Arya Honarpisheh

Arya Honarpisheh, Mustafa Bozdag, Octavia Camps et al.

State-space models (SSMs) have recently emerged as a compelling alternative to Transformers for sequence modeling tasks. This paper presents a theoretical generalization analysis of selective SSMs, the core architectural component behind the Mamba model. We derive a novel covering number-based generalization bound for selective SSMs, building upon recent theoretical advances in the analysis of Transformer models. Using this result, we analyze how the spectral abscissa of the continuous-time state matrix influences the model's stability during training and its ability to generalize across sequence lengths. We empirically validate our findings on a synthetic majority task, the IMDb sentiment classification benchmark, and the ListOps task, demonstrating how our theoretical insights translate into practical model behavior.

Arya Honarpisheh, Mario Sznaier

This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with the nuclear norm of the Loewner matrix serving as a regularization term. This formulation results in an optimization problem that can be efficiently solved using standard convex optimization techniques. We derive an upper bound on the sampled-frequency complexity of the identification process and subsequently extend this bound to characterize the identification error over all frequencies. A detailed analysis of the sample complexity is provided, along with a thorough interpretation of its terms and dependencies. Finally, the efficacy of the proposed method is demonstrated through an example, and numerical simulations validating the growth rate of the sample complexity bound.