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Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…

Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain…

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

Accurate and efficient simulation of modern robots remains challenging due to their high degrees of freedom and intricate mechanisms. Neural simulators have emerged as a promising alternative to traditional analytical simulators, capable of…

Training large language models (LLMs) poses significant challenges regarding computational resources and memory capacity. Although distributed training techniques help mitigate these issues, they still suffer from considerable communication…

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of…

In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study…

We introduce Learning-Augmented Control (LAC), an approach that integrates untrusted machine learning predictions into the control of constrained, nonlinear dynamical systems. LAC is designed to achieve the "best-of-both-worlds" guarantees,…

This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…

Distributed optimization, where the computations are performed in a localized and coordinated manner using multiple agents, is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Representation learning on dynamic graphs requires capturing complex dependencies that evolve across both time and structure. Existing approaches typically adopt fixed temporal decay schemes or predetermined structural propagation depths,…

We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks. By leveraging interval analysis and interval bound propagation, we…

We consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation of linear and angular momentum. Due to the…

We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures:…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

Behavior can be described as a temporal sequence of actions driven by neural activity. To learn complex sequential patterns in neural networks, memories of past activities need to persist on significantly longer timescales than the…

This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability…

We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language,…