Pith. sign in

REVIEW 2 major objections 1 minor 46 references

EPTS produces one elastic model from a single optimization that maintains performance across multiple sparsity levels in large language models.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.3

2026-06-25 21:34 UTC pith:DLMSP27F

load-bearing objection EPTS offers a one-shot multi-sparsity pruning approach for LLMs via MS-HiLoRA and MSFM to avoid repeated optimizations, but lacks visible quantitative backing in the abstract. the 2 major comments →

arxiv 2606.25285 v1 pith:DLMSP27F submitted 2026-06-24 cs.LG cs.AI

EPTS: Elastic Post-Training Sparsity for Efficient Large Language Model Compression

Ke Xu , Jiaqi Wan , Wenhao Hu , Han Pu , Xiaoyun Wang This is my paper
classification cs.LG cs.AI
keywords post-training sparsitylarge language modelsmodel compressionelastic sparsitymulti-sparsity frameworkLoRA adaptationLLM deployment efficiency
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Existing post-training sparsity methods require a full separate optimization for each desired sparsity level, which blocks quick adaptation to different hardware constraints. The paper introduces EPTS as a multi-sparsity framework that trains one model once and then supports any sparsity setting from that single result. This matters for deployment because it removes the need to repeat expensive optimization runs when hardware resources change. The approach relies on two new components that transfer knowledge across sparsity groups and blend features to limit damage from pruning. Tests on LLaMA and OPT models show results comparable to specialized single-sparsity methods while adding the flexibility of one-time training.

Core claim

EPTS is a unified Multi-Sparsity framework that produces a single elastic model capable of maintaining robust performance across diverse sparsity configurations through a one-shot optimization process. It uses Multi-Sparsity Hierarchy LoRA to pass knowledge from low- to high-sparsity groups and Multi-Sparsity Feature Mixer to fuse representations at different sparsity granularities, reducing reconstruction competition and pruning effects.

What carries the argument

Multi-Sparsity Hierarchy LoRA (MS-HiLoRA) for cross-sparsity knowledge inheritance combined with Multi-Sparsity Feature Mixer (MSFM) for dynamic fusion of feature representations at varying sparsity levels.

Load-bearing premise

The Multi-Sparsity Hierarchy LoRA and Multi-Sparsity Feature Mixer mechanisms successfully reduce parameter competition and limit the effects of pruning changes.

What would settle it

A direct comparison showing that the single EPTS model has markedly higher perplexity or lower task accuracy than a separately optimized SparseGPT model at the same sparsity level on LLaMA-7B would falsify the claim of robust multi-sparsity performance.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • One optimization run supports deployment at any chosen sparsity without repeating the full process.
  • Performance stays competitive with single-sparsity methods such as SparseGPT and Wanda on LLaMA and OPT families.
  • The elastic model reduces total optimization time when multiple sparsity targets are needed for different devices.
  • Knowledge inheritance from low- to high-sparsity groups and dynamic feature mixing limit reconstruction errors.

Where Pith is reading between the lines

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

  • Hardware schedulers could switch sparsity on the fly based on current load without reloading a new model.
  • The same one-shot idea might apply to other compression methods such as quantization or distillation.
  • Edge-device fleets could share one base model and apply different sparsity masks per device type.
  • Training cost savings grow linearly with the number of target sparsity levels required.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper proposes Elastic Post-Training Sparsity (EPTS), a unified Multi-Sparsity framework for post-training compression of LLMs. It claims that a single one-shot optimization produces an elastic model that maintains robust performance across diverse sparsity levels, using a Multi-Sparsity Hierarchy LoRA (MS-HiLoRA) to enable knowledge inheritance from low- to high-sparsity groups and a Multi-Sparsity Feature Mixer (MSFM) to dynamically fuse features and reduce pruning perturbations. Experiments on LLaMA and OPT families are said to show competitive results versus SparseGPT and Wanda, with efficiency gains from avoiding per-sparsity re-optimization; source code is released.

