Two-Layer Linear Auto-Regressive Models Estimate Latent States
Quick summary
arXiv:2606.12691v2 Announce Type: replace-cross Abstract: Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an open theoretical question. In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering. In particular, we show that the learned hidden representation coincides, up to a similarity transformation, with
Key takeaways
- arXiv:2606.12691v2 Announce Type: replace-cross Abstract: Auto-regressive models have emerged as powerful tools for sequential data, from language to video.
- Understanding how and why these models learn latent representations remains an open theoretical question.
- In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering.
Why it matters
“Two-Layer Linear Auto-Regressive Models Estimate Latent States” illustrates how changes in the AI ecosystem can affect products, workflows and user expectations together. Its lasting significance depends on measurable adoption, cost and safety outcomes.
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