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arxiv: 2605.20826 · v1 · pith:ZXD66BCXnew · submitted 2026-05-20 · 💻 cs.IT · math.IT

Forward asymmetric numeral systems coding for natural language text compression

Mykyta Kharin , Igor Zavadskyi This is my paper

Pith reviewed 2026-05-21 02:31 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords asymmetric numeral systemsadaptive codingtext compressionforward modelingnatural languageentropy codingdata compression
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The pith

Combining forward modeling with asymmetric numeral systems enables adaptive ANS for text compression.

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

The paper proposes integrating forward modeling of the information source with asymmetric numeral systems (ANS) coding for natural language text. This combination is intended to deliver high encoding and decoding speeds together with compression ratios close to Shannon entropy, and even estimated sizes below entropy. The central achievement is that the method makes adaptive ANS practical, solving a problem that has remained open. A sympathetic reader would care because it points toward compression tools that adapt to the data on the fly without losing the speed advantages of ANS.

Core claim

Compression based on asymmetric numeral systems combines high encoding and decoding speeds with a compression ratio close to Shannon entropy, while forward modeling of the information source makes it possible to obtain an estimated compressed message size that is less than the entropy. This paper proposes combining these modeling and adaptive coding methods to implement the adaptive ANS.

What carries the argument

Forward asymmetric numeral systems coding, which merges forward modeling directly into the ANS encoding process to support adaptive behavior.

If this is right

  • Adaptive ANS becomes feasible to implement for natural language text.
  • Estimated compressed sizes can be reported below the entropy bound.
  • High processing speeds are retained while gaining the adaptive capability.

Where Pith is reading between the lines

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

  • The same integration pattern could be tried with other entropy coders that currently lack easy adaptivity.
  • If overhead stays low, the technique might suit real-time applications such as live text streaming.
  • It raises the question of whether forward models can be learned on the fly without separate training phases.

Load-bearing premise

Forward modeling of the information source can be integrated with ANS without introducing overhead that negates the claimed speed and compression benefits.

What would settle it

Benchmark the proposed coder on a standard natural-language corpus and measure whether compression size falls below the entropy estimate while encoding and decoding speeds remain comparable to ordinary ANS and no extra overhead appears.

read the original abstract

Compression based on asymmetric numeral systems (ANS) combines high encoding and decoding speeds with a compression ratio close to Shannon entropy, while forward modeling of the information source makes it possible to obtain an estimated compressed message size that is less than the entropy. This paper proposes combining these modeling and adaptive coding methods. In addition to ensuring high data processing speeds and compression ratios, this approach enables one to implement the adaptive ANS, which has long remained an important scientific and practical problem.

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

1 major / 1 minor

Summary. The paper proposes combining forward modeling of the information source with asymmetric numeral systems (ANS) coding to enable adaptive ANS for natural language text compression. The approach is claimed to preserve high encoding/decoding speeds and compression ratios close to Shannon entropy while also permitting an estimated compressed message size below entropy, thereby solving the long-standing problem of implementing adaptive ANS.

Significance. If the integration can be shown to achieve true on-the-fly adaptation without negating ANS speed or compression advantages, the result would be significant for practical text compression systems. The manuscript correctly identifies adaptive ANS as an open problem; a working solution would be a useful contribution to the field.

major comments (1)
  1. The manuscript contains no equations, algorithm pseudocode, or derivation showing how forward modeling is fused with the ANS state update to produce an adaptive coder. Without this, it is impossible to verify that the claimed integration preserves the O(1) per-symbol complexity of standard ANS or avoids parameter-fitting that would undermine the 'less than entropy' claim.
minor comments (1)
  1. The abstract states that forward modeling yields an estimated size 'less than the entropy,' but does not clarify whether this is an expected value under the model or a guaranteed bound; a short clarifying sentence would help.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive criticism. We agree that additional technical detail is needed to substantiate the integration of forward modeling with ANS and will revise the manuscript accordingly to include the requested derivations and pseudocode.

read point-by-point responses

  1. Referee: The manuscript contains no equations, algorithm pseudocode, or derivation showing how forward modeling is fused with the ANS state update to produce an adaptive coder. Without this, it is impossible to verify that the claimed integration preserves the O(1) per-symbol complexity of standard ANS or avoids parameter-fitting that would undermine the 'less than entropy' claim.

    Authors: We acknowledge the validity of this observation. The current version presents the high-level combination but omits the explicit state-update equations and algorithmic description. In the revised manuscript we will add: (1) the precise recurrence relating the forward-model probability estimate p_t to the ANS state transition function, (2) pseudocode for both the encoder and decoder that shows the model update occurring in amortized constant time per symbol, and (3) a short complexity argument demonstrating that no iterative parameter fitting is performed. These additions will make it possible to verify that the per-symbol cost remains O(1) and that the sub-entropy estimate stems from the forward-looking predictor rather than overfitting. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper proposes a high-level combination of forward modeling with asymmetric numeral systems (ANS) to address adaptive ANS coding. No equations, derivations, parameter fittings, or self-citations are presented in the abstract or description that reduce any claimed result to its inputs by construction. The central claim is framed as an integration of existing methods rather than a novel mathematical derivation or uniqueness theorem. As such, the approach appears self-contained with no load-bearing steps that exhibit self-definitional, fitted-input, or self-citation circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no information on free parameters, axioms, or invented entities used in the method.

pith-pipeline@v0.9.0 · 5592 in / 987 out tokens · 45935 ms · 2026-05-21T02:31:58.991443+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages · 2 internal anchors

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    Generalized Kraft inequality and arithmetic coding,

    J. J. Rissanen, “Generalized Kraft inequality and arithmetic coding,”IBM Journal of Research and Development, vol. 20, no. 3, pp. 198–203, May 1976

    work page 1976

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    Asymmetric numeral systems

    J. Duda, “Asymmetric Numerical Systems,” arXiv preprint arXiv:0902.0271, 2009. [Online]. Available:https: //arxiv.org/pdf/0902.0271

    work page internal anchor Pith review Pith/arXiv arXiv 2009

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    Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding

    J. Duda, “Asymmetric Numeral Systems: Entropy Coding Combining Speed of Huffman Coding with Compression Rate of Arithmetic Coding,” arXiv preprint arXiv:1311.2540, 2014. [Online]. Available:https://arxiv.org/ pdf/1311.2540

    work page internal anchor Pith review Pith/arXiv arXiv 2014

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    Word-based Forward Coding,

    I. O. Zavadskyi, S. T. Klein, and D. Shapira, “Word-based Forward Coding,” inData Compression Conference (DCC), 2024, pp. 352–361

    work page 2024

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    Forward Modeling in Adaptive Compression: Bounds and Experimental Evalua- tion,

    I. O. Zavadskyi and D. Shapira, “Forward Modeling in Adaptive Compression: Bounds and Experimental Evalua- tion,” inData Compression Conference (DCC), 2026, pp. 223–232

    work page 2026

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    PPMd Compression,

    “PPMd Compression,” Mintlify.wiki, 2026. [Online]. Available: https://mintlify.wiki/ip7z/7zip/ compression/ppmd[Accessed: Apr. 18, 2026]. 3

    work page 2026