TL;DR
Auto-regressive models struggle to explain how they learn hidden representations from sequential data. This work introduces two-layer linear auto-regressive models that approximate Kalman filtering, a method for estimating hidden states in dynamic systems.
✦ Why It Matters
Engineers can leverage these findings to improve model design for estimating hidden states in dynamic systems.
Key Takeaways
How It Works
The two-layer linear auto-regressive model learns to estimate hidden states by approximating the Kalman filter through empirical risk minimization. This process involves training the model on data from partially observed linear dynamical systems, allowing it to capture the underlying state dynamics without explicit knowledge of them.
The optimization landscape is favorable, ensuring that all stationary points lead to effective solutions.
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