Like most learning algorithms, the multilayer perceptrons (MLP) is designed to learn a vector of parameters from data. However, in certain scenarios we are interested in learning structured parameters (predictions) in the form of symmetric positive definite matrices. Here, we introduce a variant of the MLP, referred to as the matrix MLP, that is specialized at learning symmetric positive definite matrices. We also present an application of the model within the context of the variational autoencoder (VAE). Our formulation of the VAE extends the vanilla formulation to the cases where the recognition and the generative networks can be from the parametric family of distributions with dense covariance matrices. Two specific examples are discussed in more detail: the dense covariance Gaussian and its generalization, the power exponential distribution. Our new developments are illustrated using both synthetic and real data.

In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to other methods, one distinct feature of the proposed method is to incorporate the features extracted from the low-fidelity data as the input feature, this approach not only improves the predictive capability of the neural network but also enables the decoupling the high-fidelity simulation from the online stage. Due to its nonin-trusive nature, it is applicable to general parameterized problems. We also provide several numerical examples to illustrate the effectiveness and performance of the proposed method.

The term neural networks refers to networks of neurons in the mammalian brain. Neurons are its fundamental units of computation. In the brain they are connected together in networks to process data. This can be a very complex task, and the dynamics of neural networks in the mammalian brain in response to external stimuli can therefore be quite intricate. Inputs and outputs of each neuron vary as functions of time, in the form of so-called spike trains, but also the network itself changes. We learn and improve our data-processing capacities by establishing reconnections between neurons. Neural-networkalgorithms are inspired by the architecture and the dynamics of networks of neurons in the brain. Yet the algorithms use neuron models that are highly simplified, compared with real neurons. Nevertheless, the fundamental principle is the same: artificial neural networks learn by reconnection.

An appropriate choice of the activation function (like ReLU, sigmoid or swish) plays an important role in the performance of (deep) multilayer perceptrons (MLP) for classification and regression learning. Prototype-based classification learning methods like (generalized) learning vector quantization (GLVQ) are powerful alternatives. These models also deal with activation functions but here they are applied to the so-called classifier function instead. In this paper we investigate successful candidates of activation functions known for MLPs for application in GLVQ and their influence on the performance.

A regression-based BNN model is proposed to predict spatiotemporal quantities like hourly rider demand with calibrated uncertainties. The main contributions of this paper are (i) A feed-forward deterministic neural network (DetNN) architecture that predicts cyclical time series data with sensitivity to anomalous forecasting events; (ii) A Bayesian framework applying SVGD to train large neural networks for such tasks, capable of producing time series predictions as well as measures of uncertainty surrounding the predictions. Experiments show that the proposed BNN reduces average estimation error by 10% across 8 U.S. cities compared to a fine-tuned multilayer perceptron (MLP), and 4% better than the same network architecture trained without SVGD.

Abstract-- The present paper shows a solution to the problem of automatic distress detection, more precisely the detection of holes in paved roads. To do so, the proposed solution uses a weightless neural network known as Wisard to decide whether an image of a road has any kind of cracks. In addition, the proposed architecture also shows how the use of transfer learning was able to improve the overall accuracy of the decision system. As a verification step of the research, an experiment was carried out using images from the streets at the Federal University of Tocantins, Brazil. The architecture of the developed solution presents a result of 85.71% accuracy in the dataset, proving to be superior to approaches of the state-of-the-art. I.INTRODUCTION In Brazil, most of the traffic is driven on asphalt roads.

I know that finding the weights of a neural network requires gradient descent as there is no closed form available. I know this from the books, and not knowing exactly why the derivative w.r.t. the weights is not zero-able led me to try to do it. Let's consider the traditional sigmoid MLP, with just one layer and just one datapoint $ \mathbf{x},t $. The gradient vector of the MSE loss function w.r.t. the weights is: Now, how to solve (finding the zero) of the gradient expression? What I could do is to analyze the various factors and see where they individually zero.

This paper is concerned with learning to solve tasks that require a chain of interde- pendent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational net- work, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]’s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty- CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

This paper is concerned with learning to solve tasks that require a chain of interde- pendent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational net- work, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]’s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty- CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

It seems the more I read, the more confused I get - models, algorithms, surrogates; my head is spinning. Assume the dataset is in perfect condition - pure as the driven snow, no correlated features, no null in sight, nothing; and it has "enough" observations. To simplify, let's say we are looking at binary classification. Let's also say that we want to try four different algorithms: for example - logistic regression, naive Bayes, gradient boosted tree and multilayer perceptron. And, finally, let's assume that (since all this is for educational purposes), we have no issues with time, efficiency, computing power, computing budget and whatnot; we don't care if this is an overkill or if we're going after a fly with an elephant gun: we want to throw everything, including the kitchen sink, at the problem so we can extract every last ounce of performance when it's time to make predictions on totally unseen data.