Related papers: Efficient representation and approximation of mode…

To address the computational challenges of Model Predictive Control (MPC), recent research has studied using imitation learning to approximate MPC with a computationally efficient Deep Neural Network (DNN). However, this introduces a common…

We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However,…

This paper presents a deep learning based model predictive control algorithm for control affine nonlinear discrete time systems with matched and bounded state dependent uncertainties of unknown structure. Since the structure of…

A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…

We present ApproxConv, a novel method for compressing the layers of a convolutional neural network. Reframing conventional discrete convolution as continuous convolution of parametrised functions over space, we use functional approximations…

Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…

After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…

We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb R^d)$. In other words, we establish a…

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…

Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to "unravel" the implicit neural network of MPC into an explicit…

Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…

Traditional computational methods, such as the finite element analysis, have provided valuable insights into uncovering the underlying mechanisms of brain physical behaviors. However, precise predictions of brain physics require effective…

Convolutional rectifier networks, i.e. convolutional neural networks with rectified linear activation and max or average pooling, are the cornerstone of modern deep learning. However, despite their wide use and success, our theoretical…

A deep neural network using rectified linear units represents a continuous piecewise linear (CPWL) function and vice versa. Recent results in the literature estimated that the number of neurons needed to exactly represent any CPWL function…

Neural networks allow Q-learning reinforcement learning agents such as deep Q-networks (DQN) to approximate complex mappings from state spaces to value functions. However, this also brings drawbacks when compared to other function…

Existing methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities…