Feedforward neural networks initialization based on discriminant learning

A mathematical framework for improved weight initialization of neural networks using Lagrange multipliers

A good weight initialization is crucial to accelerate the convergence of the weights in a neural network. However, training a neural network is still time-consuming, despite recent advances in weight initialization approaches. In this paper, we propose a mathematical framework for the weight initialization in the last layer of a neural network. We first derive analytically a tight constraint on the weights that accelerates the convergence of the weights during the back-propagation algorithm. We then use linear regression and Lagrange multipliers to analytically derive the optimal initial weights and initial bias of the last layer, that minimize the initial training loss given the derived tight constraint. We also show that the restrictive assumption of traditional weight initialization algorithms that the expected value of the weights is zero is redundant for our approach. We first apply our proposed weight initialization approach to a Convolutional Neural Network that predicts the Remaining Useful Life of aircraft engines. The initial training and validation loss are relatively small, the weights do not get stuck in a local optimum, and the convergence of the weights is accelerated. We compare our approach with several benchmark strategies. Compared to the best performing state-of-the-art initialization strategy (Kaiming initialization), our approach needs 34% less epochs to reach the same validation loss. We also apply our approach to ResNets for the CIFAR-100 dataset, combined with transfer learning. Here, the initial accuracy is already at least 53%. This gives a faster weight convergence and a higher test accuracy than the benchmark strategies.

High-accuracy morphological identification of bone marrow cells using deep learning-based Morphogo system

Accurate identification and classification of bone marrow (BM) nucleated cell morphology are crucial for the diagnosis of hematological diseases. However, the subjective and time-consuming nature of manual identification by pathologists hinders prompt diagnosis and patient treatment. To address this issue, we developed Morphogo, a convolutional neural network-based system for morphological examination. Morphogo was trained using a vast dataset of over 2.8 million BM nucleated cell images. Its performance was evaluated using 508 BM cases that were categorized into five groups based on the degree of morphological abnormalities, comprising a total of 385,207 BM nucleated cells. The results demonstrated Morphogo's ability to identify over 25 different types of BM nucleated cells, achieving a sensitivity of 80.95%, specificity of 99.48%, positive predictive value of 76.49%, negative predictive value of 99.44%, and an overall accuracy of 99.01%. In most groups, Morphogo cell analysis and Pathologists' proofreading showed high intragroup correlation coefficients for granulocytes, erythrocytes, lymphocytes, monocytes, and plasma cells. These findings further validate the practical applicability of the Morphogo system in clinical practice and emphasize its value in assisting pathologists in diagnosing blood disorders.

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

The Arrhenius crossover temperature, TA, corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below TA. The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates. In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T. The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature TA and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature TA was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature Tg, the melting temperature Tm, the ratio of these temperatures Tg/Tm and the fragility index m were applied as input parameters. It has been established that the temperatures Tg and Tm are significant parameters, whereas their ratio Tg/Tm and the fragility index m do not correlate much with the temperature TA. An important result of the present work is the analytical equation relating the temperatures Tg, Tm and TA, and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature TA for a large class of materials, regardless of their compositions and glass-forming abilities.

A singular Riemannian geometry approach to deep neural networks II. Reconstruction of 1-D equivalence classes

We proposed in a previous work a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing a way to build the class of equivalence of an input point: such class is defined as the set of the points on the input manifold mapped to the same output by the neural network. In other words, we build the preimage of a point in the output manifold in the input space. In particular. We focus for simplicity on the case of neural networks maps from n-dimensional real spaces to (n-1)-dimensional real spaces, we propose an algorithm allowing to build the set of points lying on the same class of equivalence. This approach leads to two main applications: the generation of new synthetic data and it may provides some insights on how a classifier can be confused by small perturbation on the input data (e.g. a penguin image classified as an image containing a chihuahua). In addition, for neural networks from 2D to 1D real spaces, we also discuss how to find the preimages of closed intervals of the real line. We also present some numerical experiments with several neural networks trained to perform non-linear regression tasks, including the case of a binary classifier.