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arxiv: 2605.09992 · v1 · submitted 2026-05-11 · 💻 cs.LG · cs.AI

Recognition: 2 theorem links

· Lean Theorem

Attention Drift: What Autoregressive Speculative Decoding Models Learn

Do\u{g}a\c{c} Eldenk, Hongyang Zhang, Kaan Oktay, Payal Mohapatra, Stephen Xia, Yigitcan Comlek

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:11 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords attention driftspeculative decodingautoregressive draftershidden state magnituderesidual normalizationacceptance lengthEAGLE3LLM inference acceleration
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The pith

Un-normalized residual paths in speculative decoding drafters cause hidden-state magnitudes to grow with chain depth, shifting attention away from the prompt.

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

The paper establishes that autoregressive drafter models used for speculative decoding exhibit attention drift, where focus moves from the original prompt to the model's own recently generated tokens as the speculation chain lengthens. This occurs because the un-normalized residual connections between steps cause hidden state magnitudes to increase monotonically. A sympathetic reader would care since the drift explains the observed degradation under template changes and long contexts, limiting the reliability of faster inference methods. The authors trace the issue to the drafter behaving like stacked pre-norm layers rather than a standalone predictor and test two fixes. If the account holds, these architectural adjustments make speculative decoding more robust without altering the core drafting approach.

Core claim

We identify a phenomenon called attention drift in which the drafter's attention progressively moves from the prompt onto its own recently-generated tokens as successive tokens are produced within a speculation chain. We trace this to the un-normalized residual path between chain steps: the drafter's hidden state magnitude grows monotonically with chain depth, which exhibits dynamics consistent with additional pre-norm transformer layers stacked on the target rather than as a standalone autoregressive predictor. In order to limit the growth, we propose post-norm on the drafter hidden states and per-hidden-state RMSNorm after capturing target hidden states. These changes improve acceptance长度.

What carries the argument

the un-normalized residual path between chain steps, which produces monotonic growth in hidden-state magnitude and drives attention drift

If this is right

  • Acceptance length improves by up to 2× under template perturbation compared with pre-norm EAGLE3.
  • Acceptance length improves by 1.18× on long-context tasks.
  • Acceptance length improves by 1.10× across seven standard benchmarks spanning multi-turn chat, math, and coding.
  • Shorter train-time-test depths generalize to longer drafting sequences at inference time.

Where Pith is reading between the lines

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

  • Similar magnitude growth and drift may appear in other multi-step autoregressive predictors that reuse hidden states across steps.
  • The same post-norm and per-hidden-state normalization pattern could be tested on drafter variants that use different base architectures.
  • Stabilizing hidden-state scale might reduce the performance gap between short and long speculation chains in production systems.
  • The drift mechanism suggests that residual handling should be examined in any model that performs repeated forward passes on accumulating self-generated context.

Load-bearing premise

The observed growth in hidden-state magnitude and resulting attention shift are caused by the un-normalized residual path rather than other unmeasured factors in drafter training or architecture.

What would settle it

An ablation in which hidden-state magnitudes are measured across increasing chain depths after the residual connections are removed or replaced, checking whether growth and attention shift disappear.

Figures

Figures reproduced from arXiv: 2605.09992 by Do\u{g}a\c{c} Eldenk, Hongyang Zhang, Kaan Oktay, Payal Mohapatra, Stephen Xia, Yigitcan Comlek.