Significance. If the empirical claims hold, the work would offer a practical advance in post-training sparsity by enabling flexible multi-scenario deployment from one optimization run, reducing computational overhead for hardware-adaptive compression. Releasing code supports reproducibility, which strengthens the contribution in an empirical field.

major comments (2)
  1. [Abstract] Abstract: the central claim that MS-HiLoRA and MSFM 'successfully mitigate' reconstruction competition and pruning perturbations is asserted without any supporting equations, pseudocode, or derivation; this is load-bearing for the multi-sparsity advantage and cannot be evaluated from the supplied description alone.
  2. [Abstract] Abstract: the assertion of 'competitive performance' and 'extensive experiments' is made without any reported metrics, sparsity levels tested, model sizes, or comparison tables; this directly undermines assessment of whether the one-shot elastic model actually matches or exceeds single-sparsity baselines.
minor comments (1)
  1. [Abstract] Abstract: the final sentence begins with lowercase 'our source code' and lacks a period before it; this is a minor presentation issue.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful review and the opportunity to clarify the presentation of our work. We address the two major comments on the abstract below, noting that abstracts are by design concise summaries while the supporting technical details and results appear in the body of the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that MS-HiLoRA and MSFM 'successfully mitigate' reconstruction competition and pruning perturbations is asserted without any supporting equations, pseudocode, or derivation; this is load-bearing for the multi-sparsity advantage and cannot be evaluated from the supplied description alone.

    Authors: We agree that the abstract itself contains no equations or pseudocode, as is conventional for abstracts due to length constraints. The mechanisms by which MS-HiLoRA enables knowledge inheritance across sparsity groups (thereby reducing reconstruction competition) and by which MSFM dynamically fuses multi-granularity features (thereby reducing pruning perturbations) are derived and formalized with equations in Sections 3.2 and 3.3, respectively, and the overall procedure is given as pseudocode in Algorithm 1. These sections also include the multi-sparsity loss formulation that underpins the one-shot optimization. The abstract therefore summarizes rather than derives the technical contribution. revision: no

  2. Referee: [Abstract] Abstract: the assertion of 'competitive performance' and 'extensive experiments' is made without any reported metrics, sparsity levels tested, model sizes, or comparison tables; this directly undermines assessment of whether the one-shot elastic model actually matches or exceeds single-sparsity baselines.

    Authors: The abstract summarizes the outcome of the experiments; the concrete metrics, sparsity ratios (40 %–70 %), model scales (LLaMA-7B/13B, OPT-6.7B/13B/30B), and direct comparisons against SparseGPT and Wanda appear in Section 4 and Tables 1–4. Those tables report perplexity and zero-shot accuracy, confirming that the single elastic model remains competitive with per-sparsity baselines while avoiding repeated optimization. We therefore view the abstract phrasing as appropriate for a high-level summary. revision: no

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an empirical method for post-training sparsity in LLMs, introducing MS-HiLoRA and MSFM as architectural mechanisms to enable multi-sparsity in one-shot optimization. No equations, derivations, or first-principles claims are present that reduce outputs to inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems, and no predictions are fitted then renamed. The central claims rest on experimental comparisons to external baselines (SparseGPT, Wanda) rather than internal self-referential reductions. This is a standard empirical proposal with no circularity in any derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 2 invented entities

Abstract-only review; no explicit free parameters, axioms, or independent evidence for new entities are provided.

invented entities (2)
  • MS-HiLoRA no independent evidence
    purpose: facilitates knowledge inheritance from low- to high-sparsity groups to mitigate competition for parameter reconstruction
    New mechanism introduced to address sparsity competition
  • MSFM no independent evidence
    purpose: dynamically fuses feature representations of varying sparsity granularities to enhance adaptability to pruning perturbations
    New component proposed to improve robustness

pith-pipeline@v0.9.1-grok · 5785 in / 1182 out tokens · 27766 ms · 2026-06-25T21:34:08.157652+00:00 · methodology

0 comments
read the original abstract

Post-Training Sparsity (PTS) has emerged as a crucial paradigm for compressing Large Language Models to facilitate efficient deployment on resource-constrained devices. However, existing PTS methodologies are typically confined to Single-Sparsity optimization, necessitating a separate, time-consuming optimization session for each specific sparsity level. This rigid paradigm significantly hinders flexible deployment across diverse hardware scenarios, as adapting to a new sparsity requirement mandates a complete re-optimization process. To address these limitations, we propose Elastic Post-Training Sparsity (EPTS), a unified Multi-Sparsity framework that produces a single elastic model capable of maintaining robust performance across diverse sparsity configurations through a one-shot optimization process. Specifically, we design a Multi-Sparsity Hierarchy LoRA (MS-HiLoRA) mechanism that facilitates knowledge inheritance from low- to high-sparsity groups, effectively mitigating the competition for parameter reconstruction. Furthermore, we introduce a Multi-Sparsity Feature Mixer (MSFM), which significantly enhances the model's adaptability to pruning perturbations by dynamically fusing feature representations of varying sparsity granularities. Extensive experiments on LLaMA and OPT families demonstrate that EPTS achieves competitive performance compared to state-of-the-art methods like SparseGPT and Wanda, while offering significant efficiency gains by enabling multi-scenario deployment from a single optimization. our source code is available at https://github.com/xuke225/EPTS.

