Error-Free Linear Attention is a Free Lunch: Exact Solution from Continuous-Time Dynamics
This provides a new theoretical foundation for scalable linear-time attention models, addressing efficiency and accuracy issues in long-context processing for language modeling applications.
The paper tackles the quadratic cost bottleneck in long-context language models by introducing Error-Free Linear Attention (EFLA), which achieves exact solution from continuous-time dynamics, resulting in lower perplexity and superior benchmark performance compared to DeltaNet without extra parameters.
Linear-time attention and State Space Models (SSMs) promise to solve the quadratic cost bottleneck in long-context language models employing softmax attention. We introduce Error-Free Linear Attention (EFLA), a numerically stable, full parallelism and generalized formulation of the delta rule. Specifically, we formulate the online learning update as a continuous-time dynamical system and prove that its exact solution is not only attainable but also computable in linear time with full parallelism. By leveraging the rank-1 structure of the dynamics matrix, we directly derive the exact closed-form solution effectively. This attention mechanism is theoretically free from error accumulation, perfectly capturing the continuous dynamics while preserving the linear-time complexity. Through an extensive suite of experiments, we show that EFLA enables robust performance in noisy environments, achieving lower language modeling perplexity and superior downstream benchmark performance than DeltaNet without introducing additional parameters. Our work provides a new theoretical foundation for building high-fidelity, scalable linear-time attention models.