SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work

Mustafa Doger; Sennur Ulukus; Weihang Cao

REVIEW 4 major objections 4 minor 43 references

SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read SEDULity replaces the PoW nonce with a machine-learning training step, and claims anyone can verify a block by re-running that step.

desk verdict A coherent PoL protocol design whose central verification mechanism quietly assumes away the one thing that makes it impossible – bit-exact SGD reproducibility. read the letter →

arxiv 2512.13666 v2 pith:K2ENGOV4 submitted 2025-12-15 cs.CR cs.DCcs.ITcs.LGmath.IT

Weihang Cao , Mustafa Doger , Sennur Ulukus This is my paper · ORCID

classification cs.CRcs.DCcs.ITcs.LGmath.IT

keywords blockchainconsensusmechanismproofofusefulworkproof-of-learningmachinelearningtrainingstochasticgradientdescentincentiveprobabilisticverification

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

This paper proposes SEDULity, a blockchain consensus that replaces the Proof-of-Work puzzle with a machine-learning training step. The central claim is that the same computation that advances an ML model can also decide who gets to append a block: a prover trains a stage of an assigned task, hashes the resulting weights together with the previous block hash, and if the hash falls below a threshold the block is valid. Because the training seed is derived from the block being built, each miner works on a different task and no solution can be stolen or reused. The framework is designed so that any node can verify a block by re-running the training stage, no committee is trusted for block validity, and a probabilistic verification plus penalty mechanism makes honest training the rational strategy. If correct, this would let blockchain infrastructure produce trained models as a by-product rather than burning energy on useless hashes.

What carries the argument

The central object is the useful work function f_U defined in equation (10), which wraps a τ-epoch SGD training step inside two hash evaluations: f_U = f_H(f_H(f_M^τ(W_{s-1}, σ_{φ_s}(D_tr))), f_H(B_{h-1})). The stage training f_M^τ is the hard-to-compute useful work; the hash-to-threshold check f_U < T_p is the easy-to-verify PoW-style condition. The seed φ_s = g(f_H(B_h), s) derived from the template block is what makes each miner's task unique and prevents model theft/reuse. Verifiability is carried by the equality check f_H(f_M^τ(W_{s-1}, σ_{φ_s}(D_tr))) = f_H(W_s), which any node can perform by re-running the training stage. The capture-the-flag flags embedded in the seed give verifiers

What would settle it

Run the same stochastic-gradient-descent stage twice on two different GPUs (or with different low-level library settings) and hash the resulting weights: if the hashes differ, the protocol's universal verification equation f_H(f_M^τ(W_{s-1}, σ_φ(D_tr))) = f_H(W_s) would reject an honestly trained block. This experiment can settle whether 'noise-resistant training reproduction' holds on commodity hardware.

Watch

Extended reading notes

Core claim

The paper's central discovery is a useful function f_U = f_H(f_H(f_M^τ(W_{s-1}, σ_{φ_s}(D_tr))), f_H(B_{h-1})) that substitutes for the PoW condition f_H(B_h) < T. In words: before a block is valid, the prover must train τ epochs of a machine-learning stage starting from previous weights and a shuffled dataset, then show that the hash of the new weights concatenated with the previous block hash is below the difficulty threshold T_p. The random seed for the epoch shuffle is derived from the template block, so the block content and the training computation are bound together; the prover cannot reuse a trained checkpoint at a different height, and an adversary who tampers with the ledger invali

Load-bearing premise

The whole scheme rests on the assumption that the same training step run twice produces exactly the same numbers; if hardware or library noise makes two honest miners compute slightly different model weights, their hashes will disagree and valid blocks will be rejected. The paper admits exact reproduction is currently impossible and simply assumes 'noise-resistant training reproduction'.

Editorial extensions

If this is right

If SEDULity works as claimed, blockchain consensus can produce trained machine-learning models rather than only consuming electricity, so mining power becomes reusable for downstream ML tasks.
A fork attack or history rewrite requires controlling a majority of total training power, the same security threshold as PoW, because every miner's training work contributes to consensus security.
Model theft and checkpoint reuse are prevented without trusted hardware or a trusted platform, because the training seed is derived from the block hash and stage index.
A small number of verified stages per task (α = O(1)) plus a modest penalty-to-reward ratio suffices to make full honesty the profit-maximizing strategy, per the paper's Theorem 1.
The same block-derived-randomness trick extends to other useful computations that can be made order-dependent, such as matrix multiplication, provided the computation cost outweighs the communication cost.

