SCALE: Scalable Cross-Attention Learning with Extrapolation for Agentic Workflow Scheduling

Aiji Liang; Jierui Lan; Jinxi He; Zhifei Xu; Zixuan Liang

arxiv: 2606.06820 · v1 · pith:HKAHOOAOnew · submitted 2026-06-05 · 💻 cs.LG · cs.AI

SCALE: Scalable Cross-Attention Learning with Extrapolation for Agentic Workflow Scheduling

Zhifei Xu , Jierui Lan , Zixuan Liang , Aiji Liang , Jinxi He This is my paper

Pith reviewed 2026-06-27 22:50 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords agentic LLM workflow schedulingDAG task schedulingdeep reinforcement learningcross-attention pointer networkscale generalizationrepresentation regularizationcluster resource allocationdistribution shift mitigation

0 comments

The pith

A cross-attention scheduler trained on 16-node clusters generalizes directly to 32- and 48-node clusters when features are regularized against scale-induced shift.

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

The paper shows that existing reinforcement-learning schedulers for workflow DAGs on server clusters must be retrained whenever the number of servers changes. SCALE replaces that requirement with a cross-attention pointer network whose architecture accepts any number of servers by construction. The authors observe that this architectural invariance is not enough: attention features shift in distribution as server count grows, degrading performance. They add Structured Representation Regularization, a combination of decorrelation loss and KL penalty toward the standard normal, to keep feature statistics stable. When trained only on 16 nodes and evaluated without further training on 48 nodes, the regularized model reduces average response time by 8.9 percent relative to the identical architecture without the regularization term.

Core claim

SCALE employs a cross-attention pointer network in which task features query server features, allowing the model to accept variable cluster sizes without architectural change. The authors demonstrate that this alone does not prevent distribution shift in the attention features as server count increases; they therefore introduce Structured Representation Regularization (decorrelation loss plus KL penalty to standard normal) that stabilizes feature statistics across input sizes. Trained exclusively on 16-node instances and tested directly on 32- and 48-node instances, the regularized model produces an 8.9 percent reduction in average response time at N=48 compared with the same network trained

What carries the argument

Cross-attention pointer network whose task-to-server queries are kept distributionally stable by Structured Representation Regularization (decorrelation loss combined with KL penalty to the standard normal).

If this is right

A single training run on a modest cluster size suffices for deployment on larger clusters without retraining.
Permutation-invariant attention architecture must be supplemented by explicit feature regularization to achieve scale generalization.
Response-time gains from SRR increase with the gap between training and test cluster sizes.
Scheduling decisions remain feasible for any number of servers once the model has been regularized on a fixed training size.

Where Pith is reading between the lines

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

The same regularization pattern could be tested on other variable-cardinality attention models that currently require per-size retraining.
Dynamic cloud environments that add or remove servers on the fly could adopt the method to avoid repeated training cycles.
If the KL term dominates, the features become approximately Gaussian regardless of input size; this could be verified by tracking higher moments at extreme scales such as N=128.

Load-bearing premise

That attention features undergo a distribution shift when the number of servers increases and that the decorrelation-plus-KL term is sufficient to keep those statistics stable for any cluster size.

What would settle it

Direct measurement showing that average response time at N=48 is no better (or is worse) when SRR is included than when the identical cross-attention architecture is used without it.

Figures

Figures reproduced from arXiv: 2606.06820 by Aiji Liang, Jierui Lan, Jinxi He, Zhifei Xu, Zixuan Liang.

**Figure 2.** Figure 2: Architecture of the SCALE algorithm with SRR. A 2-layer cross [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: 16-Node Completed primitives comparison. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: 16-Node Average response time comparison. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 6.** Figure 6: shows training curves. All methods rise quickly in the first 10% of training. CrossAttn then continues climbing with large fluctuations, eventually exceeding 1.1—likely overfitting to the 16-node configuration. SCALE plateaus near 1.0 with much smaller variance, consistent with SRR constraining the representation space. PPO and PPO+SRR converge between 0.93 and 0.95, limited by MLP capacity. SAC converges … view at source ↗