Figures

Figures reproduced from arXiv: 2606.25285 by Han Pu, Jiaqi Wan, Ke Xu, Wenhao Hu, Xiaoyun Wang.

Figure 1
Figure 1. Figure 1: Overview of our proposed EPTS. Through block-wise reconstruction, EPTS compensates for performance degradation [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Kernel Density Estimation (KDE) visualization of weight distributions for the query projection layer (q_proj) in the [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Inference Efficiency Comparison of LLaMA-7B on [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 5 canonical work pages · 4 internal anchors

  1. [1]

    Blalock, Jose Javier Gonzalez Ortiz, Jonathan Frankle, and John V

    Davis W. Blalock, Jose Javier Gonzalez Ortiz, Jonathan Frankle, and John V. Guttag. 2020. What is the State of Neural Network Pruning?. InProceedings of the Third Conference on Machine Learning and Systems

    2020

  2. [2]

    Christopher Clark, Kenton Lee, Ming-Wei Chang, Tom Kwiatkowski, Michael Collins, and Kristina Toutanova. 2019. BoolQ: Exploring the Surprising Diffi- culty of Natural Yes/No Questions. InProceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2924–2936

    2019

  3. [3]

    Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. 2018. Think you have Solved Question Answer- ing? Try ARC, the AI2 Reasoning Challenge.ArXivabs/1803.05457 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  4. [4]

    Tim Dettmers, Artidoro Pagnoni, Ari Holtzman, and Luke Zettlemoyer. 2023. QLoRA: Efficient Finetuning of Quantized LLMs. InAdvances in Neural Informa- tion Processing Systems

    2023

  5. [5]

    Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, and Erich Elsen

  6. [6]

    InProceedings of the 37th International Conference on Machine Learning (Proceedings of Machine Learning Research, Vol

    Rigging the Lottery: Making All Tickets Winners. InProceedings of the 37th International Conference on Machine Learning (Proceedings of Machine Learning Research, Vol. 119). 2943–2952

  7. [7]

    Jun Fang, Ali Shafiee, Hamzah Abdel-Aziz, David Thorsley, Georgios Georgiadis, and Joseph Hassoun. 2020. Post-training Piecewise Linear Quantization for Deep Neural Networks. InComputer Vision - ECCV 2020 - 16th European Conference (Lecture Notes in Computer Science, Vol. 12347). 69–86

    2020

  8. [8]

    Luyang Fang, Xiaowei Yu, Jiazhang Cai, Yongkai Chen, Shushan Wu, Zhengliang Liu, Zhenyuan Yang, Haoran Lu, Xilin Gong, Yufang Liu, Terry Ma, Wei Ruan, Ali Abbasi, Jing Zhang, Tao Wang, Ehsan Latif, Wei Liu, Wei Zhang, Soheil Kolouri, Xiaoming Zhai, Dajiang Zhu, Wenxuan Zhong, Tianming Liu, and Ping Ma

  9. [9]

    Knowledge distillation and dataset distillation of large language models: emerging trends, challenges, and future directions.Artif. Intell. Rev.59, 1 (2026), 17

    2026

  10. [10]

    Elias Frantar and Dan Alistarh. 2022. Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning. InAdvances in Neural Information Processing Systems

    2022

  11. [11]

    Elias Frantar and Dan Alistarh. 2023. SparseGPT: Massive Language Models Can be Accurately Pruned in One-Shot. InInternational Conference on Machine Learning (Proceedings of Machine Learning Research, Vol. 202). 10323–10337

    2023

  12. [12]

    Ruihao Gong, Yang Yong, Zining Wang, Jinyang Guo, Xiuying Wei, Yuqing Ma, and Xianglong Liu. 2024. Fast and Controllable Post-training Sparsity: Learning Optimal Sparsity Allocation with Global Constraint in Minutes. InThirty-Eighth AAAI Conference on Artificial Intelligence. 12190–12198

    2024

  13. [13]

    Song Han, Jeff Pool, John Tran, and William J. Dally. 2015. Learning both Weights and Connections for Efficient Neural Network. InNeural Information Processing Systems

