
read the original abstract

The Information Bottleneck (IB) is a well established framework that looks for a latent compact representation of a data source, by trading rate and data-size representation, for information accuracy with respect to another target data. The Gaussian IB (GIB) is its simple closed form solution, when the target is jointly Gaussian with the source. Actually, in many practical problems the latent representation has to be stored or represented by a finite number of bits, while the optimal (G)IB solution has not. First, this manuscript theoretically analyzes the effect of scalar and vector quantization of the GIB latent representation, and its impact on the (dis)informativeness with respect to the target data. Then, task-oriented quantization designs are proposed by (jointly) reformulating the GIB optimization problem under a finite-rate constraint on the latent representation. Simulation results on MMSE regression problems confirm the effectiveness of the proposed quantization designs, which show significant gains with respect to more heuristic, or separate, quantization designs of the standard GIB latent representation. Finally, the paper extends the task-oriented philosophy to non-Gaussian settings, by properly modifying the cost function used in variational auto-encoders (VAEs) of IB-inspired vector quantizers.

Figures

Figures reproduced from arXiv: 2606.10869 by the authors.

Figure 1
Figure 1. The goal-oriented feature extraction and quantizat [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Reconstr. NMSE for vector and scalar quantization. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Task NMSE for vector and scalar quantization. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Task NMSE E [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 7
Figure 7. Figure 7: Task NMSE E[ky − yˆk] vs. rate for the the interleaved, the contiguous, and a random feature permutation. modified by (31). Experiments are conducted on a synthetic multivariate Gaussian dataset generated according to (34), with nx = 50 and ny = 36, and on the Human3.6…
Figure 8
Figure 8. Figure 8: Average block size for the three feature permutation [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Left panel: Task NMSE as a function of the rate budget fo [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

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Works this paper leans on

42 extracted references · 4 canonical work pages

  1. [1]

    Information bottleneck aide d quantization for rate-limited gaussian inference,

    F. Binucci and P . Banelli, “Information bottleneck aide d quantization for rate-limited gaussian inference,” in 2026 34th European Signal Processing Conference (EUSIPCO) , 2026

    2026

  2. [2]

    The information bottleneck method,

    N. Tishby, F. C. Pereira, and W. Bialek, “The information bottleneck method,” in Proc. of the 37-th Annual Allerton Conference on Commu- nication, Control and Computing , 1999, pp. 368–377

    1999

  3. [3]

    T. M. Cover, Elements of information theory . John Wiley & Sons, 1999

    1999

  4. [4]

    6g networks: Beyond sh annon towards semantic and goal-oriented communications,

    E. C. Strinati and S. Barbarossa, “6g networks: Beyond sh annon towards semantic and goal-oriented communications,” Computer Networks , vol. 190, p. 107930, 2021

    2021

  5. [5]

    A survey on information bottleneck,

    S. Hu, Z. Lou et al., “A survey on information bottleneck,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 46, no. 8, pp. 5325–5344, 2024

    2024

  6. [6]

    Goal-oriented communications for the iot: System design and adaptive resource optimization,

    P . Di Lorenzo et al., “Goal-oriented communications for the iot: System design and adaptive resource optimization,” IEEE Internet of Things Magazine, vol. 6, no. 4, pp. 26–32, 2023

    2023

  7. [7]

    Beyond transmitting bits: Context, semantics, and task-oriented communications,

    D. G¨ und¨ uzet al. , “Beyond transmitting bits: Context, semantics, and task-oriented communications,” IEEE J. Sel. Areas Commun. , vol. 41, no. 1, pp. 5–41, 2023

    2023

  8. [8]

    Learning task-oriented co mmunication for edge inference: An information bottleneck approach,

    J. Shao, Y . Mao, and J. Zhang, “Learning task-oriented co mmunication for edge inference: An information bottleneck approach,” IEEE J. Sel. Areas Commun. , vol. 40, no. 1, pp. 197–211, 2022

    2022

Show all 42 references
  1. [9]

    Adaptive information bottleneck guided joint source and channel coding for image transmission,

    L. Sun, Y . Y ang, M. Chen et al., “Adaptive information bottleneck guided joint source and channel coding for image transmission,” IEEE J. Sel. Areas Commun. , vol. 41, no. 8, pp. 2628–2644, 2023

    2023

  2. [10]

    Robust i nformation bottleneck for task-oriented communication with digital m odulation,

    S. Xie, S. Ma, M. Ding, Y . Shi, M. Tang, and Y . Wu, “Robust i nformation bottleneck for task-oriented communication with digital m odulation,” IEEE J. Sel. Areas Commun. , vol. 41, no. 8, pp. 2577–2591, 2023

