pith. sign in

arxiv: 2604.15472 · v1 · submitted 2026-04-16 · 💻 cs.IT · cs.LG· math.IT

Lossless Compression via Chained Lightweight Neural Predictors with Information Inheritance

Yuriy Kim , Evgeny Belyaev This is my paper

Pith reviewed 2026-05-10 09:28 UTC · model grok-4.3

classification 💻 cs.IT cs.LGmath.IT
keywords lossless compressionneural networksprobability estimationMarkov sourcesinformation inheritancedata compressionneural predictorsthroughput optimization
0
0 comments X p. Extension

The pith

Chained lightweight neural predictors with inherited estimates achieve compression ratios close to the state-of-the-art PAC while delivering substantially higher GPU throughput.

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

The paper introduces a probability estimation architecture for lossless compression that uses a chain of minimal neural networks, each sized exactly for the Markov order it handles. Lower-order units pass their probability estimates forward to higher-order units through an information inheritance step, allowing the overall system to adapt the total number of weights to the statistical properties of the input. Experiments show this yields compression performance comparable to the leading PAC compressor. At the same time the design runs 1.2 to 6.3 times faster at encoding and 2.8 to 12.3 times faster at decoding on a consumer GPU.

Core claim

A chain of minimal neural predictors, each handling a successive Markov order and receiving inherited probability estimates from the preceding unit, produces accurate enough conditional probabilities for lossless compression ratios near those of the state-of-the-art PAC method while requiring only a data-dependent number of weights and delivering substantially higher encoding and decoding throughput on consumer GPUs.

What carries the argument

The chained probability estimation architecture of minimal neural networks for successive Markov orders combined with an information inheritance mechanism that passes lower-order estimates to higher-order units.

If this is right

  • The total number of weights used for probability estimation can be kept minimal by matching each network size to the observed order of the source.
  • Compression ratios remain close to those of the PAC compressor across tested data.
  • Encoding runs between 1.2 and 6.3 times faster than PAC on a consumer GPU.
  • Decoding runs between 2.8 and 12.3 times faster than PAC on a consumer GPU.
  • The architecture adapts the computational cost to the statistical properties of the input data.

Where Pith is reading between the lines

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

  • The inheritance step could be applied to other sequential modeling tasks where lower-order statistics are cheap to compute.
  • Memory-constrained devices might benefit from dynamically pruning higher-order units when data order is low.
  • The same chaining idea might extend to lossy compression or other prediction problems by replacing the arithmetic coder with a different entropy stage.

Load-bearing premise

That a chain of minimal neural networks sized for successive Markov orders plus information inheritance can generate probability estimates accurate enough to match leading compression ratios without extra weights or underfitting on real data.

What would settle it

Running the compressor on standard test corpora and obtaining compression ratios more than a few percent worse than PAC would show the estimates are not accurate enough.

Figures

Figures reproduced from arXiv: 2604.15472 by Evgeny Belyaev, Yuriy Kim.

Figure 1
Figure 1. Figure 1: The proposed neural architecture search visualization [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The proposed architecture of chained neural predictors with information inheritance [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Training of neural predictor θ6 and full encoding pipeline the same idea, but within the scope of the machine learning approach. The information inheritance at order si ̸= s1 is proposed to realize via linear weighing of the logits l ′ i+1 and l ′ i as li = αi · l ′ i + βi · l ′ i−1 , (8) where αi and βi are trainable parameters. Here, αi = 1, βi = 0 means that the information inheritance is disabled. Fina… view at source ↗
Figure 4
Figure 4. Figure 4: Compression performance for models with and without [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Compression efficiency versus processing time comparison for different compressors [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

This paper is dedicated to lossless data compression with probability estimation using neural networks. First, we propose a probability estimation architecture based on a chain of neural predictors, so that each unit of the chain is defined as a neural network with the minimum possible number of weights, which is sufficient for efficient compression of data generated by Markov sources of a given order. We show that this architecture allows us to minimize the overall number of weights participating in the probability estimation process depending on the statistical properties of the input data. Second, in order to improve compression efficiency, we introduce an information inheritance mechanism, where the probability estimate obtained by a low-order unit is used at the next higher-order unit. Experimental results show that the proposed lossless data compressor equipped with the chained probability estimation architecture provides compression ratios close to the state-of-the-art PAC compressor. At the same time, it outperforms PAC by a factor of 1.2 to 6.3 in encoding throughput and by a factor of 2.8 to 12.3 in decoding throughput on a consumer GPU.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper proposes a chained architecture of lightweight neural networks for probability estimation in lossless compression. Each unit in the chain is a minimal-weight neural predictor sized for a specific Markov order, with an information inheritance mechanism that passes probability estimates from lower-order to higher-order predictors. The central empirical claim is that the resulting compressor achieves compression ratios close to the state-of-the-art PAC method while delivering encoding throughput gains of 1.2–6.3× and decoding gains of 2.8–12.3× on a consumer GPU.

