Nesterov Method for Asynchronous Pipeline Parallel Optimization

Alexander Long; Gil Avraham; Sameera Ramasinghe; Thalaiyasingam Ajanthan; Yan Zuo

REVIEW 3 major objections 5 minor 15 references

Nesterov Method for Asynchronous Pipeline Parallel Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A discounted-gradient Nesterov update corrects stale gradients in asynchronous pipeline training and beats the synchronous baseline.

desk verdict A neat delay-correction idea with a solid ablation, but the headline empirical claim is confounded by optimizer choice and the theorem as written gives O(log t/t), not O(1/t). read the letter →

arxiv 2505.01099 v1 pith:2N5EE55G submitted 2025-05-02 cs.LG cs.DC

Thalaiyasingam Ajanthan , Sameera Ramasinghe , Yan Zuo , Gil Avraham , Alexander Long This is my paper · ORCID

classification cs.LGcs.DC MSC 68T0790C25

keywords asynchronousoptimizationpipelineparallelismNesterovacceleratedgradientstalenessdelaycorrectionlanguagemodelingNAdamconvex

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

Pipeline parallelism splits a large model across devices, and asynchronous updates would keep every device busy; the obstacle is stale gradients. The paper argues that a small variant of Nesterov Accelerated Gradient, which discounts the gradient by $(1-\gamma_t)$ in the look-ahead update, makes the momentum step itself compensate for that staleness. It proves a sublinear $O(1/t)$ convergence rate for convex smooth objectives with fixed delay, and shows experimentally that the same update, used through NAdam with $\beta_1=0.99$, reaches lower perplexity than synchronous GPipe on decoder-only language models up to 1B parameters. If true, asynchronous pipeline training can deliver full device utilization without sacrificing optimization quality, using no new hyperparameters.

What carries the argument

The load-bearing object is the modified NAG iteration with a discounted gradient. Writing $d_t=\gamma_t(w_t-w_{t-1})$ and $w_{t+1}=w_t+d_t-\eta(1-\gamma_t)\nabla f(\bar{w}_t+\bar{d}_t)$, the $(1-\gamma_t)$ factor is what makes the proof work: it lets the delay $\Delta_t$ be expanded as a sum of previous look-aheads with vanishing gradient contributions, giving $\cos(\Delta_t,\bar{d}_t)\to 1$ and $\|\Delta_t\|=O(1/t)$. That alignment is then fed into the standard NAG proof template, yielding the $O(1/t)$ theorem. In the implementation the same discount appears in NAdam, so the practical mechanism is an existing optimizer with momentum coefficient warmed up to $\beta_1=0.99$; the paper does not add a new hyperparameter.

What would settle it

Run the same decoder-only model synchronously with NAdam and $\beta_1=0.99$ under identical data, schedule, and iteration count. If synchronous NAdam matches or beats the asynchronous method's WikiText perplexity of 27.72, the claimed advantage of asynchronous delay correction over synchronous training is not supported. A second check: reduce $\beta_1$ toward 0.9 and observe whether perplexity rises and the measured $\cos(d_t,\Delta_t)$ falls, as the alignment mechanism predicts.

Watch

Extended reading notes

Core claim

The core discovery is that the Nesterov look-ahead step can be repurposed as a gradient-staleness corrector for asynchronous pipeline training. With the modified update $d_t=\gamma_t(w_t-w_{t-1})$ and $w_{t+1}=w_t+d_t-\eta(1-\gamma_t)\nabla f(\bar{w}_t+\bar{d}_t)$, where $\bar{w}_t=w_{t-\tau}$ and $\bar{d}_t=d_{t-\tau}$ are the delayed weight and look-ahead, the discount factor $(1-\gamma_t)$ makes the trajectory smooth enough that the delay $\Delta_t=w_t-w_{t-\tau}$ becomes aligned with the delayed look-ahead: $\cos(\Delta_t,\bar{d}_t)\to 1$ as $\gamma_t\to 1$. The paper proves that for convex, $\beta$-smooth objectives with bounded gradients and fixed delay, the iterates converge at $O(1/t)$; this is the same order as plain gradient descent rather than the accelerated $O(1/t^2)$, but it is obtained despite stale gradients. Empirically, the same discount is already present in NAdam, so the proposed method is literally 'use NAdam with $\beta_1=0.99$'; on WikiText, BookCorpus, and OpenWebText it reports lower validation perplexity than GPipe, PipeDream, PipeMare, and several forecasting-based delay corrections, including at 1B parameter scale.

