相关论文: Invariant Set Estimation for Piecewise Affine Dyna…

Remote sensing semantic segmentation aims to assign automatically each pixel on aerial images with specific label. In this letter, we proposed a new module, called improved-flow warp module (IFWM), to adjust semantic feature maps across…

We present a novel methodology for repairing neural networks that use ReLU activation functions. Unlike existing methods that rely on modifying the weights of a neural network which can induce a global change in the function space, our…

Deep neural networks often lack the safety and robustness guarantees needed to be deployed in safety critical systems. Formal verification techniques can be used to prove input-output safety properties of networks, but when properties are…

Neural networks have demonstrated a wide range of successes, but their ``black box" nature raises concerns about transparency and reliability. Previous research on ReLU networks has sought to unwrap these networks into linear models based…

Feed-forward ReLU neural networks partition their input domain into finitely many "affine regions" of constant neuron activation pattern and affine behaviour. We analyze their mathematical structure and provide algorithmic primitives for an…

Consider a deep neural network (DNN) that is being used to suggest the direction in which an aircraft must turn to avoid a possible collision with an intruder aircraft. Informally, such a network is well-behaved if it asks the own ship to…

To resolve the non-convex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in both the…

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…

Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…

We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann-Liouville…

We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact…

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous,…

The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU)…

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design.…

Anomaly detection and localization in industrial images are essential for automated quality inspection. PaDiM, a prominent method, models the distribution of normal image features extracted by pre-trained Convolutional Neural Networks…

In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…

In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…