ParallelFlow: Parallelizing Linear Transformers via Flow Discretization
This work addresses the problem of improving efficiency and theoretical understanding in sequence modeling for researchers and practitioners, though it appears incremental as it builds on existing linear attention and state space model concepts.
The paper tackles the analysis of linear attention models by introducing a theoretical framework that decouples temporal dynamics from implementation constraints, enabling the design of new algorithms with provably lower complexity, such as streamlined generalizations and rough paths-inspired methods.
We present a theoretical framework for analyzing linear attention models through matrix-valued state space models (SSMs). Our approach, Parallel Flows, provides a perspective that systematically decouples temporal dynamics from implementation constraints, enabling independent analysis of critical algorithmic components: chunking, parallelization, and information aggregation. Central to this framework is the reinterpretation of chunking procedures as computations of the flows governing system dynamics. This connection establishes a bridge to mathematical tools from rough path theory, opening the door to new insights into sequence modeling architectures. As a concrete application, we analyze DeltaNet in a generalized low-rank setting motivated by recent theoretical advances. Our methods allow us to design simple, streamlined generalizations of hardware-efficient algorithms present in the literature, and to provide completely different ones, inspired by rough paths techniques, with provably lower complexity. This dual contribution demonstrates how principled theoretical analysis can both explain existing practical methods and inspire fundamentally new computational approaches.