Reading between the lines

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

If the bit-reproducibility barrier is solved, this design could be adapted to train a single shared model across the network by making each block's training task a continuation of the previous block's weights; the paper instead assigns each miner a fresh task.
The same block-derived-seed trick could be applied to other iterative computations with order-dependent intermediates, such as graph traversal or numerical solvers; whether the result remains genuinely 'useful' would need a concrete downstream use.
The simulated 86.8% useful-work ratio at p = 0.00005 is a testable target: a real deployment could measure actual energy spent on productive training versus verification and redundant training, and compare against that parameter point.
Because block validity is independent of task quality, a gap remains between 'the claimed epochs were trained' and 'the resulting model is useful'; closing that gap may require a performance or data-quality check on the final weights, which the paper leaves implicit.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a real protocol proposal, not a rehash, but it has a load-bearing hole at the center. The authors build a non-competitive proof-of-learning framework where each miner trains a staged ML task, gets a block-generation opportunity per stage from a block-dependent seed, and anyone can verify a block by re-running the stage and hashing the weights. The combination is genuinely different from [27] and [39]: it avoids redundant competition, keeps verification non-interactive, and extends naturally to matrix multiplication. I'll give credit where it's due — the design is thoughtful and the incentive analysis (Section 7) is a clean derivation from the [27] lemma, even if the lemma itself is imported.

The problem is the equality check. Block verification and task verification both reduce to fH(fM^τ(W_{s−1}, σ_φ_s(D_tr))) = fH(W_s). That requires every honest miner to produce bit-identical weights from the same W_{s−1}, seed, and data. The paper's own footnote 1 says exact reproduction is impossible because of low-level noise in libraries and hardware, then simply assumes 'noise-resistant training reproduction' without proposing any mechanism. A single floating-point rounding difference changes the hash completely. So the protocol as written cannot reach consensus: honest blocks get rejected, and miners can't agree on what a valid block is. This isn't a detail; it breaks completeness and soundness, the two properties the paper sets up in Section 2. The MatMul extension avoids this because integer arithmetic is deterministic, but the core ML contribution is what needs to work.

The other soft spots are secondary. The claim that rewriting history requires more than half of total computing power is asserted, not proved. The simulations in Section 8 don't train a single model — they simulate BGOs with coin tosses and assume an ML stage takes a fixed time. So they provide no evidence for the reproducibility assumption or for the real training workload. The incentive theorem is reasonable within its model, but it inherits the verification problem: detecting a dishonest stage requires the same bit-exact re-run.

Who is this for? Anyone working on PoUW/PoL will want to know this design exists, especially the per-miner task assignment and the CTF tweak. But the paper is not usable as a consensus mechanism as written. I'd send it to a serious referee — the idea deserves engagement, and a good referee could push the authors toward a real noise-handling mechanism or reposition the contribution as a design study. I wouldn't cite it as a working system.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes SEDULity, a Proof-of-Learning (PoL) consensus framework in which each miner is assigned a distinct ML training task and receives a block generation opportunity (BGO) after every τ training epochs. Block validity is governed by the useful function f_U = fH(fH(fM^τ(W_{s-1}, σ_φ_s(D_tr))), fH(B_{h-1})) < T_p, and block verification consists of re-running the corresponding training stage and comparing hashes. Task verification is delegated to a randomly appointed committee of verifiers, who use probabilistic verification; a capture-the-flag (CTF) protocol is added to incentivize honest verification. The authors claim that the framework is fully distributed, secure, efficient in terms of useful work, and that rational miners are incentivized to train honestly via a sufficient penalty condition. The paper also sketches an extension to matrix multiplication and presents MATLAB simulations of system dynamics.

Significance. The high-level idea is timely and potentially valuable: replacing competition-based PoL with per-stage block generation opportunities on distinct tasks would address redundant training and winner-take-all security issues in earlier PoL designs. Encoding block data into the training seed is a natural way to bind proofs to the chain and prevent model theft. The formal incentive condition (Theorem 1) and the useful-work metrics (UBGR, UWR) are useful contributions if the framework is sound. However, the central block- and task-verification mechanism depends on bit-exact reproducibility of stochastic gradient descent, which the paper's own footnote (Section 3.2, Footnote 1) concedes is currently impossible and then simply assumes away without a mechanism. Because this assumption is load-bearing, the main claim of a distributed, secure, and efficient PoL framework is not currently supported.

major comments (4)

