GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling

• URL: http://arxiv.org/abs/2311.01927v2
• Date: Sat, 27 Jan 2024 14:52:52 GMT
• Title: GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling
• Authors: Tobias Katsch
• Abstract summary: We develop GateLoop, a sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet. GateLoop empirically outperforms existing models for auto-regressive language modeling. We prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $O(l \log_{2} l)$ 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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