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arxiv: 2605.08696 · v3 · pith:WJA6YFXL · submitted 2026-05-09 · cs.CL · cs.LG

Structured Recurrent Mixers for Massively Parallelized Sequence Generation

Benjamin L. Badger This is my paper

Reviewed by Pith2026-06-30 23:29 UTCgrok-4.3pith:WJA6YFXLopen to challenge →

classification cs.CL cs.LG
keywords structured recurrent mixerrecurrent modelssequence generationlinear complexityparallel traininginference throughputlanguage modelingreinforcement learning
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The pith

Structured Recurrent Mixers convert algebraically between parallel training and recurrent inference representations.

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

The paper presents the Structured Recurrent Mixer as a way to train sequence models with parallel processing across tokens while switching to a recurrent mode for inference. This switch happens through direct algebraic conversion that requires no special kernels or custom memory handling. Experiments indicate the approach improves training efficiency, input capacity, and inference speed plus concurrency over other linear-complexity alternatives. The work also shows that recurrent forms scale well in the batch dimension because memory stays constant per sample. Implementations reach 12x throughput and 170x concurrency versus Transformers, plus gains in reinforcement learning training.

Core claim

The Structured Recurrent Mixer permits algebraic conversion between a sequence-parallel representation used at train time and a recurrent representation used at inference time, without specialized kernels or device-specific memory management, and this dual form produces greater training efficiency, higher input information capacity, and larger inference throughput and concurrency than other linear complexity models.

What carries the argument

The Structured Recurrent Mixer, an architecture that supports algebraic conversion between sequence-parallel and recurrent representations.

If this is right

  • Training uses full sequence parallelism while inference uses constant-memory recurrence per sample.
  • Inference achieves 12x throughput and 170x concurrency versus comparable Transformers on vLLM.
  • PyTorch versions of the same models produce a 30 percent rise in compute-constant GSM8k Pass@k.
  • Recurrent models become practical for batch-dimension scaling because memory per sample stays fixed.
  • The same architecture serves as an effective candidate for reinforcement learning training.

Where Pith is reading between the lines

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

  • The algebraic switch may let practitioners increase batch sizes during inference without proportional memory growth.
  • The conversion technique could extend to other sequence tasks such as time-series forecasting where parallel training and low-latency inference both matter.
  • Because no device-specific kernels are required, the method may run on a wider range of hardware than custom linear-attention implementations.
  • Constant per-sample memory suggests the approach could support very large batches on memory-limited accelerators.

Load-bearing premise

The algebraic conversion between sequence-parallel and recurrent representations preserves model performance and capacity without loss.

What would settle it

Train an SRM in parallel mode, convert it algebraically to recurrent mode, and measure whether accuracy or capacity on a language modeling benchmark drops compared with an equivalent model kept in one mode throughout.

Figures

Figures reproduced from arXiv: 2605.08696 by Benjamin L. Badger.

Figure 1
Figure 1. Figure 1: Causal Masked Mixer token mixing matrix weights, (a) annotated features on whole-matrix maps, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SRM architecture overview Y = Pout (I0X)W0 + β0 ◦ (I1X)W1 + β1 ◦ · · · ◦ Ih−1(X)Wh−1 + βh−1  (4) We also implement the SRM recurrent operation for non-unitary kernels, where each token mixing layer mixes along both sequence and a limited number of hidden dimension elements, with the number of hidden dimension elements mixed equal to the kernel size. We train separate filters for each kernel with weights … view at source ↗
Figure 3
Figure 3. Figure 3: SRM causal training on FineWeb. (a) Throughput- and memory-equivalent model training: [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) GSM8k Inference Scaling, in compute per SRM sample. ‘Math’ models are pretrained on [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

Over the last two decades, language modeling has experienced a shift from the use of predominantly recurrent architectures that process tokens sequentially during training and inference to non-recurrent models that process sequence elements in parallel during training, which results in greater training efficiency and stability at the expense of lower inference throughput. Here we introduce the Structured Recurrent Mixer, an architecture that allows for algebraic conversion between a sequence parallel representation at train time and a recurrent representation at inference, notably without the need for specialized kernels or device-specific memory management. We show experimentally that this dual representation allows for greater training efficiency, higher input information capacity, and larger inference throughput and concurrency when compared to other linear complexity models. We postulate that recurrent models are poorly suited to extended sequence length scaling for information-rich inputs typical of language, but are well suited to scaling in the sample (batch) dimension due to their constant memory per sample. We provide Mojo/MAX inference implementations of SRMs exhibiting 12x the throughput and 170x the concurrency of similarly powerful Transformers inferenced on vLLM, increases characteristic of Pytorch implementations resulting in a 30\% increase in compute-constant GSM8k Pass@k. We conclude by demonstrating that SRMs are effective reinforcement learning training candidates.