Load-bearing premise

The empirical claim of surpassing the synchronous baseline assumes the comparison is fair, but the synchronous GPipe baseline uses AdamW and the proposed method uses NAdam, with no synchronous NAdam run reported; the gains in Table 1 could in principle come from the optimizer switch rather than from delay correction.

Editorial extensions

If this is right

Asynchronous pipeline training can keep full device utilization without a convergence penalty on the problems studied, because the delay is corrected in weight space rather than by predicting gradients.
Switching an asynchronous pipeline-parallel training loop to NAdam with $\beta_1=0.99$ is a drop-in delay-correction method; no extra hyperparameters, schedules, or forecasting machinery are required.
Under the paper's assumptions the method converges at $O(1/t)$ with fixed delay, so stale gradients need not push asynchronous training below the rate of plain gradient descent.
The no-weight-stash variant is competitive with synchronous GPipe on two of three datasets, suggesting the memory cost of stashed weights is not essential to the main gain.
The Nesterov step also improves other delay-correction methods when combined with them, indicating the mechanism is complementary to forecasting approaches.

Reading between the lines

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

A testable extension is to run AdamW with $\beta_1=0.99$ asynchronously; if it closes much of the gap, the benefit may be attributable to high momentum generally rather than to Nesterov's specific look-ahead.
The proof's $O(1/t)$ rate is likely not tight; a sharper analysis with stage-dependent delays could predict which pipeline depths the method tolerates before the logarithmic constant dominates.
The decentralized experiments rely on stage-dependent learning rates and momentum coefficients, so the 'no modification' claim applies most directly to the co-located setting; the decentralized gain is achieved with additional adaptations.
The reported comparisons are single training trajectories; multi-seed runs would reveal whether the 1-3 perplexity-point margin over GPipe is stable or within run-to-run variation.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Colleague,

This paper is worth a look, but the pitch oversells it. The core idea — reuse NAdam's momentum discount (1-beta1) as a delay-correction term in async pipeline parallelism — is genuinely neat, and the paper does more empirical work than most async-PP papers: three datasets, a 1B-parameter run, SWARM, ablations, and a weight-discrepancy metric. The ablation in Fig. 7, showing that removing the discount breaks training, is a clean demonstration that the mechanism does something. That is real evidence.

But two load-bearing problems stop me from believing the main claims.

First, the theory. Theorem 1 says O(1/t), but the appendix's Eq. (33) sums Omega_k = O(log t), giving an O(log t / t) rate. That is not the same thing. The authors may have a fix — the induction base for t <= tau is hand-waved as a "warmup phase," which is not a proof — but as written the theorem is wrong. This is a correctable error, but it needs to be stated honestly.

Second, the empirical headline. The synchronous GPipe baseline uses AdamW with beta1=0.9; the proposed method uses NAdam with beta1=0.99. Their own ablation (Fig. 6) shows beta1 has a large effect. So Table 1's gap (27.72 vs 30.63) could be entirely an optimizer effect, not delay correction. No synchronous NAdam run is reported. That makes the "even surpassing the synchronous baseline" claim unsupported. It is a fixable experiment — add a synchronous NAdam arm with beta1=0.99 — but without it the central novelty claim collapses.