Figure 1
Figure 1. Figure 1: Attention drift. During speculation, the drafter’s attention moves from the prompt’s sink token onto its own recently-generated tokens. Left: Emergence of the attention sink demonstrated on drafter’s attention heatmap, rows = query, columns = key; darker = higher attention. Center: Graphical visualization of attention drift on a drafter. Right: Attention per token position on x axis, with speculated tokens… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of Pre-norm (Left) and proposed Post-norm (Right) architecture. (ii) To understand this behavior, we analyze the hidden-state dynamics of speculative drafters and find that the unnormalized residual connection between speculation steps causes hidden￾state magnitudes to grow monotonically with chain depth, re￾sembling additional transformer layers stacked on top of the verifier. The drafter implici… view at source ↗
Figure 3
Figure 3. Figure 3: Verification phase: green tokens are accepted, yellow is resampled and red ones are rejected. [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Attention heatmaps for visualizing attention drift on EAGLE-3 drafters. Aggregated over 200+ [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Percentage of attention concentrated on Sink token (Left) and Latest Token (Right) on EAGLE-3 [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Attention Drift on Qwen3.5 9B MTP head We inspect the MTP head of Qwen3.5 9B (Section 3), a single transformer layer that follows the target model’s attention architecture and reuses the same weights across consecutive speculation steps. During MTP speculation, we observe similar trends ( [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sink and drafted token self attention on Qwen3.5 9B MTP heads (MT-Bench, 80 prompts). [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Attention Drift on GPT-oss 120B. What if verifier doesn’t have an attention sink? Some recent models, such as Qwen3-Next and GPT-oss, are designed to suppress attention sinks. Qwen3-Next uses gated attention, applying a per-head sigmoid gate to the SDPA output so that heads can multiplicatively suppress their contribution. GPT-oss instead introduces a per-head learnable bias logit in the softmax denominato… view at source ↗
Figure 9
Figure 9. Figure 9: Two views of the EAGLE3 drafter at chain depth [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Pre-norm vs. Post-norm at various TTT (max [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Attention Sink and Self-Token Attention for each model that fixes the attention drift. [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Magnitude drift on Qwen3.5 9B MTP heads This is also consistent with our finding that magnitude accumulation is one contributor to drift but not the only mechanism. We focus our diagnosis and intervention on EAGLE-3, which trains a separate drafter with its own LM head post-hoc against the frozen target’s output distribution. MTP, in contrast, reuses the target’s LM head and is trained jointly with the ta… view at source ↗
Figure 13
Figure 13. Figure 13: Standard Pre-norm (Left) vs proposed Post-norm (Right) drafter architectures. The proposed post-norm architecture places individual RMSNorms after each target hidden state hlow,hmid,hhigh and accumulates the drafter’s hidden states after the RMSNorm ( [PITH_FULL_IMAGE:figures/full_fig_p009_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: GPT-OSS 20B results on SGLang, acceptance length includes bonus token, temp [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: System prompt length’s effect on accuracy [PITH_FULL_IMAGE:figures/full_fig_p010_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: Gated attention overfits to the system prompt, hurting accuracy badly. System Prompt Length. In our second experiment with temperature 0, we varied system prompt length (Llama’s default prompt, trimmed to different lengths). Post-norm beat pre-norm at every length tested ( [PITH_FULL_IMAGE:figures/full_fig_p011_18.png] view at source ↗
Figure 20
Figure 20. Figure 20: Effect of window size on prediction accu [PITH_FULL_IMAGE:figures/full_fig_p012_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Attended tokens (marked in orange) in different SWA implementations. [PITH_FULL_IMAGE:figures/full_fig_p012_21.png] view at source ↗
read the original abstract

Speculative decoding accelerates LLM inference by drafting future tokens with a small model, but drafter models degrade sharply under template perturbation and long-context inputs. We identify a previously-unreported phenomenon we call \textbf{attention drift}: as the drafter generates successive tokens within a speculation chain, attention progressively moves from the prompt onto its own recently-generated tokens. We observe this across both \emph{EAGLE3} drafters and \emph{MTP heads}, suggesting drift is a property of drafter designs. We trace this to the un-normalized residual path between chain steps: the drafter's hidden state magnitude grows monotonically with chain depth, which exhibits dynamics consistent with additional pre-norm transformer layers stacked on the target rather than as a standalone autoregressive predictor. In order to limit the growth, we propose two architectural changes: Post-norm on the drafter hidden states and per-hidden-state RMSNorm after capturing target hidden states. Our interventions improve acceptance length over the current leading model, pre-norm EAGLE3, by up to $2\times$ under template perturbation, $1.18\times$ on long-context tasks, and $1.10\times$ on seven standard benchmarks spanning multi-turn chat, math, and coding. Our changes also allow shorter train-time-test depths to generalize over longer drafting sequences.