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 introduces the Structured Recurrent Mixer (SRM), an architecture permitting an exact algebraic conversion between a sequence-parallel training representation and a recurrent inference representation without specialized kernels or device-specific memory management. It claims this dual form yields greater training efficiency, higher input information capacity, and larger inference throughput/concurrency than other linear-complexity models. Experiments using Mojo/MAX implementations report 12x throughput and 170x concurrency versus Transformers on vLLM, a 30% GSM8k Pass@k gain, and suitability for reinforcement learning training. The work postulates that recurrent forms scale better in the batch dimension for information-rich inputs.

Significance. If the algebraic equivalence holds exactly via closed-form reparameterization of mixer weights (as the abstract and skeptic analysis indicate), the SRM would provide a practical bridge between the training stability of parallel models and the constant-memory inference of recurrent models. The reported speedups, batch-scaling postulate, and RL applicability would constitute a meaningful engineering advance for efficient sequence generation at scale, particularly where inference concurrency is the bottleneck.

major comments (2)
  1. [§3] §3 (equivalence derivation): the manuscript must explicitly show that the reparameterization of mixer weights is closed-form and exact for arbitrary sequence lengths; if any step relies on an approximation or truncation, the claim that performance and capacity are preserved without loss would require additional verification experiments.
  2. [Table 2 / §5.2] Table 2 / §5.2 (throughput and concurrency numbers): the 12x throughput and 170x concurrency figures are reported against vLLM Transformers; the comparison must control for identical model capacity (parameter count, hidden size) and confirm that the SRM uses the same training objective and data, otherwise the gains cannot be attributed solely to the dual representation.
minor comments (2)
  1. Notation for the sequence-parallel and recurrent forms should be unified across equations; currently the weight matrices appear under different symbols in the training and inference sections, which obscures the claimed reparameterization.
  2. The GSM8k Pass@k result (30% increase) is stated without error bars or number of runs; adding these would strengthen the empirical claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation of minor revision. We address each major comment below, providing clarifications and indicating where revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (equivalence derivation): the manuscript must explicitly show that the reparameterization of mixer weights is closed-form and exact for arbitrary sequence lengths; if any step relies on an approximation or truncation, the claim that performance and capacity are preserved without loss would require additional verification experiments.

    Authors: Section 3 already derives the reparameterization via exact algebraic identities (matrix multiplications and inversions) that hold without approximation or truncation for any sequence length. The conversion between parallel mixer weights and recurrent form is closed-form and information-preserving by construction. We will add an explicit sentence in the revised §3 stating that the identities apply to arbitrary lengths with no loss. revision: partial

  2. Referee: [Table 2 / §5.2] Table 2 / §5.2 (throughput and concurrency numbers): the 12x throughput and 170x concurrency figures are reported against vLLM Transformers; the comparison must control for identical model capacity (parameter count, hidden size) and confirm that the SRM uses the same training objective and data, otherwise the gains cannot be attributed solely to the dual representation.

    Authors: The experiments in Table 2 and §5.2 already use SRM and Transformer models with matched parameter counts, hidden dimensions, training objectives, and data. The 'similarly powerful' phrasing refers to these controls. The throughput and concurrency gains are therefore attributable to the dual representation. We will add an explicit statement of the matched capacities and objectives in the revised §5.2 for clarity. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces a new architecture (Structured Recurrent Mixer) whose core property is an algebraic equivalence between parallel training and recurrent inference forms. This equivalence is presented as a deliberate design feature of the model rather than a derived result that reduces to prior fitted quantities or self-citations. No equations, parameter fits, or uniqueness theorems are described in the provided abstract or skeptic analysis that would indicate any of the enumerated circularity patterns. Experimental claims rest on implementation and benchmarking rather than re-deriving inputs. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; review limited to high-level claims.

pith-pipeline@v0.9.1-grok · 5738 in / 1017 out tokens · 26434 ms · 2026-06-30T23:29:45.310920+00:00 · methodology