Smaller quibbles: calling beta1=0.99 "no hyperparameters" is misleading, and the code link without a commit hash is thin. The theory also uses gamma_t=(t-2)/t, which is not what the experiments run, so the theory does not actually cover the evaluated algorithm.

Who is this for? People who care about pipeline-parallel optimization and distributed training. The delay-correction idea is plausible and the empirical foundation is broader than most. But the inference from the current experiments is shaky, and the theory needs a correction.

My recommendation: send it to peer review, but flag for major revision. The synchronous-NAdam control and a corrected theorem are mandatory. If those are addressed, this could be a solid systems-ML paper. If not, the claims are not supportable.

Referee Report

3 major / 5 minor

Summary. The paper proposes a modified Nesterov Accelerated Gradient update for asynchronous pipeline-parallel training. In Eq. (10), gradients are computed at a delayed extrapolated point and discounted by (1−γ_t); the authors argue that the look-ahead step aligns with the weight-space delay as γ_t→1 (Proposition 1) and prove a sublinear convergence rate for convex, β-smooth functions with fixed delay (Theorem 1, Appendix A.3). The method is instantiated in practice by switching to NAdam with β1=0.99, and experiments on decoder-only language models up to 1B parameters report perplexity improvements over PipeDream, PipeMare, and the synchronous GPipe baseline, including a SWARM deployment.

Significance. If the claims are established, the contribution is practically attractive: a change of optimizer hyperparameters that makes asynchronous pipeline training competitive with or better than synchronous training at 1B scale, backed by a convergence theorem and a memory-efficient variant. Strengths of the paper include the simple fixed-delay analysis, the large-scale decoder-only experiments, the breadth of baselines and ablations, and the released code. However, the headline empirical claim is currently confounded by the optimizer mismatch with the synchronous baseline, and the stated convergence rate is not what the appendix proof delivers. With those issues fixed, the paper would be a solid incremental contribution to asynchronous pipeline optimization, but the central claims as written are not yet supported.

major comments (3)

[§5.1, Table 1, Figs. 2–3] The comparison does not isolate the effect of delay correction: the synchronous GPipe baseline is trained with AdamW (default β1=0.9) while the proposed method uses NAdam with β1=0.99, and no synchronous NAdam run is reported. The paper's own ablation in Fig. 6 shows that increasing β1 from 0.9 to 0.99 materially changes training loss, so the perplexity gap in Table 1 (27.72 vs 30.63) could be an optimizer effect rather than an effect of asynchronous delay correction. The authors should add a synchronous NAdam baseline with β1=0.99, including the same learning-rate tuning procedure, and report the resulting perplexity; without such a control, the abstract's claim of 'even surpassing the synchronous baseline' is not supported.
[Appendix A.3, Eq. (33); Theorem 1] The theorem states a rate of O(1/t), but the proof bounds δ_{t+1} by (1/t)∑_{k=1}^t Ω_k plus initialization terms, and Eq. (33) shows ∑_{k=1}^t Ω_k = O(log t). The resulting bound is therefore O(log t/t), not O(1/t). The theorem statement and the proof summary in §3.1 need to be corrected to match the actual bound, or the proof must be strengthened. Additionally, the key estimate ‖w_{t+1} − w_t‖ = O(1/t) is proved by induction only after the base case t ≤ τ is 'enforced using an appropriate warmup phase'; the warmup is never specified or analyzed, so the bound on ‖̄Δ_t‖, and hence the final rate, is not established from the stated assumptions alone.
[§3.1 and §5.1] There is a mismatch between the theoretical object and the empirical method. The theorem analyzes the deterministic update (10) with γ_t = (t−2)/t, γ_1 = 0, and η = 1/β, whereas the experiments run NAdam with a constant β1 = 0.99, adaptive second moments, decoupled weight decay, a cosine learning-rate schedule, and stochastic gradients. The text in §3.1 even states that the momentum coefficient is 'usually chosen to be a constant close to 1,' which is not the schedule used in the proof. The paper should either provide a convergence analysis for the constant-momentum NAdam-style update actually used, or explicitly reposition Theorem 1 as a motivating analysis for the idealized deterministic setting and add experiments that also test the theoretical γ_t schedule.

