arXiv Machine Learning By Luca Herranz-Celotti, Vincent Guigue

RunningTensor: Generalizing Linear Attention to Higher-Order Recurrent States

Read the original on arXiv Machine Learning →

RunningTensor generalizes linear attention and state‑space models by extending the recurrent memory from a second‑order tensor (matrix) to an order‑o tensor. The memory is updated via a rank‑1 outer product and read by contracting with o‑1 vector queries, with order‑2 recovering linear attention. Experiments on synthetic associative recall and real language tasks show that RunningTensor improves memory capacity from O(W²) to O(Wᵒ) and outperforms existing baselines.

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