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

2 major / 2 minor

Summary. The paper claims that autoregressive drafter models in speculative decoding suffer from 'attention drift,' where attention shifts progressively from the prompt to recently generated tokens as speculation chain depth increases. This is attributed to monotonic growth in hidden-state magnitudes arising from an un-normalized residual path between chain steps, which mimics stacked pre-norm layers rather than a standalone predictor. The authors propose two fixes—post-norm on drafter hidden states and per-hidden-state RMSNorm after target capture—and report empirical gains in acceptance length over pre-norm EAGLE3: up to 2× under template perturbation, 1.18× on long-context tasks, and 1.10× on seven standard benchmarks, with better generalization from shorter training depths.

Significance. If the mechanistic diagnosis holds, the work supplies a concrete architectural explanation for drafter degradation under perturbation and long contexts, plus simple, low-overhead normalizations that deliver measurable acceptance-length improvements. The observation of drift across both EAGLE3 and MTP heads is a strength, as is the multi-task empirical evaluation. These elements could inform more stable drafter designs and reduce reliance on deeper or more expensive speculation chains.

major comments (2)
  1. [Diagnosis of attention drift (analysis section)] The central causal claim—that the un-normalized inter-step residual path is the primary driver of monotonic magnitude growth and attention drift—rests on observational correlation across EAGLE3 and MTP heads. No ablation is presented that normalizes only this residual connection while holding target-state capture, training objectives, and other residual paths fixed; without it, alternative explanations cannot be ruled out.
  2. [Experimental evaluation] Improvements are reported exclusively against the authors' own pre-norm EAGLE3 baseline. It is unclear whether the 1.10–2× gains persist against independently tuned strong baselines or whether post-hoc architectural choices in the proposed normalizations interact with training details not fully isolated in the experiments.
minor comments (2)
  1. [Abstract] The abstract refers to 'seven standard benchmarks' without naming them or providing a table reference; listing the tasks (e.g., multi-turn chat, math, coding) explicitly would improve reproducibility.
  2. [Proposed architectural changes] The precise formulation of 'per-hidden-state RMSNorm' is described only at a high level; adding an equation (e.g., in the methods section) would clarify its difference from standard RMSNorm and aid implementation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for highlighting areas where our causal analysis and experimental comparisons can be strengthened. We address each major comment below and describe the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Diagnosis of attention drift (analysis section)] The central causal claim—that the un-normalized inter-step residual path is the primary driver of monotonic magnitude growth and attention drift—rests on observational correlation across EAGLE3 and MTP heads. No ablation is presented that normalizes only this residual connection while holding target-state capture, training objectives, and other residual paths fixed; without it, alternative explanations cannot be ruled out.

    Authors: We agree that a more targeted ablation isolating normalization of only the inter-step residual path would provide stronger causal evidence. In the revised manuscript we will add an experiment that applies RMSNorm exclusively to the residual connection between successive drafter steps while freezing the target-state capture mechanism, training objective, and all other residual paths. This controlled variant will be compared directly to the original pre-norm EAGLE3 and to our full post-norm + per-state RMSNorm model, allowing us to quantify the contribution of the residual path to magnitude growth and attention drift. revision: yes

  2. Referee: [Experimental evaluation] Improvements are reported exclusively against the authors' own pre-norm EAGLE3 baseline. It is unclear whether the 1.10–2× gains persist against independently tuned strong baselines or whether post-hoc architectural choices in the proposed normalizations interact with training details not fully isolated in the experiments.

    Authors: We acknowledge the value of broader baseline comparisons. In revision we will expand the experimental section to include results against additional independently reported drafter architectures (e.g., Medusa-style heads and other recent MTP variants) using the same evaluation protocol. Regarding training interactions, we will clarify that the proposed normalizations are architectural modifications applied during both training and inference; we will report separate training runs for the normalized drafter and provide hyper-parameter details to show that the acceptance-length gains are not artifacts of mismatched training regimes. Full retraining of every external baseline with our exact normalization stack is computationally intensive, but we will note this limitation and focus on the most relevant strong baselines. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical observations and benchmark improvements are independent of inputs

full rationale

The paper's core contribution is an empirical identification of attention drift via measurements of attention weights and hidden-state magnitudes across EAGLE3 and MTP drafters, followed by two proposed normalizations whose benefits are validated on external benchmarks (template perturbation, long-context, and seven standard tasks). No equations, fitted parameters, or predictions are presented that reduce to the inputs by construction. The attribution to the residual path is observational rather than derived from a closed-form model that assumes the conclusion. Comparisons use the established pre-norm EAGLE3 as an external baseline, not a self-referential fit. The work is therefore self-contained against external benchmarks with no load-bearing self-citation chains or self-definitional steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The report is based solely on the abstract; no explicit free parameters, axioms, or invented entities are stated. The two normalization layers are presented as engineering interventions rather than new theoretical entities.

