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REVIEW 2 major objections 13 references

Arbitrary Reduction of Validation Error for AI Decision Tests using Homomorphic AI and Repetition Codes

T0 review · 2 major / 0 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Repetition error-correcting codes combined with HbHAI can arbitrarily reduce validation error in AI decision tests.

desk verdict The repetition code claim for arbitrary error reduction only works if HbHAI keeps base AI error below 0.5 with independent trials, and the abstract gives no evidence that holds. read the letter →

arxiv 2606.28994 v1 pith:3WZOSSH3 submitted 2026-06-27 cs.CR cs.AI

Eric Filiol , Jaagup Sepp This is my paper
classification cs.CRcs.AI
keywords homomorphicAIrepetitioncodesvalidationerrorhashfunctionserror-correctingdecisiontestsprivacypreserving
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 HbHAI, which relies on key-dependent hash functions preserving similarity properties, allows standard AI algorithms to process encrypted data. When repetition codes are applied to the results of these AI decision tests, the validation error can be reduced to any desired level by increasing the number of repetitions. This also enables processing larger datasets with reduced computation time and energy use compared to plaintext processing. A reader would care because it offers a method to achieve both cryptographic security and high reliability in AI decisions without modifying existing algorithms.

What carries the argument

HbHAI techniques using key-dependent hash functions that preserve similarity properties, integrated with repetition error-correcting codes.

What would settle it

An experiment where increasing the number of repetitions in the codes fails to reduce the validation error below a fixed positive value.

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Extended reading notes

Core claim

The central discovery is that repetition error-correcting codes can be used with HbHAI to arbitrarily reduce the final validation error of AI-based decision tests, while the hash functions enable unmodified AI to work on the secure data form.

Load-bearing premise

The key-dependent hash functions naturally preserve most similarity properties that AI algorithms rely on.

Editorial extensions

If this is right

  • Validation error decreases without bound as the repetition factor increases.
  • Compression rate improves by up to a factor of 10, lowering computation time and energy footprint.
  • Native AI algorithms require no modification to process the hashed data.
  • Performance exceeds that of existing homomorphic encryption schemes and sometimes plaintext data.

Reading between the lines

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

  • This approach could allow reliable AI decisions on sensitive data without exposing it in plaintext.
  • Similar techniques might extend to other error-sensitive AI tasks like classification or prediction.
  • Further work could test the method on real-world datasets to measure the exact error reduction rates.
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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 / 0 minor

Summary. The paper claims that HbHAI, based on key-dependent hash functions that preserve most similarity properties used by AI algorithms, enables unmodified native AI algorithms to process cryptographically secure data with better performance than existing homomorphic encryption. It reports two results: compression rate reduction by a factor of up to 10, and arbitrary reduction of validation error in AI decision tests via repetition error-correcting codes.

Significance. If the core preservation property holds with error rate p<0.5 and independent trials, the repetition-code result would enable tunable error reduction in privacy-preserving AI without modifying algorithms or using heavy homomorphic schemes, which is potentially significant for secure decision systems. The compression improvement could also aid scalability. These strengths are noted only conditionally on quantitative validation of the similarity preservation.

major comments (2)
  1. [Abstract] Abstract, second paragraph: the claim that repetition codes enable arbitrary reduction of validation error requires that HbHAI-processed inputs yield AI decision errors behaving as a binary symmetric channel with crossover p<0.5 and independent repetitions; no quantitative bound is supplied on which similarity metrics (Euclidean, cosine, margins) are preserved, to what factor, or under what key regime, making the error-reduction result unsupported in the manuscript.
  2. [Abstract] Abstract, first paragraph: the statement that key-dependent hashes 'naturally preserve most similarity properties' is load-bearing for both the native-AI compatibility and the repetition-code claim, yet the manuscript provides neither a formal definition of the hash class nor any preservation theorem or empirical measurement of effective p on hashed data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's insightful comments highlighting the need for more explicit justification of the core properties of HbHAI. We provide point-by-point responses below and will make revisions to incorporate additional formal and empirical support.

read point-by-point responses

  1. Referee: [Abstract] Abstract, second paragraph: the claim that repetition codes enable arbitrary reduction of validation error requires that HbHAI-processed inputs yield AI decision errors behaving as a binary symmetric channel with crossover p<0.5 and independent repetitions; no quantitative bound is supplied on which similarity metrics (Euclidean, cosine, margins) are preserved, to what factor, or under what key regime, making the error-reduction result unsupported in the manuscript.