minor comments (5)

[§3.2, Eq. (13)] Equation (13) is not typeset unambiguously: the stage index in τ and the exponent of ρ_t are unclear, and the learning-rate discounting rule should be written with explicit subscripts and superscripts (e.g., η_t^i = η τ_i^{ρ_t} or the intended negative exponent) so that it is reproducible.
[§5.5, Fig. 5] The text says that for GPipe 'the training time increase is exponentially larger,' but the reported numbers are 8.5× versus 2.5× for the proposed method. This is a large factor difference but not an exponential one; please rephrase as 'substantially larger' or provide evidence for superpolynomial growth.
[Abstract and §6] The abstract says a 1B model is trained 'to convergence,' while the experiments run a fixed 50k iterations and report perplexity at that point. The phrase should be softened to avoid implying a separate convergence criterion was reached.
[Appendix A.3, Eq. (29)] The schedule γ_t = (t−2)/t gives γ_1 = −1, which contradicts the earlier statement γ_1 = 0. Please specify that the formula applies for t ≥ 2 and state γ_1 separately.
[§3.1 and §4] The claim that this is 'the first time a variant of the Nesterov method is shown to converge in the presence of delayed gradients' is too strong without a more careful positioning against existing delayed-momentum analyses such as Hakimi et al. (2019) and Stich and Karimireddy (2019). Please qualify the novelty claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the theoretical results are derived from explicit update equations and assumptions, and the empirical comparisons are observations rather than predictions forced by the derivation.

full rationale

The paper's theoretical claim is a convergence bound for the update in Eq. (10) under stated assumptions (convexity, smoothness, bounded gradients, fixed delay), and the proof follows standard NAG proof techniques; it does not fit any parameter to the result it then predicts. The 'look-ahead as delay correction' Proposition is a mathematical identity derived from the definition of d_t and the delayed update, not a fitted or externally assumed relation, so it is not circular. The empirical comparisons are controlled experiments, not derivations; the fact that the synchronous GPipe baseline uses AdamW while the proposed method uses NAdam with beta1=0.99 is an experimental confound and a fairness concern, but it is not a case where a fitted input is renamed as a prediction. The rate mismatch in the appendix (O(log t/t) from Eq. 33 versus the stated O(1/t) in Theorem 1) is a mathematical correctness issue, not circularity. No load-bearing self-citations or imported uniqueness theorems appear. Overall, the derivation chain is self-contained and no circular step is present.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard convex optimization assumptions, the fixed-delay model of PipeDream, and the heuristic 'update directions change slowly' premise. No invented entities are introduced. The momentum coefficient beta_1 and several schedule hyperparameters are free parameters tuned empirically.

free parameters (4)

beta_1 (momentum coefficient) = 0.99
Set to 0.99 based on the ablation in Fig. 6; the paper states 'does not introduce any hyperparameters' but this value is tuned and is central to the delay-correction mechanism.
learning rate eta = 3e-4 base; 1e-4 for 1B and 20/24 stages
Tuned by performance of GPipe on WikiText (Sec. 5.1) and reduced for larger models/stages (Sec. 5.3, 5.5); the convergence proof assumes eta=1/beta, so the empirical eta is not tied to the theory.
T (learning-rate discounting horizon) = 6000 iterations
Used in the no-weight-stash variant and Ours-No-WS, adopted from PipeMare (Yang et al., 2021) to stabilize early training; not derived from theory.
Stage-dependent rho_t and gamma_i schedules = rho_t = 1 - min(t/T,1); gamma_i = 0.9 + (P-i)/P * 0.09
Introduced for the memory-efficient/no-weight-stash variant (Eq. 13) and for SWARM; tuned choices to compensate for incorrect backpropagation.