    2023

  3. [11]

    Task-oriented communica tion for mul- tidevice cooperative edge inference,

    J. Shao, Y . Mao, and J. Zhang, “Task-oriented communica tion for mul- tidevice cooperative edge inference,” IEEE Trans. Wireless Commun. , vol. 22, no. 1, pp. 73–87, 2022

    2022

  4. [12]

    A deep variational approach to mul- titerminal joint source-channel coding based on informati on bottleneck principle,

    S. Hassanpour, M. Hummert et al., “A deep variational approach to mul- titerminal joint source-channel coding based on informati on bottleneck principle,” IEEE Open J. Commun. Soc. , vol. 6, pp. 4462–4475, 2025

    2025

  5. [13]

    D 2-jscc: Digi tal deep joint source-channel coding for semantic communications,

    J. Huang, K. Y uan, C. Huang, and K. Huang, “D 2-jscc: Digi tal deep joint source-channel coding for semantic communications, ” IEEE J. Sel. Areas Commun. , 2025

    2025

  6. [14]

    Ofdm-based digital se- mantic communication with importance awareness,

    C. Liu, C. Guo, Y . Y ang, W. Ni, and T. Q. Quek, “Ofdm-based digital se- mantic communication with importance awareness,” IEEE Transactions on Communications , vol. 72, no. 10, pp. 6301–6315, 2024

    2024

  7. [15]

    Info rmation bottleneck for gaussian variables,

    G. Chechik, A. Globerson, N. Tishby, and Y . Weiss, “Info rmation bottleneck for gaussian variables,” J. Mach. Learn. Res. , vol. 6, p. 165–188, Dec. 2005

    2005

  8. [16]

    Neural discrete representation learning,

    A. V an Den Oord et al. , “Neural discrete representation learning,” Advances in Neural Information Processing Systems , vol. 30, 2017

    2017

  9. [17]

    On the rela tion between the gaussian information bottleneck and mse-optimal rate- distortion quantization,

    M. Meidlinger, A. Winkelbauer, and G. Matz, “On the rela tion between the gaussian information bottleneck and mse-optimal rate- distortion quantization,” in 2014 IEEE W orkshop on Statistical Signal Processing (SSP). IEEE, 2014, pp. 89–92

    2014

  10. [18]

    Rate-information-optima l gaussian chan- nel output compression,

    A. Winkelbauer and G. Matz, “Rate-information-optima l gaussian chan- nel output compression,” in 2014 48th Annual Conference on Informa- tion Sciences and Systems (CISS) , 2014, pp. 1–5

    2014

  11. [19]

    Forward-aware information bottleneck-based vector quantization for noisy channels,

    S. Hassanpour, T. Monsees et al. , “Forward-aware information bottleneck-based vector quantization for noisy channels, ” IEEE Trans- actions on Communications , vol. 68, no. 12, pp. 7911–7926, 2020

    2020

  12. [20]

    Reduced-complexity optimization of distributed quan- tization using the information bottleneck principle,

    S. Steiner et al., “Reduced-complexity optimization of distributed quan- tization using the information bottleneck principle,” IEEE Open J. of the Commun. Soc. , vol. 2, pp. 1267–1278, 2021

    2021

  13. [21]

    Scalable vec tor gaussian information bottleneck,

    M. M. Mahvari, M. Kobayashi, and A. Zaidi, “Scalable vec tor gaussian information bottleneck,” in 2021 IEEE International Symposium on Information Theory (ISIT) . IEEE, 2021, pp. 37–42

    2021

  14. [22]

    The deterministic infor mation bottle- neck,

    D. J. Strouse and D. J. Schwab, “The deterministic infor mation bottle- neck,” Neural computation, vol. 29, no. 6, pp. 1611–1630, 2017

    2017

  15. [23]

    A parametric in formation bottleneck algorithm for gaussian random variables and gau ssian mix- tures,

    M. Stark, J. Lewandowsky, and G. Bauch, “A parametric in formation bottleneck algorithm for gaussian random variables and gau ssian mix- tures,” in SCC 2019; 12th International ITG Conference on Systems, Communications and Coding , 2019, pp. 1–6

    2019

  16. [24]

    Dee p variational information bottleneck,

    A. A. Alemi, I. Fischer, J. V . Dillon, and K. Murphy, “Dee p variational information bottleneck,” arXiv preprint arXiv:1612.00410 , 2016

    2016 arXiv

  17. [25]

    V ector quantization and information bottleneck- inspired type based multiple access in semantic-aware remo te estima- tion,