Significance. If the performance claims are reproducible, the work provides a practical neural architecture that adapts total parameter count to data statistics and improves throughput without sacrificing ratio, which could be valuable for high-speed lossless compression applications on GPU hardware. The emphasis on minimal per-order networks and inheritance is a concrete contribution to context-adaptive modeling.

major comments (2)
  1. [Experimental results] The experimental results section does not specify the datasets, training procedures, hyperparameter choices, number of runs, or statistical significance testing for the reported throughput and ratio figures. Without these, the claimed advantages over PAC cannot be independently assessed or reproduced.
  2. [Architecture description] The description of the chained predictors does not include the precise network architectures (layer sizes, activation functions) or the exact mechanism by which the total weight count adapts to input statistics; this information is load-bearing for verifying the 'minimum possible number of weights' claim.
minor comments (2)
  1. Define 'information inheritance' more formally, perhaps with a short equation showing how the low-order estimate is incorporated into the higher-order predictor.
  2. Add a table comparing total parameter counts and compression ratios across different Markov orders for the proposed method versus PAC.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the detailed review of our manuscript. We have carefully considered the major comments and will make revisions to enhance the clarity and reproducibility of our work.

read point-by-point responses

  1. Referee: [Experimental results] The experimental results section does not specify the datasets, training procedures, hyperparameter choices, number of runs, or statistical significance testing for the reported throughput and ratio figures. Without these, the claimed advantages over PAC cannot be independently assessed or reproduced.

    Authors: We agree that additional details are necessary for reproducibility. In the revised manuscript, we will provide a comprehensive description of the experimental setup, including the datasets employed, the training procedures for the neural predictors, specific hyperparameter values, the number of independent runs performed, and statistical measures such as standard deviations to assess significance. This will enable independent verification of the reported compression ratios and throughput improvements over PAC. revision: yes

  2. Referee: [Architecture description] The description of the chained predictors does not include the precise network architectures (layer sizes, activation functions) or the exact mechanism by which the total weight count adapts to input statistics; this information is load-bearing for verifying the 'minimum possible number of weights' claim.

    Authors: We acknowledge the need for more precise architectural details. The revised paper will include explicit specifications of the network architectures for each predictor in the chain, such as the number of layers, neuron counts per layer, and activation functions used. Additionally, we will elaborate on the information inheritance mechanism and how the chain dynamically selects and adapts the total number of weights based on the estimated Markov order of the input data, thereby minimizing the parameter count while maintaining compression efficiency. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes an empirical neural architecture for probability estimation in lossless compression, consisting of chained minimal-weight predictors with information inheritance. No mathematical derivation chain, first-principles predictions, or fitted parameters are presented that reduce to their own inputs by construction. Claims rest on experimental throughput and ratio comparisons to PAC, which are externally falsifiable and contain no self-definitional, self-citation load-bearing, or ansatz-smuggling steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract contains no explicit free parameters, mathematical axioms, or newly postulated entities; the approach relies on standard neural-network training assumptions and Markov-source modeling that are treated as background.

pith-pipeline@v0.9.0 · 5483 in / 1140 out tokens · 50218 ms · 2026-05-10T09:28:19.270389+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

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

  1. [1]

    Worldwide idc global datas- phere forecast, 2025–2029,

    A. Wright, “Worldwide idc global datas- phere forecast, 2025–2029,” 2025. [Online]. Available: https://my.idc.com/getdoc.jsp?containerId=US53363625

    2025

  2. [2]

    A universal algorithm for sequential data compression,

    J. Ziv and A. Lempel, “A universal algorithm for sequential data compression,”IEEE Transactions on Information Theory, vol. 23, no. 3, pp. 337–343, 1977

    1977

  3. [3]

    Data compression using adaptive coding and partial string matching,

    J. Cleary and I. Witten, “Data compression using adaptive coding and partial string matching,”IEEE transactions on Communications, vol. 32, no. 4, pp. 396–402, 2003

    2003

  4. [4]

    Arithmetic coding for data compression,

    I. H. Witten, R. M. Neal, and J. G. Cleary, “Arithmetic coding for data compression,”Communications of the ACM, vol. 30, no. 6, pp. 520–540, 1987