assumptions (5)

domain assumption f is convex, beta-smooth, and has bounded gradients
Assumed in Theorem 2 and used throughout the proof (Appendix A.3, Eq. 21). Not satisfied by transformer training, but standard for proving convergence rates.
domain assumption Gradient delay tau is fixed (and constant per stage)
The algorithm and theory take tau constant as in Eq. (5) for PipeDream's 1F1B schedule; the proof's perturbation bound relies on fixed tau.
domain assumption Update directions change slowly over iterations
Sec. 3 states this is the key assumption for weight-space delay correction: 'the only assumption is that the update directions change slowly with respect to iterations'.
ad hoc to paper Momentum coefficient increases to 1 (or is chosen close to 1)
Proposition 1 requires lim gamma_t = 1; Theorem 2 sets gamma_t=(t-2)/t; experiments use fixed beta_1=0.99, which only approximately satisfies this premise.
domain assumption Weight stashing stores the forward-pass weights and gives correct backpropagation
The main method relies on PipeDream's weight stashing (Eq. 6) so that only the optimization step is asynchronous; the no-weight-stash variant deliberately violates this.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Nesterov Method for Asynchronous Pipeline Parallel Optimization." pith.science (2026). https://pith.science/paper/2N5EE55G

@misc{pith2026250501099,
  author       = {Pith},
  title        = {Pith review of: Nesterov Method for Asynchronous Pipeline Parallel Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2N5EE55G}},
  note         = {Machine review of arXiv:2505.01099}
}

read the original abstract

Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100% pipeline utilization by construction. However, it is inherently challenging as the weights and gradients are no longer synchronized, leading to stale (or delayed) gradients. To alleviate this, we introduce a variant of Nesterov Accelerated Gradient (NAG) for asynchronous optimization in PP. Specifically, we modify the look-ahead step in NAG to effectively address the staleness in gradients. We theoretically prove that our approach converges at a sublinear rate in the presence of fixed delay in gradients. Our experiments on large-scale language modelling tasks using decoder-only architectures with up to 1B parameters, demonstrate that our approach significantly outperforms existing asynchronous methods, even surpassing the synchronous baseline.

Figures

Figures reproduced from arXiv: 2505.01099 by the authors.

**Figure 1.** Original NAG (left) and our modified version (right) for delayed gradients (denoted with g¯𝑡 ). Our method discounts the gradient term by (1 − 𝛾𝑡). When 𝛾𝑡 → 1, the angle 𝛼 → 0, making the weight trajectory smoother. Consequently, the look-ahead d𝑡 can be shown to act as delay correction, alleviating gradient staleness. Here, since the last update step aligns with the delay direction, one may wonder what if we extra… view at source ↗

**Figure 2.** Training trajectory comparison on three language modelling datasets. In all scenarios, our method significantly outperforms the asynchronous methods while surpassing the synchronous GPipe method throughout training. Our memory efficient version clearly outperforms the asynchronous methods while being competitive to GPipe in two out of three datasets [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Training and validation trajectory for the 1B parameter model. Similar to the base model, our method outperforms GPipe while the memory efficient version is competitive with GPipe. on two out of the three datasets. Notably, the training trajectories of PipeDream and PipeMare reveal the optimization challenges inherent in asynchronous setups,3 while our Nesterov-based delay correction effectively bridges the gap b… view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Comparison with other delay correction methods on WikiText. Our method, outperforms all other delay correction methods in terms of training loss and weight discrepancy. Additionally, NAG improves all previous delay correction methods, while NAG alone yields the best pe…

**Figure 5.** Figure 5: Performance with respect to the number of stages. Even though, performance slightly degrades for our method compared to GPipe, the training time increase is exponentially larger for GPipe. the percentage increase in runtime for our approach is significantly lower comp…