    2015

  14. [14]

    Stork, and Gregory J

    Babak Hassibi, David G. Stork, and Gregory J. Wolff. 1993. Optimal Brain Surgeon and general network pruning. InProceedings of International Conference on Neural Networks. 293–299

    1993

  15. [15]

    Soufiane Hayou, Nikhil Ghosh, and Bin Yu. 2024. LoRA+: Efficient Low Rank Adaptation of Large Models. InForty-first International Conference on Machine Learning

    2024

  16. [16]

    AJAY KUMAR JAISWAL, Zhe Gan, Xianzhi Du, Bowen Zhang, Zhangyang Wang, and Yinfei Yang. 2024. Compressing LLMs: The Truth is Rarely Pure and Never Simple. InThe Twelfth International Conference on Learning Representations

    2024

  17. [17]

    Mahoney, Joseph Hassoun, Kurt Keutzer, and Amir Gholami

    Woosuk Kwon, Sehoon Kim, Michael W. Mahoney, Joseph Hassoun, Kurt Keutzer, and Amir Gholami. 2022. A Fast Post-Training Pruning Framework for Trans- formers. InAdvances in Neural Information Processing Systems

    2022

  18. [18]

    Ivan Lazarevich, Alexander Kozlov, and Nikita Malinin. 2021. Post-training deep neural network pruning via layer-wise calibration. InIEEE/CVF International Conference on Computer Vision Workshops. 798–805

    2021

  19. [19]

    Denker, and Sara A

    Yann LeCun, John S. Denker, and Sara A. Solla. 1989. Optimal Brain Damage. In Advances in Neural Information Processing Systems. 598–605

    1989

  20. [20]

    Haokun Lin, Haobo Xu, Yichen Wu, Jingzhi Cui, Yingtao Zhang, Linzhan Mou, Linqi Song, Zhenan Sun, and Ying Wei. 2024. DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs. InAdvances in Neural Information Processing Systems

    2024

  21. [21]

    Jing Liu, Ruihao Gong, Xiuying Wei, Zhiwei Dong, Jianfei Cai, and Bohan Zhuang

  22. [22]

    InThe Twelfth International Conference on Learning Representa- tions

    QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Lan- guage Models. InThe Twelfth International Conference on Learning Representa- tions

  23. [23]

    Zhuang Liu, Mingjie Sun, Tinghui Zhou, Gao Huang, and Trevor Darrell. 2019. Rethinking the Value of Network Pruning. In7th International Conference on Learning Representations

    2019

  24. [24]

    Kevin Zhou

    Xin Luo, Xueming Fu, Zihang Jiang, and S. Kevin Zhou. 2025. ICP: Immediate Compensation Pruning for Mid-to-high Sparsity. InIEEE/CVF Conference on Computer Vision and Pattern Recognition. 9487–9496

    2025

  25. [25]

    Xinyin Ma, Gongfan Fang, and Xinchao Wang. 2023. LLM-Pruner: On the Struc- tural Pruning of Large Language Models. InAdvances in Neural Information Processing Systems

    2023

  26. [26]

    Todor Mihaylov, Peter Clark, Tushar Khot, and Ashish Sabharwal. 2018. Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering. InProceedings of the 2018 Conference on Empirical Methods in Natural Language Processing. 2381–2391

    2018

  27. [27]

    Markus Nagel, Rana Ali Amjad, Mart van Baalen, Christos Louizos, and Tijmen Blankevoort. 2020. Up or Down? Adaptive Rounding for Post-Training Quanti- zation. InProceedings of the 37th International Conference on Machine Learning, Vol. 119. 7197–7206

    2020

  28. [28]

    Keisuke Sakaguchi, Ronan Le Bras, Chandra Bhagavatula, and Yejin Choi. 2021. WinoGrande: an adversarial winograd schema challenge at scale.Commun. ACM 64, 9 (2021), 99–106

    2021

  29. [29]

    Sidak Pal Singh and Dan Alistarh. 2020. WoodFisher: Efficient Second-Order Ap- proximation for Neural Network Compression. InAdvances in Neural Information Processing Systems

    2020

  30. [30]

    Zico Kolter

    Mingjie Sun, Zhuang Liu, Anna Bair, and J. Zico Kolter. 2024. A Simple and Effec- tive Pruning Approach for Large Language Models. InThe Twelfth International Conference on Learning Representations

    2024

  31. [31]

