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Deep neural networks (DNNs) are widely used in perception systems for safety-critical applications, such as autonomous driving and robotics. However, DNNs remain vulnerable to various safety concerns, including generalization errors,…

Graph neural networks (GNNs) have achieved extraordinary enhancements in various areas including the fields medical imaging and network neuroscience where they displayed a high accuracy in diagnosing challenging neurological disorders such…

Interpretability of neural networks and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work,…

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…

With the increased deployment of face recognition systems in our daily lives, face presentation attack detection (PAD) is attracting much attention and playing a key role in securing face recognition systems. Despite the great performance…

Deep neural network (DNN) architecture based models have high expressive power and learning capacity. However, they are essentially a black box method since it is not easy to mathematically formulate the functions that are learned within…

Automatic face recognition is a research area with high popularity. Many different face recognition algorithms have been proposed in the last thirty years of intensive research in the field. With the popularity of deep learning and its…

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…

Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but…

Dense facial landmark detection is one of the key elements of face processing pipeline. It is used in virtual face reenactment, emotion recognition, driver status tracking, etc. Early approaches were suitable for facial landmark detection…

In recent times, an increasing number of researchers have been devoted to utilizing deep neural networks for end-to-end flight navigation. This approach has gained traction due to its ability to bridge the gap between perception and…

Reinforcement Learning (RL) algorithms have achieved remarkable performance in decision making and control tasks due to their ability to reason about long-term, cumulative reward using trial and error. However, during RL training, applying…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Deep Neural Networks (DNNs) are powerful tools that have shown extraordinary results in many scenarios, ranging from pattern recognition to complex robotic problems. However, their intricate designs and lack of transparency raise safety…

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the…

Click-Through Rate(CTR) estimation has become one of the most fundamental tasks in many real-world applications and it's important for ranking models to effectively capture complex high-order features. Shallow feed-forward network is widely…

In analyzing of modern biological data, we are often dealing with ill-posed problems and missing data, mostly due to high dimensionality and multicollinearity of the dataset. In this paper, we have proposed a system based on matrix…

In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…