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This paper analyzes representations of continuous piecewise linear functions with infinite width, finite cost shallow neural networks using the rectified linear unit (ReLU) as an activation function. Through its integral representation, a…

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS)…

We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller…

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix…

We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the fact that a variety of key control objectives, such as stability, safety,…

The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic approach to inserting new layers during the training process. Our method eliminates the need to choose a fixed…

In this paper, we study the trainability of rectified linear unit (ReLU) networks. A ReLU neuron is said to be dead if it only outputs a constant for any input. Two death states of neurons are introduced; tentative and permanent death. A…

Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…

This paper investigates the ability of finite samples to identify two-layer irreducible shallow networks with various nonlinear activation functions, including rectified linear units (ReLU) and analytic functions such as the logistic…

Safety-critical control of piecewise affine (PWA) systems under bounded additive disturbances requires guarantees not for individual states but for entire state sets simultaneously: a single control action must steer every state in the set…

Linear Quadratic Regulator (LQR) is often combined with feedback linearization (FBL) for nonlinear systems that have the nonlinearity additive to the input. Conventional approaches estimate and cancel the nonlinearity based on the first…

As machine learning models grow in complexity, they increasingly struggle with three conflicting demands: the need for high accuracy, the requirement for hardware efficiency, and the necessity of functional stability. Traditional…

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the…

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

Neural networks (NNs) have been successfully deployed in various fields. In NNs, a large number of multiplyaccumulate (MAC) operations need to be performed. Most existing digital hardware platforms rely on parallel MAC units to accelerate…

The increasing demand on precision and throughput within high-precision mechatronics industries requires a new generation of feedforward controllers with higher accuracy than existing, physics-based feedforward controllers. As neural…

We propose a policy search approach to learn controllers from specifications given as Signal Temporal Logic (STL) formulae. The system model, which is unknown but assumed to be an affine control system, is learned together with the control…

Robustness with respect to weight perturbations underpins guarantees for generalization, pruning and quantization. Existing guarantees rely on Lipschitz bounds in parameter space, cover only plain feed-forward MLPs, and break under the…

Modelling long-term dependencies is a challenge for recurrent neural networks. This is primarily due to the fact that gradients vanish during training, as the sequence length increases. Gradients can be attenuated by transition operators…

Training reinforcement learning (RL) agents often requires significant computational resources and prolonged training durations. To address this challenge, we build upon prior work that introduced a neural architecture with…