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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…

Transfer learning for feature extraction can be used to exploit deep representations in contexts where there is very few training data, where there are limited computational resources, or when tuning the hyper-parameters needed for training…

We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent…

We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…

The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…

The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…

ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

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…

In this paper, we explore some basic questions on the complexity of training neural networks with ReLU activation function. We show that it is NP-hard to train a two-hidden layer feedforward ReLU neural network. If dimension of the input…

While most state-of-the-art instance segmentation methods produce binary segmentation masks, geographic and cartographic applications typically require precise vector polygons of extracted objects instead of rasterized output. This paper…

Deep learning has significantly advanced image edge detection (ED), primarily through improved feature extraction. However, most existing ED models apply uniform feature fusion across all pixels, ignoring critical differences between…

The growing demand for high-resolution maps across various applications has underscored the necessity of accurately segmenting building vectors from overhead imagery. However, current deep neural networks often produce raster data outputs,…

Nucleus image segmentation is a crucial step in the analysis, pathological diagnosis, and classification, which heavily relies on the quality of nucleus segmentation. However, the complexity of issues such as variations in nucleus size,…

Brain extraction is a fundamental step for most brain imaging studies. In this paper, we investigate the problem of skull stripping and propose complementary segmentation networks (CompNets) to accurately extract the brain from T1-weighted…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

We explore design principles for general pixel-level prediction problems, from low-level edge detection to mid-level surface normal estimation to high-level semantic segmentation. Convolutional predictors, such as the fully-convolutional…

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…