Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

An Incremental Construction of Deep Neuro Fuzzy System for Continual Learning of Non-stationary Data Streams

Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically extracted from data streams or removed if they play limited role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely gClass, drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of dimensionality of input space due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using seven datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four popular continual learning algorithms and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy. Moreover, it is also shown that the concept drift detection method is an effective tool to control the depth of network structure while the hidden layer merging scenario is capable of simplifying the network complexity of a deep network with negligible compromise of generalization performance.Comment: This paper has been published in IEEE Transactions on Fuzzy System

Importance Estimation with Random Gradient for Neural Network Pruning

Global Neuron Importance Estimation is used to prune neural networks for efficiency reasons. To determine the global importance of each neuron or convolutional kernel, most of the existing methods either use activation or gradient information or both, which demands abundant labelled examples. In this work, we use heuristics to derive importance estimation similar to Taylor First Order (TaylorFO) approximation based methods. We name our methods TaylorFO-abs and TaylorFO-sq. We propose two additional methods to improve these importance estimation methods. Firstly, we propagate random gradients from the last layer of a network, thus avoiding the need for labelled examples. Secondly, we normalize the gradient magnitude of the last layer output before propagating, which allows all examples to contribute similarly to the importance score. Our methods with additional techniques perform better than previous methods when tested on ResNet and VGG architectures on CIFAR-100 and STL-10 datasets. Furthermore, our method also complements the existing methods and improves their performances when combined with them.Comment: 7 pages, 2 figures, ICLR 2023 Workshop on Sparsity in Neural Networks. arXiv admin note: text overlap with arXiv:2306.1320

Photometric redshifts with Quasi Newton Algorithm (MLPQNA). Results in the PHAT1 contest

Context. Since the advent of modern multiband digital sky surveys, photometric redshifts (photo-z's) have become relevant if not crucial to many fields of observational cosmology, from the characterization of cosmic structures, to weak and strong lensing. Aims. We describe an application to an astrophysical context, namely the evaluation of photometric redshifts, of MLPQNA, a machine learning method based on Quasi Newton Algorithm. Methods. Theoretical methods for photo-z's evaluation are based on the interpolation of a priori knowledge (spectroscopic redshifts or SED templates) and represent an ideal comparison ground for neural networks based methods. The MultiLayer Perceptron with Quasi Newton learning rule (MLPQNA) described here is a computing effective implementation of Neural Networks for the first time exploited to solve regression problems in the astrophysical context and is offered to the community through the DAMEWARE (DAta Mining & ExplorationWeb Application REsource) infrastructure. Results. The PHAT contest (Hildebrandt et al. 2010) provides a standard dataset to test old and new methods for photometric redshift evaluation and with a set of statistical indicators which allow a straightforward comparison among different methods. The MLPQNA model has been applied on the whole PHAT1 dataset of 1984 objects after an optimization of the model performed by using as training set the 515 available spectroscopic redshifts. When applied to the PHAT1 dataset, MLPQNA obtains the best bias accuracy (0.0006) and very competitive accuracies in terms of scatter (0.056) and outlier percentage (16.3%), scoring as the second most effective empirical method among those which have so far participated to the contest. MLPQNA shows better generalization capabilities than most other empirical methods especially in presence of underpopulated regions of the Knowledge Base.Comment: Accepted for publication in Astronomy & Astrophysics; 9 pages, 2 figure