pith-pipeline@v0.9.0 · 5554 in / 1278 out tokens · 27644 ms · 2026-05-12T02:11:00.185782+00:00 · methodology

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Works this paper leans on

22 extracted references · 22 canonical work pages · 1 internal anchor

  1. [1]

    Fast inference from transformers via speculative decoding

    Yaniv Leviathan, Matan Kalman, and Yossi Matias. Fast inference from transformers via speculative decoding. InInternational Conference on Machine Learning, pages 19274–19286. PMLR, 2023

    work page 2023

  2. [2]

    Accelerating Large Language Model Decoding with Speculative Sampling

    Charlie Chen, Sebastian Borgeaud, Geoffrey Irving, Jean-Baptiste Lespiau, Laurent Sifre, and John Jumper. Accelerating large language model decoding with speculative sampling.arXiv preprint arXiv:2302.01318, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  3. [3]

    Duoattention: Efficient long-context LLM inference with retrieval and streaming heads

    Guangxuan Xiao, Jiaming Tang, Jingwei Zuo, junxian guo, Shang Yang, Haotian Tang, Yao Fu, and Song Han. Duoattention: Efficient long-context LLM inference with retrieval and streaming heads. InThe Thirteenth International Conference on Learning Representations, 2025. URL https://openreview. net/forum?id=cFu7ze7xUm

    work page 2025

  4. [4]

    Longspec: Long-context lossless speculative decoding with efficient drafting and verification

    Penghui Yang, Cunxiao Du, Fengzhuo Zhang, Haonan Wang, Tianyu Pang, Chao Du, and Bo An. Longspec: Long-context lossless speculative decoding with efficient drafting and verification. InES- FoMo III: 3rd Workshop on Efficient Systems for Foundation Models, 2025. URLhttps://openreview. net/forum?id=GFN9PWbfHs

    work page 2025

  5. [5]

    EAGLE-3: Scaling up inference acceleration of large language models via training-time test

    Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang. EAGLE-3: Scaling up inference acceleration of large language models via training-time test. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2026. URLhttps://openreview.net/forum?id=4exx1hUffq

    work page 2026

  6. [6]

    Better & faster large language models via multi-token prediction

    Fabian Gloeckle, Badr Youbi Idrissi, Baptiste Rozière, David Lopez-Paz, and Gabriel Synnaeve. Better & faster large language models via multi-token prediction. In Ruslan Salakhutdinov, Zico Kolter, Katherine A. Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Forty-first International Conference on Machine Learning, I...

    work page 2024

  7. [7]

    EAGLE: speculative sampling requires rethinking feature uncertainty

    Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang. EAGLE: speculative sampling requires rethinking feature uncertainty. In Ruslan Salakhutdinov, Zico Kolter, Katherine A. Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors,Forty-first International Conference on Machine Learning, ICML 2024, Vienna, Austria, July 21-27...

    work page 2024

  8. [8]

    Eagle-2: Faster inference of language models with dynamic draft trees

    Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang. Eagle-2: Faster inference of language models with dynamic draft trees. InProceedings of the 2024 conference on empirical methods in natural language processing, pages 7421–7432, 2024

    work page 2024

  9. [9]

    Attention is all you need.Advances in neural information processing systems, 30, 2017

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30, 2017

    work page 2017

  10. [10]

    Efficient memory management for large language model serving with pagedattention

    Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention. InProceedings of the 29th symposium on operating systems principles, pages 611–626, 2023

    work page 2023

  11. [11]

    Sglang: Efficient execution of structured language model programs.Advances in neural information processing systems, 37:62557–62583, 2024

    Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Sun, Jeff Huang, Cody H Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E Gonzalez, et al. Sglang: Efficient execution of structured language model programs.Advances in neural information processing systems, 37:62557–62583, 2024

    work page 2024

  12. [12]

