8 papers
Extracting Algorithms in Pre-trained LLMs: A Case on Hidden Markov Models
Yijia Dai, Zhaolin Gao, Yahya Sattar +2
Large language models (LLMs) display a striking ability to predict next observations from Hidden Markov Models (HMMs) via in-context learning (ICL), but the algorithm underlying th…
Two-Layer Linear Auto-Regressive Models Estimate Latent States
Yahya Sattar, Sunmook Choi, Leo Maynard-Zhang +3
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 op…
Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control
Daniel Cao, Beixi Du, Andrew Lowitt +3
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observat…
Pre-trained Large Language Models Learn Hidden Markov Models In-context
Yijia Dai, Zhaolin Gao, Yahya Sattar +2
Hidden Markov Models (HMMs) are foundational tools for modeling sequential data with latent Markovian structure, yet fitting them to real-world data remains computationally challen…
Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observations
Yahya Sattar, Sunmook Choi, Yassir Jedra +2
We consider the problem of controlling a linear dynamical system from bilinear observations with minimal quadratic cost. Despite the similarity of this problem to standard linear q…
Finite Sample Identification of Partially Observed Bilinear Dynamical Systems
Yahya Sattar, Yassir Jedra, Maryam Fazel +1
We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output s…