[Section 3.2 (Footnote 1) and Sections 4.3, 4.4] The verification of both blocks and task proofs reduces to the equality fH(fM^τ(W_{s-1}, σ_φ_s(D_tr))) = fH(W_s). This requires every honest miner's SGD execution to produce bit-identical weights from the same W_{s-1}, shuffled data, and seed. Section 3.2, Footnote 1 states that exact reproduction is impossible due to low-level library/hardware noise, citing [38], and simply "assumes noise-resistant training reproduction" without specifying any mechanism. Because a cryptographic hash has an avalanche effect, any floating-point or non-deterministic GPU difference changes the hash completely, so honest miners on different hardware/software stacks would produce different fH(W_s). This breaks both completeness (valid blocks rejected) and soundness (miners cannot agree on a valid block). This is not a minor implementation detail: it invalidates the core consensus mechanism as written. The sim
[Section 5.1, last paragraph] The unstated security theorem of the paper is that "rewriting the history requires more than half of the total computational power." This is asserted without proof or a formal adversary model. In PoW, the statement follows from the independence of hash trials and a well-defined chain-growth process. Here, block generation opportunities are tied to ML training stages of arbitrary tasks: the probability of producing a block depends on task assignment, download times, stage duration τ, and the computational cost of fM, and these are not interchangeable with hash invocations. No theorem for chain growth, common prefix, liveness, or fork resolution is provided. The paper needs a formal security analysis of the longest-chain protocol under this new block generation process before the central security claim can be accepted.
[Section 7, Theorem 1 and Lemma 1] The incentive-security result relies entirely on Lemma 1 imported from [27], which bounds the probability q(ρ) of a dishonest prover passing verification by (1−κ+κρ)^α. The manuscript does not verify that the assumptions of this lemma hold in the SEDULity protocol, where (i) some stages are publicly verified by all miners because they generated blocks, (ii) the CTF protocol changes the verifier's strategy to a two-attempt flag-search procedure, and (iii) verification is performed by a committee of gv verifiers rather than a single verifier. The statement after Eq. (42) that committee verification is "similar to just increasing α to gvα" is a heuristic, not a proof. Without a formal justification, the claim that rational miners are incentivized to train fully honestly is not established.
[Section 8] The simulations do not train any ML model and do not execute the hash-based verification of Eq. (9). Block generation opportunities are "realized by coin tosses with success probability p" (Section 8), which models the lottery aspect but omits the actual useful function f_U, the training reproducibility assumption, and the cost of re-running fM^τ for verification. Consequently, the reported UBGR/UWR values and fork rates are derived from assumed timing parameters rather than from measurements of the proposed consensus mechanism. The simulations therefore cannot validate the feasibility of the central block/task verification procedure, nor can they compensate for the lack of a reproducibility mechanism.

minor comments (4)

[Section 3.2, Footnote 1] Typo: "noise-resistant training reproduction is this paper" should read "in this paper."
[Section 5.2] The phrase "if we were to give a single opportunity for each task (τ = S)" appears to be a notational slip: with a single stage, τ should be the total number of training epochs E, not the number of stages S.
[Table 1] The last row, "Ours", reads "Above limitations are overcome and decentralized"; this should be rephrased grammatically, e.g., "Overcomes the above limitations and is decentralized."
[General] Several references are to arXiv preprints (e.g., [27], [38]) that have since appeared at peer-reviewed venues; the authors may want to cite the published versions.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the incentive theorem imports an external lemma, and the main weakness is an admitted reproducibility assumption rather than a circular derivation.

full rationale

The derivation chain is not circular in the sense defined here. The core useful function f_U = fH(fH(f^τ_M(W_{s-1}, σ_φs(D_tr))), fH(B_{h-1})) is the protocol's definition (Section 4.3, Eq. 10), not a prediction obtained from fitted parameters; block validity is defined by fU < Tp and by the equality check fH(f^τ_M(...)) = fH(W_s). No fitted constant is later relabeled as an output. The incentive theorem (Section 7, Theorem 1) imports Lemma 1 from [27] (Zhao et al.), an external reference, and derives the sufficient penalty condition γ ≥ (1−κ)^α/(1−(1−κ)^α) algebraically from the honest-condition definition; it does not assume the desired conclusion. The only author self-citation is [15] in the related-work discussion (the importance of preventing solution theft), which is contextual and not load-bearing for the framework's security or incentive claims. The paper does contain an explicitly admitted load-bearing assumption in Footnote 1 (Section 3.2): exact SGD reproduction is impossible per [38], and the paper 'assumes noise-resistant training reproduction' without specifying a mechanism. This is a real completeness/soundness gap and a correctness risk, but it is not a circular reduction: the verification equality is conditional on an unproven assumption rather than being equivalent to its own output by construction. The simulations are parameter sweeps (p, α, γ) of a hand-built MATLAB model, not predictions forced by a fitted input. Overall circularity burden is low: one minor self-citation, no definitional or fitted-input circularity.

