Parallelizing non-linear sequential models over the sequence length
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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.
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Citing papers per year: 2024: 6; 2025: 18; 2026: 21.
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- 2025Accelerated Training through Iterative Gradient Propagation Along the Residual Path28 Jan 2025
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- 2025Parallelization of Non-linear State-Space Models: Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modeling27 May 2025
- 2025Fixed-Point RNNs: Interpolating from Diagonal to Dense13 Mar 2025
- 2024Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues19 Nov 2024
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- 2024Real-Time Recurrent Learning using Trace Units in Reinforcement Learning2 Sep 2024
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- 2025It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimizationcited by 64
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- 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 18
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- 2026GradLev: Token-Parallel Test-Time Training Via Costate Prediction28 Sep 2026
- 2026HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps26 Sep 2026
- 2026Length-Independent State Tracking Under a Parallel Scan26 Sep 2026
- 2026Liquid Gated Attention31 Aug 2026
- 2026Proteus: Incremental Memory Activation for Long-Context Sequence Modeling17 Aug 2026
- 2026Maglev: Sliding Recurrent Memory3 Aug 2026
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