read the original abstract

Agentic Large Language Model (LLM) systems decompose complex tasks into workflow Directed Acyclic Graphs (DAGs) whose primitives must be scheduled on heterogeneous clusters. Existing deep reinforcement learning (DRL) schedulers are tied to a fixed cluster size and require retraining whenever the number of servers changes. We propose SCALE (Scalable Cross-Attention Learning with Extrapolation), a DRL scheduler that generalizes to unseen cluster scales without fine-tuning. SCALE employs a cross-attention pointer network where task features query against server features, so the architecture accepts any number of servers by construction. We observe, however, that permutation-invariant architecture alone does not guarantee good performance at new scales - the attention feature undergoes distribution shift as the server count grows. To counter this, we introduce Structured Representation Regularization (SRR): a decorrelation loss combined with a KL penalty toward the standard normal, which keeps feature statistics stable regardless of input size. Trained on 16 nodes and tested directly on 32 and 48 nodes, SCALE reduces average response time by 8.9% at N=48 relative to the same architecture without SRR, confirming that explicit regularization is necessary to close the scale-generalization gap.

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.

Desk Editor's Note private letter to a colleague

SCALE offers a cross-attention DRL scheduler with SRR to generalize across cluster sizes, but the abstract supplies no evidence that feature shift occurs or that SRR fixes it.

read the letter

SCALE is a DRL scheduler that uses cross-attention to handle any number of servers and adds regularization to generalize from small to large clusters without retraining. The reported 8.9% better response time at 48 nodes is the main empirical claim.

The work is new in pairing the pointer network with this Structured Representation Regularization specifically for scale-induced shift in scheduling DAGs from agentic LLMs. It does a decent job framing the problem of fixed-size DRL models in growing clusters.

The architecture itself is a reasonable extension of existing pointer networks for variable inputs. The regularization combines decorrelation and KL to normal, which is a standard way to stabilize representations.

The main weakness is that the abstract provides no supporting data for the claimed mechanism. There are no results showing that attention features actually shift with server count in the baseline or stay stable with SRR. The performance delta could be due to generic benefits of the loss rather than scale-specific stabilization. The stress-test concern holds up here because the paper does not include the necessary ablations or feature statistics.

No variance or multiple runs are mentioned, so the 8.9% figure is difficult to assess for reliability.

This paper would interest researchers working on reinforcement learning for resource allocation in AI systems or on generalization in graph-based scheduling. A practitioner looking for schedulers that adapt to cluster growth might find the high-level idea useful.

It deserves peer review because the problem is practical and the method is described clearly enough to evaluate with more details. The full paper likely has the experiments that the abstract omits.

I would send it to referees to check the experimental rigor and see if the claims about feature stability are backed up.

Referee Report

2 major / 1 minor

Summary. The paper presents SCALE, a deep reinforcement learning scheduler for agentic LLM workflow DAGs on heterogeneous clusters. It employs a cross-attention pointer network that accepts variable numbers of servers by construction, combined with Structured Representation Regularization (SRR: decorrelation loss plus KL penalty to N(0,1)) to counteract distribution shift in attention features as cluster size N grows. Trained on 16 nodes and evaluated directly on 32 and 48 nodes, SCALE reports an 8.9% reduction in average response time at N=48 relative to the identical architecture without SRR.

Significance. If the mechanism and results are substantiated, the work would address a practical barrier in DRL scheduling by enabling scale extrapolation without retraining, which is relevant for dynamic cluster environments in agentic systems. The explicit regularization strategy for stabilizing features under variable input cardinality offers a concrete direction for improving generalization in pointer-network architectures.

major comments (2)

[Abstract] Abstract: The claim that attention features undergo distribution shift with growing server count and that SRR is required to close the scale-generalization gap rests solely on the end-to-end 8.9% response-time improvement. No feature-level evidence (means, variances, correlations, or histograms) is supplied showing divergence in the unregularized model or stability under SRR across N=16/32/48; the performance delta alone does not distinguish scale-specific stabilization from generic regularization effects. This is load-bearing for the central contribution.
[Abstract] Abstract: The reported 8.9% improvement supplies no experimental details on baselines beyond the no-SRR ablation, number of independent runs, variance or standard error, or statistical tests. Without these, the reliability of the generalization claim cannot be assessed.

minor comments (1)

[Abstract] The pointer-network architecture is described as permutation-invariant and variable-length by construction; a short clarification on why this alone is insufficient (beyond the stated observation) would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful comments, which identify key areas where the manuscript's claims require stronger substantiation. We address each major comment below and will revise the paper to incorporate the requested evidence and details.

read point-by-point responses

Referee: [Abstract] Abstract: The claim that attention features undergo distribution shift with growing server count and that SRR is required to close the scale-generalization gap rests solely on the end-to-end 8.9% response-time improvement. No feature-level evidence (means, variances, correlations, or histograms) is supplied showing divergence in the unregularized model or stability under SRR across N=16/32/48; the performance delta alone does not distinguish scale-specific stabilization from generic regularization effects. This is load-bearing for the central contribution.

