“GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling”, Tobias Katsch2023-11-03 (RNN, self-attention)⁠:

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 log₂ l) parallel mode making use of highly-optimized associative scan implementations.

Furthermore, we derive an 𝒪(l²) 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.