    1987

  5. [5]

    Dzip: Improved general-purpose loss less compression based on novel neural network modeling,

    M. Goyal, K. Tatwawadi, S. Chandak, and I. Ochoa, “Dzip: Improved general-purpose loss less compression based on novel neural network modeling,” in2021 data compression conference (DCC). IEEE, 2021, pp. 153–162

    2021

  6. [6]

    Language Modeling Is Compression

    G. Del ´etang, A. Ruoss, P.-A. Duquenne, E. Catt, T. Genewein, C. Mat- tern, J. Grau-Moya, L. K. Wenliang, M. Aitchison, L. Orseauet al., “Language modeling is compression,”arXiv preprint arXiv:2309.10668, 2023

    work page internal anchor Pith review arXiv 2023

  7. [7]

    Trace: A fast transformer- based general-purpose lossless compressor,

    Y . Mao, Y . Cui, T.-W. Kuo, and C. J. Xue, “Trace: A fast transformer- based general-purpose lossless compressor,” inProceedings of the ACM Web Conference 2022, 2022, pp. 1829–1838

    2022

  8. [8]

    Faster and stronger lossless compression with optimized autoregressive framework,

    Y . Mao, J. Li, Y . Cui, and J. C. Xue, “Faster and stronger lossless compression with optimized autoregressive framework,” in2023 60th ACM/IEEE Design Automation Conference (DAC). IEEE, 2023, pp. 1–6

    2023

  9. [9]

    Complexity reduction of neural lossless data compression via cascade probability modeling,

    Y . Kim and E. Belyaev, “Complexity reduction of neural lossless data compression via cascade probability modeling,” in2025 XIX Inter- national Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 2025, pp. 1–5

    2025

  10. [10]

    Ppm: one step to practicality,

    D. Shkarin, “Ppm: one step to practicality,” inProceedings DCC 2002. Data Compression Conference, 2002, pp. 202–211

    2002

  11. [11]

    Large text compression benchmark,

    M. Mahoney, “Large text compression benchmark,” 2011

    2011

  12. [12]

    A new algorithm for data compression,

    P. Gage, “A new algorithm for data compression,”C Users J., vol. 12, no. 2, p. 23–38, Feb. 1994

    1994

  13. [13]

    Excp: Extreme llm checkpoint compression via weight-momentum joint shrinking,

    W. Li, X. Chen, H. Shu, Y . Tang, and Y . Wang, “Excp: Extreme llm checkpoint compression via weight-momentum joint shrinking,” inInternational Conference on Machine Learning, 2024. [Online]. Available: https://api.semanticscholar.org/CorpusID:270560683

    2024

  14. [14]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,”Advances in neural information processing systems, vol. 30, 2017

    2017

  15. [15]

    Imagenet: A large-scale hierarchical image database,

    J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, “Imagenet: A large-scale hierarchical image database,” in2009 IEEE conference on computer vision and pattern recognition. Ieee, 2009, pp. 248–255

    2009

  16. [16]

    Esc: Dataset for environmental sound classification,

    K. J. Piczak, “Esc: Dataset for environmental sound classification,” in Proceedings of the 23rd ACM international conference on Multimedia, 2015, pp. 1015–1018

    2015

  17. [17]

    Fpc: A high-speed compressor for double-precision floating-point data,

    M. Burtscher and P. Ratanaworabhan, “Fpc: A high-speed compressor for double-precision floating-point data,”IEEE transactions on comput- ers, vol. 58, no. 1, pp. 18–31, 2008

    2008

  18. [18]

    A dna sequence corpus for compression benchmark,

    D. Pratas and A. J. Pinho, “A dna sequence corpus for compression benchmark,” inInternational Conference on Practical Applications of Computational Biology & Bioinformatics. Springer, 2018, pp. 208–215

    2018

  19. [19]

    7-zip: File archiver,

    I. Pavlov, “7-zip: File archiver,” https://www.7-zip.org/, 1999, accessed: 2026-03-25

    1999

  20. [20]

    Gzip file format specification version 4.3,

    P. Deutsch, “Gzip file format specification version 4.3,” Tech. Rep., 1996

    1996

  21. [21]

    Zstandard compression and the applica- tion/zstd media type,

    Y . Collet and M. Kucherawy, “Zstandard compression and the applica- tion/zstd media type,” Tech. Rep., 2018. 9 Yuriy Kimis a PhD student at ITMO University, Saint-Petersburg, Russia. His current research interests include neural data and image compression. He received a Master’s degree in 2024 from ITMO University, Saint-Petersburg, Russia. Contact him a...

    2018