Authors: We agree that the manuscript currently supports the distribution-shift claim only through the end-to-end performance delta and does not supply direct feature-level statistics or visualizations. This leaves open the possibility that SRR provides generic regularization benefits rather than scale-specific stabilization. In the revision we will add an appendix section with means, variances, pairwise correlations, and histograms of the cross-attention features for both the unregularized and SRR models at N=16, 32, and 48, thereby distinguishing the two effects. revision: yes
Referee: [Abstract] Abstract: The reported 8.9% improvement supplies no experimental details on baselines beyond the no-SRR ablation, number of independent runs, variance or standard error, or statistical tests. Without these, the reliability of the generalization claim cannot be assessed.

Authors: We acknowledge the omission of run counts, variance measures, and statistical tests. The revised manuscript will report results aggregated over 10 independent random seeds, include standard errors, and provide paired t-test p-values comparing SCALE against the no-SRR baseline at each scale. These details will be added to both the abstract and the experimental section. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical scale-extrapolation result stands on measured performance delta

full rationale

The paper's central claim is an empirical observation: a cross-attention pointer network (permutation-invariant and variable-length by architectural construction) is trained at N=16 and evaluated at N=32/48; adding SRR (decorrelation + KL) yields an 8.9% response-time reduction versus the identical architecture without SRR. No derivation, equation, or self-citation reduces the reported improvement to a fitted parameter or prior result by construction. The architecture's variable-length property is stated as given, and the necessity of SRR is supported only by the held-out scale test, not by re-deriving the same quantity from the training objective. This is a standard empirical generalization experiment with no load-bearing self-referential step.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract alone supplies no concrete free parameters, axioms, or invented entities; the SRR loss is mentioned at a high level but its exact formulation and any fitted coefficients are not stated.

pith-pipeline@v0.9.1-grok · 5759 in / 1054 out tokens · 23511 ms · 2026-06-27T22:50:46.181800+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Y. Bengio, A. Lodi, A. Prouvost, Machine learning for combinatorial optimization: Amethodologicaltourd’horizon,EuropeanJournalofOp- erational Research 290 (2) (2021) 405–421. Author Biographies ZhifeiXuiscurrentlypursuingabachelor’sde- greeintheFacultyofArtsandSciences,Beijing Normal University at Zhuhai, China. His main researchinterestsincludeedgecomput...

2021

[1] [1]

Plaat, M

A. Plaat, M. van Duijn, N. Van Stein, M. Preuss, P. van der Putten, K. J. Batenburg, Agentic large language models, a survey, Journal of Artificial Intelligence Research 84 (2025)

2025

[2] [2]

S. Kim, S. Moon, R. Tabrizi, N. Lee, M. W. Mahoney, K. Keutzer, A. Gholami, An llm compiler for parallel function calling, arXiv preprint arXiv:2312.04511 (2023)

work page arXiv 2023

[3] [3]

Armbrust, A

M. Armbrust, A. Fox, R. Griffith, A. D. Joseph, R. Katz, A. Konwin- ski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, et al., A view of cloud computing, Communications of the ACM 53 (4) (2010) 50–58

2010

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J. Dean, S. Ghemawat, Mapreduce: simplified data processing on large clusters, Communications of the ACM 51 (1) (2008) 107–113

2008

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G. I. Chaudhry, E. Choukse, H. Qiu, Í. Goiri, R. Fonseca, A. Belay, R. Bianchini, Murakkab: Resource-efficient agentic workflow orchestra- tion in cloud platforms, arXiv preprint arXiv:2508.18298 (2025)

work page arXiv 2025

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J. Shen, N. Wadlom, Y. Lu, Batch query processing and optimization for agentic workflows, arXiv preprint arXiv:2509.02121 (2025)

work page arXiv 2025

[8] [8]

Cheng, W

K. Cheng, W. Hu, Z. Wang, H. Peng, J. Li, S. Zhang, Slice-level schedul- ing for high throughput and load balanced llm serving, arXiv preprint arXiv:2406.13511 (2024)

work page arXiv 2024

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C. Ma, A. Li, Y. Du, H. Dong, Y. Yang, Efficient and scalable reinforce- mentlearningforlarge-scalenetworkcontrol,NatureMachineIntelligence 6 (9) (2024) 1006–1020

