Learning in the Recurrent State: Gradient Descent with Linear Recurrent Networks

📰 ArXiv cs.AI

Learn to apply gradient descent with linear recurrent networks for efficient sequence modeling

advanced Published 16 Jun 2026
Action Steps
  1. Implement a diagonal recurrent state in your LRNN model to enable linear-time sequence modeling
  2. Apply multiplicative readout to the recurrent state for supervised learning
  3. Configure a short sliding-window cross-product self-attention update for the recurrent state
  4. Use gradient descent to optimize the model parameters in-context
  5. Test the model on a sequence modeling task to evaluate its performance
Who Needs to Know This

ML researchers and engineers working on sequence modeling tasks can benefit from this technique to improve model performance and efficiency

Key Insight

💡 Linear recurrent networks with diagonal recurrent state and multiplicative readout can be optimized using gradient descent for improved performance

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🚀 Efficient sequence modeling with linear recurrent networks using gradient descent!

Key Takeaways

Learn to apply gradient descent with linear recurrent networks for efficient sequence modeling

Full Article

Title: Learning in the Recurrent State: Gradient Descent with Linear Recurrent Networks

Abstract:
arXiv:2410.11687v3 Announce Type: replace-cross Abstract: Linear recurrent networks (LRNNs) offer linear-time sequence modeling, but standard recurrent updates do not directly expose the supervised products needed for in-context gradient descent. We propose a sufficient constructive inductive bias for LRNNs: equip a diagonal recurrent state with multiplicative readout and a short sliding-window cross-product self-attention update. The resulting architecture, Gradient-based Recurrent In-context L
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