**Figure 6.** Figure 6: Ablation study of our methods. Constant momentum coefficient of 0.99 performs slightly better than the adaptive version (denoted with ‘-a’) and it also shows the best alignment in (b). For the memory efficient version, in addition to adaptive momentum, delay dependent …

**Figure 7.** Figure 7: Our approach with and without the gradient discounting term for the Nesterov method. Without the discounting term, training is significantly disrupted due to gradient staleness, validating our insight. ference is also empirically demonstrated, matching our theoretical …

**Figure 9.** Figure 9: Validation loss trajectory for the base model. The behaviour is the same as training loss where our method consistently outperforms all methods including GPipe [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: Training loss vs. wall-clock time for the 1B model, where all models were trained for 50k iterations. For faster GPUs (A100 in this case), the runtime discrepancy between GPipe and other asynchronous methods is more pronounced. Note, overhead of our method over PipeDr…

**Figure 11.** Figure 11: Ablation study of our main methods additionally showing weight discrepancy at Stage-1 in (b). Constant momentum coefficient of 0.99 performs slightly better than the adaptive version (denoted with ‘-a’). It also shows the best delay correction and alignment between lo…

**Figure 12.** Figure 12: WikiText results for the base model for the XPipe method (Guan et al., 2019) for completeness. XPipe is a direct weight prediction method, that extrapolates the previous AdamW step based on the delay. We implemented XPipe following the description from the paper, howe…

**Figure 13.** Figure 13: Validation loss on WikiText for the SWARM experiment. The observed performance follows a similar trend to the training performance where our method significantly outperforms the other methods. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 5 canonical work pages

[1]

Now, to enable telescoping sum, we want, 𝜆𝑡¯h𝑡 + w𝑡 +𝜆𝑡d𝑡− w* = w𝑡+1 +𝜆𝑡+1d𝑡+1− w* = w𝑡 + d𝑡 + ¯h𝑡 +𝜆𝑡+1𝛾𝑡+1(d𝑡 + ¯h𝑡)− w*

2𝛽 ‖¯g𝑡‖2 + ¯g𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), (26) = Ω𝑡− 𝜆𝑡(1 +𝛾𝑡)𝛽 2(1−𝛾𝑡) ¯h2 𝑡− 𝛽 1−𝛾𝑡 ¯h𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), A ≤ Ω𝑡− 𝜆𝑡𝛽 2(1−𝛾𝑡) ¯h2 𝑡− 𝛽 1−𝛾𝑡 ¯h𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), B = Ω𝑡− 𝛽 2𝜆𝑡(1−𝛾𝑡) (︀ ‖𝜆𝑡¯h𝑡 + w𝑡 +𝜆𝑡d𝑡− w*‖2−‖ w𝑡 +𝜆𝑡d𝑡− w*‖2)︀ , C where, A substitutes Ω𝑡 = 𝜆𝑡𝛽 2 ‖ ¯Δ𝑡‖2 +𝜆𝑡(𝛾𝑡− 1)¯g𝑡· ¯Δ𝑡, B is due to 0<𝛾 𝑡< 0,𝜆𝑡> 0,𝛽 >0, and C follows from𝑎2 + 2𝑎𝑏 = (𝑎 +𝑏)2−𝑏2. ...

work page 2023
[10]

Asynchronous sgd beats mini- batch sgd under arbitrary delays

Konstantin Mishchenko, Francis Bach, Mathieu Even, and Blake Woodworth. Asynchronous sgd beats mini- batch sgd under arbitrary delays. URL https://arxiv. org/abs/2206.07638, 2(6):7,

arXiv
[11]

Asynchrony begets momentum, with an application to deep learning

Ioannis Mitliagkas, Ce Zhang, Stefan Hadjis, and Christopher Ré. Asynchrony begets momentum, with an application to deep learning. In 2016 54th Annual Allerton Conference on Communication, Con- trol, and Computing (Allerton), pages 997–1004. IEEE,

work page 2016
[13]