    H. Zhang, Z. Liu et al., “V ector quantization and information bottleneck- inspired type based multiple access in semantic-aware remo te estima- tion,” IEEE Trans. V eh. Technol., pp. 1–15, 2026

    2026

  18. [26]

    Channel-aware vector quantization for robust semantic communication on discret e channels,

    Z. Meng, Q. Li, W. Tang, M. Y an, and X. Ge, “Channel-aware vector quantization for robust semantic communication on discret e channels,” arXiv preprint arXiv:2510.18604 , 2025. 15

    2025

  19. [27]

    Vq- vae based digital semantic communication with importance- aware ofdm transmission,

    M. Lyu, H. Chen, D. Wang, C. Qiu, G. Feng, N. Ma, and X. Xu, “ Vq- vae based digital semantic communication with importance- aware ofdm transmission,” arXiv preprint arXiv:2508.08686 , 2025

    2025

  20. [28]

    Robust semantic communications with masked vq-vae enabled codebook,

    Q. Hu, G. Zhang, Z. Qin, Y . Cai, G. Y u, and G. Y . Li, “Robust semantic communications with masked vq-vae enabled codebook,” IEEE Trans. Wireless Commun., vol. 22, no. 12, pp. 8707–8722, 2023

    2023

  21. [29]

    Task-driven semantic quantization and imitation learning for goal-oriented communications,

    Y .-C. Chao, Y . Chen et al. , “Task-driven semantic quantization and imitation learning for goal-oriented communications,” in ICC 2025-IEEE International Conference on Communications . IEEE, 2025, pp. 1–6

    2025

  22. [30]

    Opportunistic information-bottleneck for goal-oriented feature extraction and communication,

    F. Binucci, P . Banelli et al. , “Opportunistic information-bottleneck for goal-oriented feature extraction and communication,” IEEE Open J. Commun. Soc. , vol. 5, pp. 2418–2432, 2024

    2024

  23. [31]

    Opportunistic information bottleneck for edge-assisted goal-oriented communications,

    F. Binucci and P . Banelli, “Opportunistic information bottleneck for edge-assisted goal-oriented communications,” in 2024 58th Asilomar Conference on Signals, Systems, and Computers , 2024, pp. 748–753

    2024

  24. [32]

    Quantization,

    R. M. Gray and D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory , vol. 44, no. 6, pp. 2325–2383, 2002

    2002

  25. [33]

    Information rates of pre/post-fi ltered dithered quantizers,

    R. Zamir and M. Feder, “Information rates of pre/post-fi ltered dithered quantizers,” IEEE Trans. Inf. Theory , vol. 42, no. 5, pp. 1340–1353, 2002

    2002

  26. [34]

    Boyd and L

    S. Boyd and L. V andenberghe, Convex optimization . Cambridge university press, 2004

    2004

  27. [35]

    Fast sequence segmentation using log-linea r models,

    N. Tatti, “Fast sequence segmentation using log-linea r models,” Data Mining and Knowledge Discovery , vol. 27, no. 3, pp. 421–441, 2013

    2013

  28. [36]

    Towards h uman-agent communication via the information bottleneck principle,

    M. Tucker, J. Shah, R. Levy, and N. Zaslavsky, “Towards h uman-agent communication via the information bottleneck principle,” arXiv preprint arXiv:2207.00088, 2022

    2022

  29. [37]

    The im algorithm: a variationa l approach to information maximization,

    D. Barber and F. Agakov, “The im algorithm: a variationa l approach to information maximization,” Advances in Neural Information Processing Systems, vol. 16, no. 320, p. 201, 2004

    2004

  30. [38]

    Learnab ility for the information bottleneck,

    T. Wu, I. Fischer, I. L. Chuang, and M. Tegmark, “Learnab ility for the information bottleneck,” in Uncertainty in Artificial Intelligence . PMLR, 2020, pp. 1050–1060

    2020

  31. [39]

    Statistical signal processing: estimation theory,

    S. M. Kay, “Statistical signal processing: estimation theory,” Prentice Hall, vol. 1, pp. Chapter–3, 1993

    1993

  32. [40]

    Human3.6m: Large scale datasets and predictive methods for 3d human sensing in natural environments,

    C. Ionescu et al. , “Human3.6m: Large scale datasets and predictive methods for 3d human sensing in natural environments,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 36, no. 7, pp. 1325–1339, 2014

    2014

  33. [41]

    J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups . Springer Science & Business Media, 2013, vol. 290

    2013

  34. [42]

    The minimum information principle in le arning and neural data analysis,

    A. Globerson, “The minimum information principle in le arning and neural data analysis,” Ph.D. dissertation, Citeseer, 2005 . 16

    2005

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