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arxiv: 2605.12935 · v1 · pith:TTFSYLQYnew · submitted 2026-05-13 · 💻 cs.DC

Communication Efficient Byzantine Agreement with Predictions

Muhammad Ayaz Dzulfikar , Seth Gilbert This is my paper

Pith reviewed 2026-06-30 21:51 UTC · model grok-4.3

classification 💻 cs.DC
keywords Byzantine agreementcommunication complexitypredictionsfault tolerancedistributed computingauthentication
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The pith

Byzantine agreement with classification predictions can reach agreement using Õ(n^{2.5}) communication unauthenticated or O(n²κ) with authentication.

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

The paper develops protocols for Byzantine agreement where each process starts with its own input and a set of unreliable predictions that label every other process as honest or faulty. It shows that previous approaches, which exchanged enough messages to roughly agree on the entire prediction matrix, were not optimal. Instead, the new algorithms keep the optimal number of rounds even when predictions contain arbitrarily many errors, yet reduce total communication to Õ(n^{2.5}) bits without authentication and to the information-theoretically optimal O(n²κ) bits when authentication is available.

Core claim

We present an unauthenticated algorithm that solves Byzantine agreement with classification predictions in Õ(n^{2.5}) communication and an authenticated algorithm that uses O(n²κ) communication; both achieve optimal round complexity for any number of prediction errors in the standard Byzantine model.

What carries the argument

Classification predictions that label each process as honest or faulty, used inside a communication-efficient protocol that avoids broadcasting the full prediction matrix.

If this is right

  • High communication is not required to tolerate many incorrect predictions.
  • Optimal communication is achievable once authentication is present.
  • Round complexity stays optimal regardless of how many predictions are wrong.
  • The results apply directly to the standard unauthenticated and authenticated Byzantine settings.

Where Pith is reading between the lines

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

  • The same prediction labels could be reused across multiple agreement instances to amortize cost further.
  • The techniques may apply to other prediction-assisted primitives such as reliable broadcast or leader election.
  • If prediction accuracy can be bounded, even lower communication might be possible, though the paper does not assume any accuracy.

Load-bearing premise

The model allows arbitrary errors in the classification predictions and uses only the standard unauthenticated or authenticated Byzantine communication and fault assumptions.

What would settle it

A proof that any correct algorithm for Byzantine agreement with classification predictions requires ω(n^{2.5}) communication in the unauthenticated setting would falsify the main claim.

read the original abstract

In Byzantine agreement with predictions each process begins with an input value and some (unreliable) prediction bits. Recently, it has been shown that with \emph{classification predictions} -- where the predictions predict each process to be honest or faulty -- Byzantine agreement can be completed more quickly than without predictions, circumventing the traditional $\Omega(f)$ round lower bound. However, existing algorithms either handle limited prediction errors or send too many messages. Moreover, they all exchange $\Omega(n^3)$ bits -- enough to allow the processes to approximately agree on the classifications. In fact, it almost seemed necessary to share a significant number of prediction bits if one wanted to tolerate a high number of incorrect predictions. In this paper, we show that this high level of communication (and sharing of predictions) is not inherent by developing an unauthenticated algorithm with $\tilde{O}(n^{2.5})$ communication complexity. Furthermore, with authentication, we give an algorithm with optimal $O(n^2\kappa)$ communication complexity (where $\kappa$ is a security parameter). All of our results have optimal round complexity for any number of errors in the predictions.

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

0 major / 3 minor

Summary. The manuscript presents algorithms for Byzantine agreement (BA) using classification predictions, where each process is predicted as honest or faulty, with arbitrary errors allowed. It claims an unauthenticated algorithm achieving ilde{O}(n^{2.5}) communication complexity and an authenticated algorithm with O(n^2 \kappa) communication (\kappa security parameter), both with optimal round complexity independent of the number of prediction errors. This is positioned as an improvement over prior work requiring \Omega(n^3) communication by showing that extensive prediction sharing is not necessary.

