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The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…
It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…
Industrial control applications require high performance under strict constraints. Control barrier functions (CBFs) provide principled safety mechanisms, but constructing CBF-based safety filters for large-scale systems is challenging. We…
We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a…
It is shown that any continuous piecewise affine (CPA) function $\mathbb{R}^2\to\mathbb{R}$ with $p$ pieces can be represented by a ReLU neural network with two hidden layers and $O(p)$ neurons. Unlike prior work, which focused on convex…
This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and…
In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…
Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety…
The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed…
This paper addresses the challenge of collision-free motion planning in automated navigation within complex environments. Utilizing advancements in Deep Reinforcement Learning (DRL) and sensor technologies like LiDAR, we propose the TD3-DWA…
Most adaptive optics (AO) systems using pyramid wavefront sensors (PyWFS) to estimate the phase of the pupil field use mechanical modulation of the beam in order to increase the dynamic range in low-order modes so the PyWFS can usefully…
We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in…
Explainable Artificial Intelligence (XAI) has mainly focused on static learning scenarios so far. We are interested in dynamic scenarios where data is sampled progressively, and learning is done in an incremental rather than a batch mode.…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
We consider approximations of general continuous functions on finite-dimensional cubes by general deep ReLU neural networks and study the approximation rates with respect to the modulus of continuity of the function and the total number of…
This paper presents an ellipsoidal set-theoretic framework for robust safety filter synthesis in constrained linear systems subject to additive bounded disturbances and input constraints. We formulate the safety filter design as a convex…
Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property,…
Reinforcement learning (RL) is attracting attention as an effective way to solve sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Many such problems involve constraints…