Related papers: Stability and Generalization in Looped Transformer…

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped…

This paper investigates the design of a robust fixed-order controller for single-input-single-output (SISO) polytopic systems with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the…

We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…

Theoretical efforts to prove advantages of Transformers in comparison with classical architectures such as feedforward and recurrent neural networks have mostly focused on representational power. In this work, we take an alternative…

Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we…

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…

We consider a nonlinear control system modeled as an ordinary differential equation subject to disturbance, with a state feedback controller parameterized as a feedforward neural network. We propose a framework for training controllers with…

Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…

We discuss the role of monotonicity in enabling numerically tractable modular control design for networked nonlinear systems. We first show that the variational systems of monotone systems can be embedded into positive systems. Utilizing…

We train a linear attention transformer on millions of masked-block matrix completion tasks: each prompt is masked low-rank matrix whose missing block may be (i) a scalar prediction target or (ii) an unseen kernel slice of Nystr\"om…

We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…

Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…

Replicability is essential in science as it allows us to validate and verify research findings. Impagliazzo, Lei, Pitassi and Sorrell (`22) recently initiated the study of replicability in machine learning. A learning algorithm is…

A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…

With the research into development of quadruped robots picking up pace, learning based techniques are being explored for developing locomotion controllers for such robots. A key problem is to generate leg trajectories for continuously…

Normalization layers are a staple in state-of-the-art deep neural network architectures. They are widely believed to stabilize training, enable higher learning rate, accelerate convergence and improve generalization, though the reason for…

This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of…

Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…

Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…