    Authors: The repetition code result is predicated on the similarity preservation leading to decision errors that can be modeled as independent trials with p < 0.5. While the manuscript demonstrates the application, we acknowledge the lack of explicit bounds. In revision, we will add quantitative analysis including bounds on preserved similarity for key metrics and empirical validation of p under various conditions to support the claim. revision: yes

  2. Referee: [Abstract] Abstract, first paragraph: the statement that key-dependent hashes 'naturally preserve most similarity properties' is load-bearing for both the native-AI compatibility and the repetition-code claim, yet the manuscript provides neither a formal definition of the hash class nor any preservation theorem or empirical measurement of effective p on hashed data.

    Authors: The hash class and its properties are defined in the referenced prior works. This paper applies them to AI tasks. To make the manuscript self-contained, we will revise to include a formal definition of the hash class, a statement of the preservation theorem, and empirical measurements of the effective error rate p on hashed data. revision: yes

Circularity Check

1 steps flagged · score 8.0 of 10

Arbitrary validation error reduction claim reduces to self-cited HbHAI similarity-preservation assumption

  1. self citation load bearing [Abstract]
    "This paper presents new results and breakthrough obtained with the HbHAI techniques (Hash-based Homomorphic Artificial Intelligence) proposed in \cite{filiol0,sepp}. HbHAI is based on a novel class of key-dependent hash functions that naturally preserve most similarity properties, most AI algorithms rely on. It enables to analyse and process data in its cryptographically secure form while using existing native AI algorithms without modification..."

    The arbitrary reduction result via repetition codes presupposes that the hashed data yields AI decision errors behaving like a BSC with p < 0.5. This property is justified solely by self-citation to \cite{filiol0,sepp} (same authors) rather than by any derivation, bound, or experiment internal to the present paper.

full rationale

The paper's central result (arbitrary error reduction via repetition codes on AI decision tests) requires that HbHAI-processed data permits unmodified native AI algorithms to achieve per-trial error rate p < 0.5 with independent errors. This premise is asserted only by citing the authors' prior works for the 'key-dependent hash functions that naturally preserve most similarity properties.' No independent quantitative bounds, metric preservation proofs, or external verification appear in the provided text; the repetition-code step is standard but its applicability is imported wholesale from self-citation. This matches self_citation_load_bearing with no countervailing independent grounding.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Abstract-only review provides no details on free parameters, axioms, or invented entities beyond the high-level assumption about hash function properties; full paper required for complete ledger.

assumptions (1)
  • domain assumption Key-dependent hash functions preserve similarity properties for AI algorithms
    Invoked as the basis for HbHAI enabling unmodified AI processing on encrypted data.

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Cite this review

Pith. "Pith review of Arbitrary Reduction of Validation Error for AI Decision Tests using Homomorphic AI and Repetition Codes." pith.science (2026). https://pith.science/paper/3WZOSSH3

@misc{pith2026260628994,
  author       = {Pith},
  title        = {Pith review of: Arbitrary Reduction of Validation Error for AI Decision Tests using Homomorphic AI and Repetition Codes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3WZOSSH3}},
  note         = {Machine review of arXiv:2606.28994}
}
read the original abstract

This paper presents new results and breakthrough obtained with the HbHAI techniques (Hash-based Homomorphic Artificial Intelligence) proposed in \cite{filiol0,sepp}. HbHAI is based on a novel class of key-dependent hash functions that naturally preserve most similarity properties, most AI algorithms rely on. It enables to analyse and process data in its cryptographically secure form while using existing native AI algorithms without modification, with unprecedented performances compared to existing homomorphic encryption schemes and most notably compared to the same processing on corresponding plaintext data. Two major results have been obtained further. First we enable to reduce the compression rate up to a factor of 10 thus allowing to process massive datasets while reducing the computation time and the energy footprint in the same order. Second, we show how it is possible to arbitrarily reduce the final validation error of AI-based decision tests by using repetition error-correcting codes.

Figures

Figures reproduced from arXiv: 2606.28994 by the authors.

Figure 1
Figure 1. Illustrative description of HbHAI principle The interested reader can refer to [3] for a formalization of threat model (with respect to AI) we must consider and which security properties must be fulfilled. The use of hash functions (non-injective transformations) invalidates the con￾cept of decryption in HE. With HbHAI, a different approach has been defined. Only the owner of the data knows the correspondence betwee… view at source ↗

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

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    work page 2024

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    Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone (2007).Handbook of Applied Cryptography. CRC Press. Available at http://www.cacr.math.uwater loo.ca/hac/

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Reviewed June 30, 2026 · model on record in the stance chip above.