Max Ryabinin, Alexander Borzunov, Michael Diskin, Anton Gusev, Denis Mazur, Vsevolod Plokhot- nyuk, Alexey Bukhtiyarov, Pavel Samygin, Anton Sinitsin, and Artem Chumachenko

URL https: //proceedings.neurips.cc/paper/2020/ file/25ddc0f8c9d3e22e03d3076f98d83cb2- Paper.pdf. Max Ryabinin, Alexander Borzunov, Michael Diskin, Anton Gusev, Denis Mazur, Vsevolod Plokhot- nyuk, Alexey Bukhtiyarov, Pavel Samygin, Anton Sinitsin, and Artem Chumachenko. Hivemind: Decentralized Deep Learning in PyT orch, April

work page 2020
[2004]

Language models are few-shot learners

T om Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in neural information processing systems , 33: 1877–1901,

work page 1901
[2011]

Advances in asynchronous parallel and distributed optimization

Mahmoud Assran, Arda Aytekin, Hamid Reza Feyzmah- davian, Mikael Johansson, and Michael G Rabbat. Advances in asynchronous parallel and distributed optimization. Proceedings of the IEEE, 108(11):2013– 2031,

work page 2013
[2014]

Deepseek-v3 technical report

Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al. Deepseek-v3 technical report. arXiv preprint arXiv:2412.19437 , 2024a. 10 Nesterov Method for Asynchronous Pipeline Parallel Optimization Bo Liu, Rachita Chhaparia, Arthur Douillard, Satyen Kale, Andrei A Rusu, Jiajun Shen, A...

arXiv
[2015]

Efficient and robust parallel dnn training through model parallelism on multi-gpu platform

Chi-Chung Chen, Chia-Lin Yang, and Hsiang-Yun Cheng. Efficient and robust parallel dnn training through model parallelism on multi-gpu platform. arXiv preprint arXiv:1809.02839,

arXiv

Show all 15 references

[2016]

The llama 3 herd of models

Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783,

arXiv
[2019]

Xpipe: Efficient pipeline model parallelism for multi- gpu dnn training

Lei Guan, Wotao Yin, Dongsheng Li, and Xicheng Lu. Xpipe: Efficient pipeline model parallelism for multi- gpu dnn training. arXiv preprint arXiv:1911.04610 ,

1911 arXiv
[2020]

Gap aware mitigation of gradient staleness

Saar Barkai, Ido Hakimi, and Assaf Schuster. Gap aware mitigation of gradient staleness. arXiv preprint arXiv:1909.10802,

1909 arXiv
[2022]

Adam: A method for stochastic optimization

Diederik P Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980,

arXiv
[2023]

The error-feedback framework: Better rates for sgd with delayed gradients and compressed communication

Sebastian U Stich and Sai Praneeth Karimireddy. The error-feedback framework: Better rates for sgd with delayed gradients and compressed communication. arXiv preprint arXiv:1909.05350,

1909 arXiv
[2024]

Taming momentum in a dis- tributed asynchronous environment

Ido Hakimi, Saar Barkai, Moshe Gabel, and As- saf Schuster. Taming momentum in a dis- tributed asynchronous environment. arXiv preprint arXiv:1907.11612,

1907 arXiv
[2025]

Penghui Qi, Xinyi Wan, Guangxing Huang, and Min Lin

Accessed: 2025-01-16. Penghui Qi, Xinyi Wan, Guangxing Huang, and Min Lin. Zero bubble pipeline parallelism. arXiv preprint arXiv:2401.10241,

2025 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Now, to enable telescoping sum, we want, 𝜆𝑡¯h𝑡 + w𝑡 +𝜆𝑡d𝑡− w* = w𝑡+1 +𝜆𝑡+1d𝑡+1− w* = w𝑡 + d𝑡 + ¯h𝑡 +𝜆𝑡+1𝛾𝑡+1(d𝑡 + ¯h𝑡)− w*