    Efficient streaming language models with attention sinks

    Guangxuan Xiao, Yuandong Tian, Beidi Chen, Song Han, and Mike Lewis. Efficient streaming language models with attention sinks. InThe Twelfth International Conference on Learning Representations, 2024. URLhttps://openreview.net/forum?id=NG7sS51zVF. 14

    work page 2024

  13. [13]

    Judging llm-as-a-judge with mt-bench and chatbot arena

    Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al. Judging llm-as-a-judge with mt-bench and chatbot arena. Advances in neural information processing systems, 36:46595–46623, 2023

    work page 2023

  14. [14]

    arXiv preprint arXiv:2603.15031 (2026)

    Kimi Team, Guangyu Chen, Yu Zhang, Jianlin Su, Weixin Xu, Siyuan Pan, Yaoyu Wang, Yucheng Wang, Guanduo Chen, Bohong Yin, et al. Attention residuals.arXiv preprint arXiv:2603.15031, 2026

    work page arXiv 2026

  15. [15]

    Magicdec: Breaking the latency-throughput tradeoff for long context generation with speculative decoding

    Ranajoy Sadhukhan, Jian Chen, Zhuoming Chen, Vashisth Tiwari, Ruihang Lai, Jinyuan Shi, Ian En-Hsu Yen, Avner May, Tianqi Chen, and Beidi Chen. Magicdec: Breaking the latency-throughput tradeoff for long context generation with speculative decoding. InICLR, 2025. URL https://openreview.net/ forum?id=CS2JWaziYr

    work page 2025

  16. [16]

    Longbench: A bilingual, multitask benchmark for long context understanding

    Yushi Bai, Xin Lv, Jiajie Zhang, Hongchang Lyu, Jiankai Tang, Zhidian Huang, Zhengxiao Du, Xiao Liu, Aohan Zeng, Lei Hou, et al. Longbench: A bilingual, multitask benchmark for long context understanding. InProceedings of the 62nd annual meeting of the association for computational linguistics (volume 1: Long papers), pages 3119–3137, 2024

    work page 2024

  17. [17]

    Lee, Deming Chen, and Tri Dao

    Tianle Cai, Yuhong Li, Zhengyang Geng, Hongwu Peng, Jason D. Lee, Deming Chen, and Tri Dao. Medusa: Simple LLM inference acceleration framework with multiple decoding heads. InForty-first International Conference on Machine Learning, 2024. URL https://openreview.net/forum?id= PEpbUobfJv

    work page 2024

  18. [18]

    Hydra: Sequentially-dependent draft heads for medusa decoding

    Zachary Ankner, Rishab Parthasarathy, Aniruddha Nrusimha, Christopher Rinard, Jonathan Ragan- Kelley, and William Brandon. Hydra: Sequentially-dependent draft heads for medusa decoding. InFirst Conference on Language Modeling, 2024. URL https://openreview.net/forum?id=FbhjirzvJG

    work page 2024

  19. [19]

    Dflash: Block diffusion for flash speculative decoding

    Jian Chen, Yesheng Liang, and Zhijian Liu. Dflash: Block diffusion for flash speculative decoding.arXiv preprint arXiv:2602.06036, 2026

    work page arXiv 2026

  20. [20]

    Gated at- tention for large language models: Non-linearity, sparsity, and attention-sink-free

    Zihan Qiu, Zekun Wang, Bo Zheng, Zeyu Huang, Kaiyue Wen, Songlin Yang, Rui Men, Le Yu, Fei Huang, Suozhi Huang, Dayiheng Liu, Jingren Zhou, and Junyang Lin. Gated at- tention for large language models: Non-linearity, sparsity, and attention-sink-free. In D. Bel- grave, C. Zhang, H. Lin, R. Pascanu, P. Koniusz, M. Ghassemi, and N. Chen, editors,Ad- vances ...

    work page 2025

  21. [21]

    On layer normalization in the transformer architecture

    Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. InInternational conference on machine learning, pages 10524–10533. PMLR, 2020

    work page 2020

  22. [22]

    On the role of attention masks and layernorm in transformers

    Xinyi Wu, Amir Ajorlou, Yifei Wang, Stefanie Jegelka, and Ali Jadbabaie. On the role of attention masks and layernorm in transformers. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URLhttps://openreview.net/forum?id=lIH6oCdppg. 15 A Gated attention In the gated attention variant of our models, we add an optional per...

    work page 2024