Deep Learning Topological Invariants of Band Insulators

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.Comment: 8 pages, 5 figure

The identification of sub-pixel components from remotely sensed data: an evaluation of an artificial neural network approach

Until recently, methodologies to extract sub-pixel information from remotely sensed data have focused on linear un-mixing models and so called fuzzy classifiers. Recent research has suggested that neural networks have the potential for providing sub- pixel information. Neural networks offer an attractive alternative as they are non- parametric, they are not restricted to any number of classes, they do not assume that the spectral signatures of pixel components mix linearly and they do not necessarily have to be trained with pure pixels. The thesis tests the validity of neural networks for extracting sub-pixel information using a combination of qualitative and quantitative analysis tools. Previously published experiments use data sets that are often limited in terms of numbers of pixels and numbers of classes. The data sets used in the thesis reflect the complexity of the landscape. Preparation for the experiments is canied out by analysing the data sets and establishing that the network is not sensitive to particular choices of parameters. Classification results using a conventional type of target with which to train the network show that the response of the network to mixed pixels is different from the response of the network to pure pixels. Different target types are then tested. Although targets which provide detailed compositional information produce higher accuracies of classification for subsidiary classes, there is a trade off between the added information and added complexity which can decrease classification accuracy. Overall, the results show that the network seems to be able to identify the classes that are present within pixels but not their proportions. Experiments with a very accurate data set show that the network behaves like a pattern matching algorithm and requires examples of mixed pixels in the training data set in order to estimate pixel compositions for unseen pixels. The network does not function like an unmixing model and cannot interpolate between pure classes

A training data selection in on-line training for multilayer neural networks

金沢大学大学院自然科学研究科情報システムIn this paper, a training data selection method for multilayer neural networks (MLNNs) in on-line training is proposed. Purpose of the reduction in training data is reducing the computation complexity of the training and saving the memory to store the data without losing generalization performance. This method uses a pairing method, which selects the nearest neighbor data by finding the nearest data in the different classes. The network is trained by the selected data. Since the selected data located along data class boundary, the trained network can guarantee generalization performance. Efficiency of this method for the on-line training is evaluated by computer simulation

OSLNet:Deep Small-Sample Classification with an Orthogonal Softmax Layer

A deep neural network of multiple nonlinear layers forms a large function space, which can easily lead to overfitting when it encounters small-sample data. To mitigate overfitting in small-sample classification, learning more discriminative features from small-sample data is becoming a new trend. To this end, this paper aims to find a subspace of neural networks that can facilitate a large decision margin. Specifically, we propose the Orthogonal Softmax Layer (OSL), which makes the weight vectors in the classification layer remain orthogonal during both the training and test processes. The Rademacher complexity of a network using the OSL is only $\frac{1}{K}$, where $K$ is the number of classes, of that of a network using the fully connected classification layer, leading to a tighter generalization error bound. Experimental results demonstrate that the proposed OSL has better performance than the methods used for comparison on four small-sample benchmark datasets, as well as its applicability to large-sample datasets. Codes are available at: https://github.com/dongliangchang/OSLNet.Comment: TIP 2020. Code available at https://github.com/dongliangchang/OSLNe