Assumptions & free parameters 8 free parameters · 7 assumptions · 2 invented entities

The central protocol rests on standard crypto assumptions, a deterministic-training assumption that the paper's own footnote acknowledges is contradicted by [38], and a set of simulation parameters chosen by hand. No code or data are shipped.

free parameters (8)

Block win probability p = 1e-4 baseline; 5e-5 gives peak UWR in Fig. 3
Sets difficulty of the useful-work puzzle; hand-tuned in simulation, not derived from a security analysis.
Stage length τ = 4 epochs
Chosen to balance foregone BGOs, storage of intermediate weights, and fork rate; no optimization procedure given.
Number of verified stages α = 10 in baseline; 1,2,5,10 in Fig. 4
Together with γ it satisfies the honest condition in Theorem 1; chosen to make dishonest passing probability small.
Penalty-to-task-reward ratio γ = 0, 0.05, 0.1 in Fig. 4
Incentive parameter; Fig. 4 shows γ=0.05 with α=1 suffices assuming CTF detection probability κ=1/2.
Task length E = 4000 epochs (jittered 0.9E-1.1E)
Simulated average number of training epochs per task; arbitrary.
Group size g and verifier count gv = g=25, gv=5
Defines committee size; arbitrary but affects assignment overhead and verification load.
Latency cost model = 8 epochs download, 4 epochs weight transfer, 2-4 stages block verification
Arbitrary staging assumptions inserted into the simulator; no measured network profile.
CTF flag ratio ξ = not specified
Probability that flags 1/2 are used in CTF; needed to compute detection probability but no concrete value is given in simulations.

assumptions (7)

standard math Hash functions are uniformly random, preimage-resistant, and avalanche-like (Section 3.1).
Used to turn training output into a lottery and to bind identities/ledgers; standard cryptographic assumption.
ad hoc to paper ML training is deterministic: Ws is a unique function of Ws-1 and shuffled data (Eq. 3), and bit-exact reproduction across provers/verifiers is assumed (Footnote 1).
This is the load-bearing reproducibility assumption; the paper cites [38] showing exact reproduction is impossible and provides no mechanism.
domain assumption Longest-chain rule with first-seen tie-breaking yields eventual consensus (Section 3.1).
Standard but unproved here in the presence of non-negligible verification delays.
domain assumption All miners have equal computing power; adversaries are unions of honest-size miners (Section 3.1).
Used to argue security proportional to total power.
domain assumption All miners interrupt useful training to verify every block (Section 5.2).
Required for Nakamoto-style validation; paper models this as 2-4 stages of latency.
standard math The upper bound q(ρ) ≤ (1-κ+κρ)^α from [27, Appendix E.3] is valid for this protocol (Lemma 1).
External lemma imported for Theorem 1; no independent proof in this paper.
domain assumption Verifiers are rational but not colluding; CTF flags force honest verification with extra reward (Section 6).
Incentive analysis assumes individual rationality; collusion between prover and verifier is not modeled.

invented entities (2)

Noise-resistant training reproduction
purpose: Makes SGD checkpoints bit-exact across heterogeneous hardware so hashes can be re-verified
Postulated in footnote 1; no implementation or reference is given, and [38] argues exact reproducibility is currently impossible.
CTF random flags ω_s
purpose: Randomize the per-stage seed so verifiers must recompute a stage to report the correct flag
Internal protocol construct; no falsifiable external prediction. Its security depends on verifiers not colluding.

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Cite this review

Pith. "Pith review of SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work." pith.science (2026). https://pith.science/paper/K2ENGOV4

@misc{pith2026251213666,
  author       = {Pith},
  title        = {Pith review of: SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K2ENGOV4}},
  note         = {Machine review of arXiv:2512.13666}
}

read the original abstract

The security and decentralization of Proof-of-Work (PoW) have been well-tested in existing blockchain systems. However, its tremendous energy waste has raised concerns about sustainability. Proof-of-Useful-Work (PoUW) aims to redirect the meaningless computation to meaningful tasks such as solving machine learning (ML) problems, giving rise to the branch of Proof-of-Learning (PoL). While previous studies have proposed various PoLs, they all, to some degree, suffer from security, decentralization, or efficiency issues. In this paper, we propose a PoL framework that trains ML models efficiently while maintaining blockchain security in a fully distributed manner. We name the framework SEDULity, which stands for a Secure, Efficient, Distributed, and Useful Learning-based blockchain system. Specifically, we encode the template block into the training process and design a useful function that is difficult to solve but relatively easy to verify, as a substitute for the PoW puzzle. We show that our framework is distributed, secure, and efficiently trains ML models. We further demonstrate that the proposed PoL framework can be extended to other types of useful work and design an incentive mechanism to incentivize task verification. We show theoretically that a rational miner is incentivized to train fully honestly with well-designed system parameters. Finally, we present simulation results to demonstrate the performance of our framework and validate our analysis.

Figures

Figures reproduced from arXiv: 2512.13666 by the authors.

**Figure 3.** Useful block generation ratio, useful work ratio and [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Average reward rate under different honest training [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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