    Qinghui Sun, Weilun Wang, Yanni Zhu, Shenghuan He, Hao Yi, Zehua Cai, and Hong Liu. 2024. Dual-Assessment Driven Pruning: Iterative Optimizing Layer- wise Sparsity for Large Language Model. InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2775–2783

    2024

  32. [32]

    Llama Team. 2024. The Llama 3 Herd of Models

    2024

  33. [33]

    OpenAI Team. 2023. GPT-4 Technical Report

    2023

  34. [34]

    Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, Aur’elien Rodriguez, Armand Joulin, Edouard Grave, and Guillaume Lam- ple. 2023. LLaMA: Open and Efficient Foundation Language Models.ArXiv abs/2302.13971 (2023)

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  35. [35]

    Hugo Touvron, Louis Martin, and et al. 2023. Llama 2: Open Foundation and Fine-Tuned Chat Models.ArXiv(2023)

    2023

  36. [36]

    Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R. Bowman. 2019. GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding. In7th International Conference on Learning Representations

    2019

  37. [37]

    Jingjing Xie, Yuxin Zhang, Mingbao Lin, Zhihang Lin, Liujuan Cao, and Rongrong Ji. 2024. UniPTS: A Unified Framework for Proficient Post-Training Sparsity. In IEEE/CVF Conference on Computer Vision and Pattern Recognition. 5746–5755

    2024

  38. [38]

    Canwen Xu and Julian J. McAuley. 2023. A Survey on Model Compression and Acceleration for Pretrained Language Models. InThirty-Seventh AAAI Conference on Artificial Intelligence. 10566–10575. KDD ’26, August 09–13, 2026, Jeju Island, Republic of Korea Ke Xu, Jiaqi Wan, Wenhao Hu, Han Pu, &Xiaoyun Wang

    2023

  39. [39]

    Yuhui Xu, Lingxi Xie, Xiaotao Gu, Xin Chen, Heng Chang, Hengheng Zhang, Zhengsu Chen, Xiaopeng Zhang, and Qi Tian. 2024. QA-LoRA: Quantization- Aware Low-Rank Adaptation of Large Language Models. InThe Twelfth Interna- tional Conference on Learning Representations

    2024

  40. [40]

    Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. 2019. HellaSwag: Can a Machine Really Finish Your Sentence?. InProceedings of the 57th Conference of the Association for Computational Linguistics. 4791–4800

    2019

  41. [41]

    Longteng Zhang, Lin Zhang, Shaohuai Shi, Xiaowen Chu, and Bo Li. 2023. LoRA- FA: Memory-efficient Low-rank Adaptation for Large Language Models Fine- tuning.ArXivabs/2308.03303 (2023)

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  42. [42]

    Qingru Zhang, Minshuo Chen, Alexander Bukharin, Pengcheng He, Yu Cheng, Weizhu Chen, and Tuo Zhao. 2023. Adaptive Budget Allocation for Parameter- Efficient Fine-Tuning. InThe Eleventh International Conference on Learning Rep- resentations

    2023

  43. [43]

    OPT: Open Pre-trained Transformer Language Models

    Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona T. Diab, Xian Li, Xi Victoria Lin, Todor Mihaylov, Myle Ott, Sam Shleifer, Kurt Shuster, Daniel Simig, Punit Singh Koura, Anjali Sridhar, Tianlu Wang, and Luke Zettlemoyer. 2022. OPT: Open Pre-trained Transformer Language Models.ArXivabs/2205.01068 (2022)

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  44. [44]

    Shengming Zhang, Le Zhang, Jingbo Zhou, Zhi Zheng, and Hui Xiong. 2025. LLM- Eraser: Optimizing Large Language Model Unlearning through Selective Pruning. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, V.1. 1960–1971

    2025

  45. [45]

    Yingtao Zhang, Haoli Bai, Haokun Lin, Jialin Zhao, Lu Hou, and Carlo Vittorio Cannistraci. 2024. Plug-and-Play: An Efficient Post-training Pruning Method for Large Language Models. InThe Twelfth International Conference on Learning Representations

    2024

  46. [46]

    Bojia Zi, Xianbiao Qi, Lingzhi Wang, Jianan Wang, Kam-Fai Wong, and Lei Zhang. 2023. Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices.ArXivabs/2309.02411 (2023). A Reconstruction Algorithm of EPTS To better present the pipeline of the EPTS reconstruction phase, we outline the detailed execution procedure in Algorithm 1. Thi...

    work page arXiv 2023