2024

[10] [10]

Proximal Policy Optimization Algorithms

J. Schulman, F. Wolski, P. Dhariwal, A. Radford, O. Klimov, Proximal policy optimization algorithms, arXiv preprint arXiv:1707.06347 (2017)

work page internal anchor Pith review Pith/arXiv arXiv 2017

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Z. Liu, L. Huang, Z. Gao, M. Luo, S. Hosseinalipour, H. Dai, Ga-drl: Graph neural network-augmented deep reinforcement learning for dag task scheduling over dynamic vehicular clouds, IEEE Transactions on Network and Service Management 21 (4) (2024) 4226–4242

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Vaswani, N

A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, I. Polosukhin, Attention is all you need, Advances in neural information processing systems 30 (2017)

2017

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Vinyals, M

O. Vinyals, M. Fortunato, N. Jaitly, Pointer networks, Advances in neural information processing systems 28 (2015)

2015

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Significant-Gravitas,Autogpt: Anautonomousgpt-4experiment,https: //github.com/Significant-Gravitas/AutoGPT, gitHub repository (2023)

2023

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Chase, Langchain: Building applications with llms through com- posability,https://github.com/langchain-ai/langchain,gitHub repository (2022)

H. Chase, Langchain: Building applications with llms through com- posability,https://github.com/langchain-ai/langchain,gitHub repository (2022)

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S. Hong, X. Zheng, J. Chen, Y. Cheng, C. Wang, Y. Zhang, Z. Wang, S.K.S.Yau,Z.Lin,L.Zhou,etal.,Metagpt: Metaprogrammingformulti- agent collaborative framework, in: International Conference on Learning Representations (ICLR), 2024

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LangChain Inc., Langgraph: Building stateful multi-agent applica- tions,https://langchain-ai.github.io/langgraph/,documenta- tion (2024)

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Q. Wu, G. Bansal, J. Zhang, Y. Wu, S. Zhang, E. Zhu, B. Li, L. Jiang, X. Zhang, C. Wang, Autogen: Enabling next-gen llm applications via multi-agent conversation, arXiv preprint arXiv:2308.08155 (2023)

work page internal anchor Pith review Pith/arXiv arXiv 2023

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Topcuoglu, S

H. Topcuoglu, S. Hariri, M.-Y. Wu, Task scheduling algorithms for het- erogeneous processors, Proceedings. Eighth Heterogeneous Computing Workshop (1999) 3–14

1999

[20] [20]

H. Mao, M. Alizadeh, I. Menache, S. Kandula, Resource management with deep reinforcement learning, in: ACM Workshop on Hot Topics in Networks (HotNets), 2016, pp. 50–56

2016

[21] [21]

H. Mao, M. Schwarzkopf, S. B. Venkatakrishnan, Z. Meng, M. Alizadeh, Learning scheduling algorithms for data processing clusters, in: ACM SIGCOMM Conference, 2019, pp. 270–288. 9

2019

[22] [22]

T. N. Kipf, M. Welling, Semi-supervised classification with graph convo- lutional networks, in: International Conference on Learning Representa- tions (ICLR), 2017

2017

[23] [23]

Zaheer, S

M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. Salakhutdinov, A. Smola, Deep sets, in: Advances in neural information processing systems, 2017

2017

[24] [24]

3744–3753

J.Lee,Y.Lee,J.Kim,A.R.Kosiorek,S.Choi,Y.W.Teh,Settransformer: A framework for attention-based permutation-invariant neural networks, in: International Conference on Machine Learning (ICML), 2019, pp. 3744–3753

2019

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W.Kool,H.vanHoof,M.Welling,Attention,learntosolveroutingprob- lems!, in: International Conference on Learning Representations (ICLR), 2019

2019

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J. Park, J. Chun, S. H. Kim, Y. Kim, J. Park, Learning to schedule job- shop problems with attention networks, in: International Conference on Automated Planning and Scheduling (ICAPS), 2021, pp. 301–309

2021

[27] [27]

Bengio, A

Y. Bengio, A. Lodi, A. Prouvost, Machine learning for combinatorial optimization: Amethodologicaltourd’horizon,EuropeanJournalofOp- erational Research 290 (2) (2021) 405–421. Author Biographies ZhifeiXuiscurrentlypursuingabachelor’sde- greeintheFacultyofArtsandSciences,Beijing Normal University at Zhuhai, China. His main researchinterestsincludeedgecomput...

2021