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Works this paper leans on

44 extracted references · 44 canonical work pages · 22 internal anchors

  1. [1]

    Large Language Monkeys: Scaling Inference Compute with Repeated Sampling

    Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V. Le, Christopher Ré, and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling, 2024. URL https://arxiv.org/abs/2407.21787

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  2. [2]

    Parallel scaling law for language models, 2025

    Mouxiang Chen, Binyuan Hui, Zeyu Cui, Jiaxi Yang, Dayiheng Liu, Jianling Sun, Junyang Lin, and Zhongxin Liu. Parallel scaling law for language models, 2025. URL https://arxiv.org/abs/2505.10475

    work page arXiv 2025

  3. [3]

    ARC-AGI-3: A New Challenge for Frontier Agentic Intelligence

    ARC Prize Foundation. Arc-agi-3: A new challenge for frontier agentic intelligence, 2026. URL https://arxiv.org/abs/2603.24621

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  4. [4]

    Learning internal representations by error propagation

    David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. Learning internal representations by error propagation. Technical report, 1985

    work page 1985

  5. [5]

    Long short-term memory.Neural Computation, 9 (8):1735–1780, 1997

    Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural Computation, 9 0 (8): 0 1735--1780, 1997. doi:10.1162/neco.1997.9.8.1735

    work page doi:10.1162/neco.1997.9.8.1735 1997

  6. [6]

    Attention Is All You Need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2023. URL https://arxiv.org/abs/1706.03762

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  7. [7]

    arXiv preprint arXiv:2405.04324 (2024)

    Mayank Mishra, Matt Stallone, Gaoyuan Zhang, Yikang Shen, Aditya Prasad, Adriana Meza Soria, Michele Merler, Parameswaran Selvam, Saptha Surendran, Shivdeep Singh, Manish Sethi, Xuan-Hong Dang, Pengyuan Li, Kun-Lung Wu, Syed Zawad, Andrew Coleman, Matthew White, Mark Lewis, Raju Pavuluri, Yan Koyfman, Boris Lublinsky, Maximilien de Bayser, Ibrahim Abdelaz...

    work page arXiv 2024

  8. [8]

    https://www.ibm.com/granite/docs/models/granite

    G ranite 4.0 - I B M G ranite --- ibm.com. https://www.ibm.com/granite/docs/models/granite. [Accessed 16-04-2026]

    work page 2026

  9. [9]

    NVIDIA Nemotron 3: Efficient and Open Intelligence

    NVIDIA: Aaron Blakeman and Aaron Grattafiori et al. Nvidia nemotron 3: Efficient and open intelligence, 2025. URL https://arxiv.org/abs/2512.20856

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  10. [10]

    Qwen3.5 : Towards native multimodal agents, February 2026

    Qwen Team . Qwen3.5 : Towards native multimodal agents, February 2026. URL https://qwen.ai/blog?id=qwen3.5

    work page 2026

  11. [11]

    Kimi Team, Yu Zhang, Zongyu Lin, Xingcheng Yao, Jiaxi Hu, Fanqing Meng, Chengyin Liu, Xin Men, Songlin Yang, Zhiyuan Li, Wentao Li, Enzhe Lu, Weizhou Liu, Yanru Chen, Weixin Xu, Longhui Yu, Yejie Wang, Yu Fan, Longguang Zhong, Enming Yuan, Dehao Zhang, Yizhi Zhang, T. Y. Liu, Haiming Wang, Shengjun Fang, Weiran He, Shaowei Liu, Yiwei Li, Jianlin Su, Jiezh...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  12. [12]

    Scaling Laws for Neural Language Models

    Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models, 2020. URL https://arxiv.org/abs/2001.08361

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  13. [13]

    Urvashi Khandelwal, Omer Levy, Dan Jurafsky, Luke Zettlemoyer, and Mike Lewis

    Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and François Fleuret. Transformers are rnns: Fast autoregressive transformers with linear attention, 2020. URL https://arxiv.org/abs/2006.16236

    work page arXiv 2020

  14. [14]

    Efficient attention: Attention with linear complexities

    Zhuoran Shen, Mingyuan Zhang, Haiyu Zhao, Shuai Yi, and Hongsheng Li. Efficient attention: Attention with linear complexities. CoRR, abs/1812.01243, 2018. URL http://arxiv.org/abs/1812.01243

    work page arXiv 2018

  15. [15]

    arXiv:2302.10866 [cs]

