Issue #100 Theory Edwin Dong, Anurag Shinde
Kalman State Space Models, Simply Explained
Free editionPRO edition
This week’s PRO issue includes a Colab notebook, diving into the fundamental concepts of the KOSS paper. We cover Kalman filtering, IDS, and spectral filtration. Please do read the full article before attempting the code tutorial.
As always, the code in this issue can be executed on a normal home PC and does not require a large amount of VRAM.
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For decades, the Kalman filter has been widely used for estimation theory, providing a mathematically elegant method to track hidden states through noisy observations.
At the same time, deep sequence models have evolved from simple recurrent networks to transformer architectures and, most recently, selective state space models.
The Kalman area and the sequence model path have largely developed side-by-side, sometimes borrowing from each other but never fully combining.
The Kalman-Optimal Selective State Space Model (KOSS) (Wang et al., 2025) changes that.
KOSS offers a strong mathematical combination of these two areas.
By using Kalman filters to estimate what important details to remember in a sequence (the selection problem), it’s able to be grounded in mathematics rather than heuristic design choices.
The result is a model that is not only theoretically motivated but practically better.
It consistently outperforms state-of-the-art baselines across nine forecasting benchmarks while using fewer parameters and less memory than its competitors.
This edition is for PRO members.
