GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling

Code

• github.com/tobiaskatsch/GateLoop
  Officialjax★ 30
• github.com/axrwl/gateloop
  jax★ 1
• github.com/fabianwinter93/JAX/tree/main/GateLoop
  jax★ 0

Abstract

Linear Recurrence has proven to be a powerful tool for modeling long sequences efficiently. In this work, we show that existing models fail to take full advantage of its potential. Motivated by this finding, we develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Utilizing this theoretical advance, GateLoop empirically outperforms existing models for auto-regressive language modeling. Our method comes with a low-cost O(l) recurrent mode and an efficient O(l _2 l) parallel mode making use of highly optimized associative scan implementations. Furthermore, we derive an O(l^2) surrogate attention mode, revealing remarkable implications for Transformer and recently proposed architectures. Specifically, we prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

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Benchmark Results

Reproductions