Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12602 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we introduce Exact Flow Linear Attention~(EFLA), an exact-flow formulation of delta-rule linear attention. We show that the delta-rule update can be interpreted as an explicit Euler discretization of an underlying continuous-time system. EFLA replaces this first-order update with the exact closed-form flow. By exploiting the rank-1 structure of the dynamics matrix, both the matrix exponential and the input integral collapse to a simple update that preserves delta-rule linear attention's algebraic structure, parameter count, linear-time complexity, and chunkwise parallelism. This attention mechanism removes the Euler discretization error of the delta-rule dynamics without introducing additional parameters. Experiments on robustness tests, language modeling benchmarks, and the MAD synthetic benchmark show that EFLA improves stability under corrupted and high-energy inputs, reduces perplexity, and achieves stronger downstream performance compared to SSM and Euler-style baselines. These results establish exact-flow integration as a principled and scalable update mechanism for delta-rule linear attention.