2𝛽 ‖¯g𝑡‖2 + ¯g𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), (26) = Ω𝑡− 𝜆𝑡(1 +𝛾𝑡)𝛽 2(1−𝛾𝑡) ¯h2 𝑡− 𝛽 1−𝛾𝑡 ¯h𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), A ≤ Ω𝑡− 𝜆𝑡𝛽 2(1−𝛾𝑡) ¯h2 𝑡− 𝛽 1−𝛾𝑡 ¯h𝑡· (w𝑡 +𝜆𝑡d𝑡− w*), B = Ω𝑡− 𝛽 2𝜆𝑡(1−𝛾𝑡) (︀ ‖𝜆𝑡¯h𝑡 + w𝑡 +𝜆𝑡d𝑡− w*‖2−‖ w𝑡 +𝜆𝑡d𝑡− w*‖2)︀ , C where, A substitutes Ω𝑡 = 𝜆𝑡𝛽 2 ‖ ¯Δ𝑡‖2 +𝜆𝑡(𝛾𝑡− 1)¯g𝑡· ¯Δ𝑡, B is due to 0<𝛾 𝑡< 0,𝜆𝑡> 0,𝛽 >0, and C follows from𝑎2 + 2𝑎𝑏 = (𝑎 +𝑏)2−𝑏2. ...

work page 2023

[2] [10]

Asynchronous sgd beats mini- batch sgd under arbitrary delays

Konstantin Mishchenko, Francis Bach, Mathieu Even, and Blake Woodworth. Asynchronous sgd beats mini- batch sgd under arbitrary delays. URL https://arxiv. org/abs/2206.07638, 2(6):7,

arXiv

[3] [11]

Asynchrony begets momentum, with an application to deep learning

Ioannis Mitliagkas, Ce Zhang, Stefan Hadjis, and Christopher Ré. Asynchrony begets momentum, with an application to deep learning. In 2016 54th Annual Allerton Conference on Communication, Con- trol, and Computing (Allerton), pages 997–1004. IEEE,

work page 2016

[4] [13]

Max Ryabinin, Alexander Borzunov, Michael Diskin, Anton Gusev, Denis Mazur, Vsevolod Plokhot- nyuk, Alexey Bukhtiyarov, Pavel Samygin, Anton Sinitsin, and Artem Chumachenko

URL https: //proceedings.neurips.cc/paper/2020/ file/25ddc0f8c9d3e22e03d3076f98d83cb2- Paper.pdf. Max Ryabinin, Alexander Borzunov, Michael Diskin, Anton Gusev, Denis Mazur, Vsevolod Plokhot- nyuk, Alexey Bukhtiyarov, Pavel Samygin, Anton Sinitsin, and Artem Chumachenko. Hivemind: Decentralized Deep Learning in PyT orch, April

work page 2020

[5] [2004]

Language models are few-shot learners

T om Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in neural information processing systems , 33: 1877–1901,

work page 1901

[6] [2011]

Advances in asynchronous parallel and distributed optimization

Mahmoud Assran, Arda Aytekin, Hamid Reza Feyzmah- davian, Mikael Johansson, and Michael G Rabbat. Advances in asynchronous parallel and distributed optimization. Proceedings of the IEEE, 108(11):2013– 2031,

work page 2013

[7] [2014]

Deepseek-v3 technical report

Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al. Deepseek-v3 technical report. arXiv preprint arXiv:2412.19437 , 2024a. 10 Nesterov Method for Asynchronous Pipeline Parallel Optimization Bo Liu, Rachita Chhaparia, Arthur Douillard, Satyen Kale, Andrei A Rusu, Jiajun Shen, A...

arXiv

[8] [2015]

Efficient and robust parallel dnn training through model parallelism on multi-gpu platform

Chi-Chung Chen, Chia-Lin Yang, and Hsiang-Yun Cheng. Efficient and robust parallel dnn training through model parallelism on multi-gpu platform. arXiv preprint arXiv:1809.02839,

arXiv