mlsanityData to 14 Oct 2026

Parallelizing non-linear sequential models over the sequence length

arXiv 2309.12252 ↗First posted 21 Sep 2023cs.LG cs.DC physics.comp-phcited by 45

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Abstract (arXiv)

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought sequential models could not be parallelized. We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy. The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures. Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results. Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples. By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). Builds on 44 of its 66 references that are in the map. First posted on arXiv 21 Sep 2023.

Builds on

44 of 66 references.

References · 44

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32 more
  1. 2021Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layerscited by 608
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 18; 2026: 21.

45 papers.

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  1. 2024Gated Delta Networks: Improving Mamba2 with Delta Rulecited by 532
  2. 2024Unlocking State-Tracking in Linear RNNs Through Negative Eigenvaluescited by 101
  3. 2025ATLAS: Learning to Optimally Memorize the Context at Test Timecited by 66
  4. 2025It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimizationcited by 64
  5. 2024Towards Scalable and Stable Parallelization of Nonlinear RNNscited by 38
  6. 2024Accelerating Parallel Sampling of Diffusion Modelscited by 30
  7. 2025Implicit Language Models are RNNs: Balancing Parallelization and Expressivitycited by 22
  8. 2025Lattice: Learning to Efficiently Compress the Memorycited by 19
  9. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 18
  10. 2025ParaRNN: Unlocking Parallel Training of Nonlinear RNNs for Large Language Modelscited by 15
  11. 2026Memory Caching: RNNs with Growing Memorycited by 15
  12. 2024Real-Time Recurrent Learning using Trace Units in Reinforcement Learningcited by 10
33 more
  1. 2025Parallelization of Non-linear State-Space Models: Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modelingcited by 10
  2. 2024Rethinking Transformers in Solving POMDPscited by 9
  3. 2025TNT: Improving Chunkwise Training for Test-Time Memorizationcited by 8
  4. 2025Predictability Enables Parallelization of Nonlinear State Space Modelscited by 7
  5. 2026Learning State-Tracking from Code Using Linear RNNscited by 6
  6. 2025Fixed-Point RNNs: Interpolating from Diagonal to Densecited by 5
  7. 2025Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexitycited by 5
  8. 2025Trellis: Learning to Compress Key-Value Memory in Attention Modelscited by 5
  9. 2026Pretraining Recurrent Networks without Recurrencecited by 5
  10. 2025Accelerated Training through Iterative Gradient Propagation Along the Residual Pathcited by 4
  11. 2025A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systemscited by 4
  12. 2026Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modelingcited by 4
  13. 2026Parallelizable memory recurrent unitscited by 3
  14. 2026Maglev: Sliding Recurrent Memorycited by 3
  15. 2025PCM : Picard Consistency Model for Fast Parallel Sampling of Diffusion Modelscited by 2
  16. 2025Context-Selective State Space Models: Feedback is All You Needcited by 2
  17. 2025Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processescited by 1
  18. 2026SNLP: Layer-Parallel Inference via Structured Newton Correctionscited by 1
  19. 2026Proteus: Incremental Memory Activation for Long-Context Sequence Modelingcited by 1
  20. 2025Generalized Orders of Magnitude for Scalable, Parallel, High-Dynamic-Range Computationcited by 0
  21. 2026State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoningcited by 0
  22. 2026LBI: Parallel Scan Backpropagation via Latent Bounded Interfacescited by 0
  23. 2026Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstructioncited by 0
  24. 2026Parallel Recursive LSTMcited by 0
  25. 2026Universal Time Series Generation with Neural Controlled Differential Equationscited by 0
  26. 2026Layer-Parallel Inference Reduces Encrypted Nonlinear Depth in Transformerscited by 0
  27. 2026Liquid Gated Attentioncited by 0
  28. 2026Length-Independent State Tracking Under a Parallel Scancited by 0
  29. 2026HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Mapscited by 0
  30. 2026GradLev: Token-Parallel Test-Time Training Via Costate Predictioncited by 0
  31. 2026Riccati State Space Models: Non-iterative Parallelization for Nonlinear Sequence Modelingcited by 0
  32. 2026Pretraining Latent Information Feedback Transformers with Teacher Supervisioncited by 0
  33. 2026Switching Linear Attentioncited by 0