This paper mainly discusses the generation of personalized fonts as the problem of image style transfer. The main purpose of this paper is to design a network framework that can extract and recombine the content and style of the characters. These attempts can be used to synthesize the entire set of fonts with only a small amount of characters. The paper combines various depth networks such as Convolutional Neural Network, Multi-layer Perceptron and Residual Network to find the optimal model to extract the features of the fonts character. The result shows that those characters we have generated is very close to real characters, using Structural Similarity index and Peak Signal-to-Noise Ratio evaluation criterions.

We propose Generative Well-intentioned Networks (GWINs), a novel framework for increasing the accuracy of certainty-based, closed-world classifiers. A conditional generative network recovers the distribution of observations that the classifier labels correctly with high certainty. We introduce a reject option to the classifier during inference, allowing the classifier to reject an observation instance rather than predict an uncertain label. These rejected observations are translated by the generative network to high-certainty representations, which are then relabeled by the classifier. This architecture allows for any certainty-based classifier or rejection function and is not limited to multilayer perceptrons.

We propose a novel, conceptually simple and general framework for instance segmentation on 3D point clouds. Our method, called 3D-BoNet, follows the simple design philosophy of per-point multilayer perceptrons (MLPs). It consists of a backbone network followed by two parallel network branches for 1) bounding box regression and 2) point mask prediction. Moreover, it is remarkably computationally efficient as, unlike existing approaches, it does not require any post-processing steps such as non-maximum suppression, feature sampling, clustering or voting. Extensive experiments show that our approach surpasses existing work on both ScanNet and S3DIS datasets while being approximately 10x more computationally efficient. Comprehensive ablation studies demonstrate the effectiveness of our design.

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on asymptotic stability of the depth-flows, leading to robustness against input perturbations and low computational burden for the numerical solver. The learning procedure is cast as an optimal control problem, and an approximate solution is proposed based on adjoint sensivity analysis. We further introduce novel regularizers designed to ease the optimization process and speed up convergence. The proposed model class is evaluated on non-linear classification and function approximation tasks.

Comprehensive surveys on GNNs were provided by Hamilton et al. (2017a), Zhou et al. (2018), and Wu et al. (2019). Despite GNNs' empirical successes in various fields, Xu et al. (2019) and Morris et al. (2019) demonstrated that GNNs cannot distinguish some pairs of graphs. This indicates that GNNs cannot correctly classify these graphs with any parameters unless the labels of these graphs are the same. This result contrasts with the universal approximation power of multi layer perceptrons (Cybenko, 1989; Hornik et al., 1989; Hornik, 1991). Furthermore, Sato et al. (2019a) showed that GNNs are at most as powerful as distributed local algorithms (Angluin, 1980; Suomela, 2013). Thus there are many combinatorial problems that GNNs cannot solve other than the graph isomorphism problem. Consequently, various provably powerful GNN models have been proposed to overcome the limitations of GNNs. This survey provides an extensive overview of the expressive power of GNNs and various GNN models to overcome these limitations.

So, it is easy to notice that with b 0, the function will always pass through the origin [0,0]. And when we introduced values to b keeping a fixed, the new functions will always be parallel to each other. So, what could we learn from it? We can say that a component determines the angulation of the function, while the b component determines where the function cuts the x-axis. I think you already noticed the problem in that, right?

Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis. The dilation-erosion perceptron (DEP) is a morphological neural network obtained by a convex combination of a dilation and an erosion followed by the application of a hard-limiter function for binary classification tasks. A DEP classifier can be trained using a convex-concave procedure along with the minimization of the hinge loss function. As a lattice computing model, the DEP classifier assumes the feature and class spaces are partially ordered sets. In many practical situations, however, there is no natural ordering for the feature patterns. Using concepts from multi-valued mathematical morphology, this paper introduces the reduced dilation-erosion (r-DEP) classifier. An r-DEP classifier is obtained by endowing the feature space with an appropriate reduced ordering. Such reduced ordering can be determined using two approaches: One based on an ensemble of support vector classifiers (SVCs) with different kernels and the other based on a bagging of similar SVCs trained using different samples of the training set. Using several binary classification datasets from the OpenML repository, the ensemble and bagging r-DEP classifiers yielded in mean higher balanced accuracy scores than the linear, polynomial, and radial basis function (RBF) SVCs as well as their ensemble and a bagging of RBF SVCs.

Multi-layer perceptrons have been an important family of machine learning methods, whose history alternates between periods of wide popularity and periods of fading interest [21, 18, 11]. Described in a mathematical language, a multi-layer perceptron is the iterated composition of parameterized affine maps and nonlinear maps, ultimately composed with a prediction map either for the purpose of predicting a scalar value as in curve fitting or regression, or a binary label as in supervised classification. As the number of layers or network depth grows, the parameterized map resulting from this iterated composition may change in terms of smoothness properties. However the impact of network depth on the regularity of the resulting deep network function is, quite surprisingly, still not fully understood, in particular for multi-layer perceptrons. Consider the setting, where the number of datapoints is finite, the number of hidden layers is finite, and the number of weights per layers is finite.

Neural networks are important tools for data-intensive analysis and are commonly applied to model non-linear relationships between dependent and independent variables. However, neural networks are usually seen as "black boxes" that offer minimal information about how the input variables are used to predict the response in a fitted model. This article describes the \pkg{NeuralSens} package that can be used to perform sensitivity analysis of neural networks using the partial derivatives method. Functions in the package can be used to obtain the sensitivities of the output with respect to the input variables, evaluate variable importance based on sensitivity measures and characterize relationships between input and output variables. Methods to calculate sensitivities are provided for objects from common neural network packages in \proglang{R}, including \pkg{neuralnet}, \pkg{nnet}, \pkg{RSNNS}, \pkg{h2o}, \pkg{neural}, \pkg{forecast} and \pkg{caret}. The article presents an overview of the techniques for obtaining information from neural network models, a theoretical foundation of how are calculated the partial derivatives of the output with respect to the inputs of a multi-layer perceptron model, a description of the package structure and functions, and applied examples to compare \pkg{NeuralSens} functions with analogous functions from other available \proglang{R} packages.

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.