Significance. If the results hold, this work is significant for distributed computing as it reduces communication from cubic to sub-cubic/quadratic while preserving optimal rounds and tolerating arbitrary prediction errors in the standard Byzantine model. The explicit demonstration that high communication for prediction sharing is not inherent strengthens the case for using unreliable oracles in practice without hidden distribution assumptions on predictions.

minor comments (3)
  1. Abstract: the ilde{O} notation should be defined explicitly (e.g., hiding polylog(n) factors) to allow precise comparison with the ilde{\Omega}(n^3) lower bound referenced from prior work.
  2. Abstract: the optimal round complexity is stated but not quantified (e.g., O(1) or O(log n)); a brief parenthetical would clarify the claim without lengthening the abstract.
  3. The manuscript should include a short table or paragraph contrasting the new bounds with the prior ilde{\Omega}(n^3) results cited, including the exact round complexities achieved in each case.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and the recommendation of minor revision. The report provides no specific major comments to address.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents algorithmic constructions for Byzantine agreement under classification predictions in the standard unauthenticated/authenticated models. The abstract and description claim new communication bounds ( ilde{O}(n^{2.5}) and O(n^2 \kappa)) with optimal rounds for arbitrary prediction errors, but no equations, derivations, fitted parameters, or self-citations are visible that reduce any result to its own inputs by construction. The central claims rest on explicit algorithm design rather than self-referential definitions or renamings, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no free parameters, invented entities, or non-standard axioms are described. The work relies on the standard Byzantine fault model and classification prediction model.

axioms (1)
  • domain assumption Standard Byzantine agreement model with up to f faulty processes and unreliable classification predictions
    Invoked implicitly as the setting for the new algorithms.

pith-pipeline@v0.9.1-grok · 5723 in / 1177 out tokens · 25893 ms · 2026-06-30T21:51:14.315188+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

6 extracted references

  1. [1]

    R., Goodson, G

    [1]Abd-El-Malek, M., Ganger, G. R., Goodson, G. R., Reiter, M. K., and Wylie, J. J.Fault-Scalable Byzantine Fault-Tolerant Services. InProceedings of the 20th ACM Symposium on Operating Systems Principles 2005, SOSP 2005, Brighton, UK, October 23-26, 2005(2005), ACM, pp. 59–74. [2]Azar, Y., Panigrahi, D., and Touitou, N.Online Graph Algorithms with Predic...

    2005

  2. [2]

    InProceedings of the Third Symposium on Operating Systems Design and Implementation(USA, 1999), OSDI ’99, USENIX Association, p

    [7]Castro, M., and Liskov, B.Practical Byzantine fault tolerance. InProceedings of the Third Symposium on Operating Systems Design and Implementation(USA, 1999), OSDI ’99, USENIX Association, p. 173–186. [8]Chandra, T. D., Hadzilacos, V., and Toueg, S.The weakest failure detector for solving consensus.J. ACM 43, 4 (1996), 685–722. [9]Chandra, T. D., and T...

    1999

  3. [3]

    27 [12]Civit, P., Dzulfikar, M. A., Gilbert, S., Gramoli, V., Guerraoui, R., Komatovic, J., and Vidigueira, M.Byzantine consensus is Θ(n 2): the Dolev-Reischuk bound is tight even in partial synchrony!Distributed Computing 37, 2 (Jun 2024), 89–119. [13]Civit, P., Dzulfikar, M. A., Gilbert, S., Guerraoui, R., Komatovic, J., and Vidigueira, M.DARE to Agree:...

    2024

  4. [4]

    Accessed: 2026-02-05

    [21]Darktrace.https://darktrace.com. Accessed: 2026-02-05. [22]Dolev, D., and Reischuk, R.Bounds on information exchange for Byzantine agreement. Journal of the ACM (JACM) 32, 1 (1985), 191–204. [23]Dolev, D., Reischuk, R., and Strong, H. R.Early stopping in Byzantine agreement.J. ACM 37, 4 (1990), 720–741. [24]Dolev, D., and Strong, H. R.Authenticated Al...

    2026

  5. [5]

    ACM 65, 7 (June 2022), 33–35

    [34]Mitzenmacher, M., and V assilvitskii, S.Algorithms with predictions.Commun. ACM 65, 7 (June 2022), 33–35. [35]Momose, A., and Ren, L.Optimal Communication Complexity of Authenticated Byzan- tine Agreement. In35th International Symposium on Distributed Computing (DISC

    2022

  6. [6]

    209 ofLeibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl – Leibniz-Zentrum f¨ ur Informatik, pp

    (2021), vol. 209 ofLeibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl – Leibniz-Zentrum f¨ ur Informatik, pp. 32:1–32:16. [36]Pease, M. C., Shostak, R. E., and Lamport, L.Reaching agreement in the presence of faults.J. ACM 27, 2 (1980), 228–234. [37]Purohit, M., Svitkina, Z., and Kumar, R.Improving online algorithms via ml predic-...

    2021