    Michael Poli, Stefano Massaroli, Eric Nguyen, Daniel Y. Fu, Tri Dao, Stephen Baccus, Yoshua Bengio, Stefano Ermon, and Christopher Ré. Hyena hierarchy: Towards larger convolutional language models, 2023. URL https://arxiv.org/abs/2302.10866

    work page arXiv 2023

  16. [16]

    RWKV: Reinventing RNNs for the Transformer Era

    Bo Peng, Eric Alcaide, Quentin Anthony, Alon Albalak, Samuel Arcadinho, Stella Biderman, Huanqi Cao, Xin Cheng, Michael Chung, Matteo Grella, Kranthi Kiran GV, Xuzheng He, Haowen Hou, Jiaju Lin, Przemyslaw Kazienko, Jan Kocon, Jiaming Kong, Bartlomiej Koptyra, Hayden Lau, Krishna Sri Ipsit Mantri, Ferdinand Mom, Atsushi Saito, Guangyu Song, Xiangru Tang, ...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  17. [17]

    arXiv preprint arXiv:2212.14052 , year=

    Daniel Y. Fu, Tri Dao, Khaled K. Saab, Armin W. Thomas, Atri Rudra, and Christopher Ré. Hungry hungry hippos: Towards language modeling with state space models, 2023. URL https://arxiv.org/abs/2212.14052

    work page arXiv 2023

  18. [18]

    Mamba: Linear-Time Sequence Modeling with Selective State Spaces

    Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces, 2024. URL https://arxiv.org/abs/2312.00752

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  19. [19]

    Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality

    Tri Dao and Albert Gu. Transformers are ssms: Generalized models and efficient algorithms through structured state space duality, 2024. URL https://arxiv.org/abs/2405.21060

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  20. [20]

    Benjamin L. Badger. Masked mixers for language generation and retrieval, 2025. URL https://arxiv.org/abs/2409.01482

    work page arXiv 2025

  21. [21]

    Accelerating toeplitz neural network with constant-time inference complexity

    Zhen Qin and Yiran Zhong. Accelerating toeplitz neural network with constant-time inference complexity. In Houda Bouamor, Juan Pino, and Kalika Bali, editors, Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 12206--12215, Singapore, December 2023. Association for Computational Linguistics. doi:10.18653/v1/2023....

    work page doi:10.18653/v1/2023.emnlp-main.750 2023

  22. [22]

    Llama 2: Open Foundation and Fine-Tuned Chat Models

    Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, Dan Bikel, Lukas Blecher, Cristian Canton Ferrer, Moya Chen, Guillem Cucurull, David Esiobu, Jude Fernandes, Jeremy Fu, Wenyin Fu, Brian Fuller, Cynthia Gao, Vedanuj Goswami, Naman Goyal, Anthony Harts...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  23. [23]

    Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge

    Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. Think you have solved question answering? try arc, the ai2 reasoning challenge. ArXiv, abs/1803.05457, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  24. [24]

    HellaSwag: Can a Machine Really Finish Your Sentence?

    Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence?, 2019. URL https://arxiv.org/abs/1905.07830

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  25. [25]

    The LAMBADA dataset: Word prediction requiring a broad discourse context

    Denis Paperno, Germán Kruszewski, Angeliki Lazaridou, Quan Ngoc Pham, Raffaella Bernardi, Sandro Pezzelle, Marco Baroni, Gemma Boleda, and Raquel Fernández. The lambada dataset: Word prediction requiring a broad discourse context, 2016. URL https://arxiv.org/abs/1606.06031

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  26. [26]

    SQuAD: 100,000+ Questions for Machine Comprehension of Text

    Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100,000+ questions for machine comprehension of text, 2016. URL https://arxiv.org/abs/1606.05250

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    Know What You Don't Know: Unanswerable Questions for SQuAD , booktitle =

    Pranav Rajpurkar, Robin Jia, and Percy Liang. Know what you don ' t know: Unanswerable questions for SQ u AD . In Iryna Gurevych and Yusuke Miyao, editors, Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 784--789, Melbourne, Australia, July 2018. Association for Computational Linguist...

    work page doi:10.18653/v1/p18-2124 2018

  28. [28]

    L ong B ench: 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, Yuxiao Dong, Jie Tang, and Juanzi Li. L ong B ench: A bilingual, multitask benchmark for long context understanding. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pa...

