Liquid Gated Attention

arXiv:2608.30695v1 Announce Type: new Abstract: Real-world time series often exhibit irregular sampling and extended temporal horizons, requiring models to capture continuous-time dynamics across arbitrary intervals without prohibitive scaling costs. Discrete-time methods collapse variable time intervals into static positional steps; solver-dependent continuous-time models preserve temporal structure but rely on sequential integration, precluding parallelization; and solver-free approximations avoid this cost yet none couples observed time intervals with input-driven state modulation. We propose Liquid Gated Attention (LGA), a solver-free parallel temporal operator. By parameterizing an input-driven gating mechanism with observed time intervals, LGA introduces a continuous-time inductive bias and formulates hidden state evolution as a fast-weight associative memory, enabling parallel computation across the temporal dimension. Using matrix associativity in non-causal encoding and a prefix scan in causal encoding, LGA attains linear temporal complexity in sequence length in both modes. A sequence-level normalization bounds cumulative temporal decay for stable long-horizon optimization. Building on LGA, we instantiate LFormer, a modular backbone for continuous-time representation learning. Across six tasks and sixteen datasets spanning up to 17,984 steps, LFormer demonstrates long-range dependency modeling, fine-grained state tracking, and trajectory reconstruction from sparse and noisy observations, while delivering competitive performance against state-of-the-art discrete-time and continuous-time baselines with linear scaling efficiency.

Abstract:Real-world time series often exhibit irregular sampling and extended temporal horizons, requiring models to capture continuous-time dynamics across arbitrary intervals without prohibitive scaling costs. Discrete-time methods collapse variable time intervals into static positional steps; solver-dependent continuous-time models preserve temporal structure but rely on sequential integration, precluding parallelization; and solver-free approximations avoid this cost yet none couples observed time intervals with input-driven state modulation. We propose Liquid Gated Attention (LGA), a solver-free parallel temporal operator. By parameterizing an input-driven gating mechanism with observed time intervals, LGA introduces a continuous-time inductive bias and formulates hidden state evolution as a fast-weight associative memory, enabling parallel computation across the temporal dimension. Using matrix associativity in non-causal encoding and a prefix scan in causal encoding, LGA attains linear temporal complexity in sequence length in both modes. A sequence-level normalization bounds cumulative temporal decay for stable long-horizon optimization. Building on LGA, we instantiate LFormer, a modular backbone for continuous-time representation learning. Across six tasks and sixteen datasets spanning up to 17,984 steps, LFormer demonstrates long-range dependency modeling, fine-grained state tracking, and trajectory reconstruction from sparse and noisy observations, while delivering competitive performance against state-of-the-art discrete-time and continuous-time baselines with linear scaling efficiency.

Machine Learning (cs.LG)

arXiv:2608.30695 [cs.LG]

(or arXiv:2608.30695v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.30695 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Liquid Gated Attention

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