Kalman Linear Attention: A Parallel Bayesian Filtering Approach for Language Models
Researchers introduced Kalman Linear Attention (KLA), a new sequence mixing layer that applies Bayesian filtering principles to language models, achieving linear computational complexity while maintaining parallelizability. The method reparameterizes classical Kalman filters into information form, enabling non-linear per-token updates that remain temporally parallel. KLA demonstrates improved expressivity over existing linear state-space models and matches or exceeds performance of modern alternatives on benchmarks.
A new preprint from arXiv proposes Kalman Linear Attention (KLA), a sequence mixer for language models that combines the efficiency of linear-complexity architectures with probabilistic state tracking through Bayesian filtering. The approach addresses a key limitation of existing state-space models like Mamba and gated linear attention (GLA): their linear state updates constrain expressivity and robust state tracking. By reformulating Kalman filters in information form, the authors show that the recurrent update becomes an associative scan operation—enabling non-linear (Möbius/precision) recursions while preserving temporal parallelization. The method carries explicit uncertainty estimates about model state and solves permutation-composition tasks that linear SSMs cannot. Evaluated at billion-token scale, KLA matches or improves performance on synthetic token-manipulation and zero-shot commonsense benchmarks, positioning it as a practical drop-in replacement for existing sequence mixers.
What's missing
The preprint does not discuss computational memory overhead or wall-clock training time comparisons against baseline methods, focusing primarily on theoretical complexity and benchmark accuracy. Practical deployment considerations and inference latency on standard hardware are not addressed.
What different sources said
- arXiv cs.LGCenter
Kalman Linear Attention: Parallel Bayesian Filtering For Efficient Language Modelling and State Tracking
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