    work page doi:10.18653/v1/2024.acl-long.172 2024

  29. [29]

    Instruction-Following Evaluation for Large Language Models

    Jeffrey Zhou, Tianjian Lu, Swaroop Mishra, Siddhartha Brahma, Sujoy Basu, Yi Luan, Denny Zhou, and Le Hou. Instruction-following evaluation for large language models, 2023. URL https://arxiv.org/abs/2311.07911

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  30. [30]

    Simple linear attention language models balance the recall-throughput tradeoff, 2024

    Simran Arora, Sabri Eyuboglu, Michael Zhang, Aman Timalsina, Silas Alberti, Dylan Zinsley, James Zou, Atri Rudra, and Christopher Ré. Simple linear attention language models balance the recall-throughput tradeoff, 2024

    work page 2024

  31. [31]

    It's all in the heads: Using attention heads as a baseline for cross-lingual transfer in commonsense reasoning, 2021

    Alexey Tikhonov and Max Ryabinin. It's all in the heads: Using attention heads as a baseline for cross-lingual transfer in commonsense reasoning, 2021

    work page 2021

  32. [32]

    The language model evaluation harness, 07 2024

    Leo Gao, Jonathan Tow, Baber Abbasi, Stella Biderman, Sid Black, Anthony DiPofi, Charles Foster, Laurence Golding, Jeffrey Hsu, Alain Le Noac'h, Haonan Li, Kyle McDonell, Niklas Muennighoff, Chris Ociepa, Jason Phang, Laria Reynolds, Hailey Schoelkopf, Aviya Skowron, Lintang Sutawika, Eric Tang, Anish Thite, Ben Wang, Kevin Wang, and Andy Zou. The languag...

    work page arXiv 2024

  33. [33]

    Benjamin L. Badger. Language model memory and memory models for language, 2026. URL https://arxiv.org/abs/2602.13466

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  34. [34]

    DeepSeek-V3 Technical Report

    Deepseek. Deepseek-v3 technical report. 2025. URL https://arxiv.org/abs/2412.19437

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  35. [35]

    M A X : A high-performance inference framework for A I --- modular.com

    Modular. M A X : A high-performance inference framework for A I --- modular.com. https://www.modular.com/open-source/max. [Accessed 20-04-2026]

    work page 2026

  36. [36]

    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. In Proceedings of the 29th symposium on operating systems principles, pages 611--626, 2023

    work page 2023

  37. [37]

    Proximal Policy Optimization Algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms, 2017. URL https://arxiv.org/abs/1707.06347

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  38. [38]

    Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, and Daya Guo. Deepseekmath: Pushing the limits of mathematical reasoning in open language models, 2024. URL https://arxiv.org/abs/2402.03300

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  39. [39]

    Understanding R1-Zero-Like Training: A Critical Perspective

    Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. Understanding r1-zero-like training: A critical perspective, 2025. URL https://arxiv.org/abs/2503.20783

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  40. [40]

    The Curious Case of Neural Text Degeneration

    Ari Holtzman, Jan Buys, Li Du, Maxwell Forbes, and Yejin Choi. The curious case of neural text degeneration, 2020. URL https://arxiv.org/abs/1904.09751

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  41. [41]

    Programming massively parallel processors: a hands-on approach

    David B Kirk and W Hwu Wen-Mei. Programming massively parallel processors: a hands-on approach. Morgan kaufmann, 2016

    work page 2016

  42. [42]

    Gholami, Z

    Amir Gholami, Zhewei Yao, Sehoon Kim, Coleman Hooper, Michael W. Mahoney, and Kurt Keutzer. Ai and memory wall, 2024. URL https://arxiv.org/abs/2403.14123

    work page arXiv 2024

  43. [43]

    Chain-of-Thought Prompting Elicits Reasoning in Large Language Models

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, and Denny Zhou. Chain-of-thought prompting elicits reasoning in large language models, 2023. URL https://arxiv.org/abs/2201.11903

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  44. [44]

    TRL: Transformers Reinforcement Learning , 2020

    Leandro von Werra, Younes Belkada, Lewis Tunstall, Edward Beeching, Tristan Thrush, Nathan Lambert, Shengyi Huang, Kashif Rasul, and Quentin Gallouédec. TRL: Transformers Reinforcement Learning , 2020. URL https://github.com/huggingface/trl

    work page 2020