We consider a decentralized learning problem where training data samples are distributed over agents (processing nodes) of an underlying communication network topology without any central (master) node. Due to information privacy and security issues in a decentralized setup, nodes are not allowed to share their training data and only parameters of the neural network are allowed to be shared. This article investigates decentralized learning of randomization-based neural networks that provides centralized equivalent performance as if the full training data are available at a single node. We consider five randomization-based neural networks that use convex optimization for learning. Two of the five neural networks are shallow, and the others are deep. The use of convex optimization is the key to apply alternating-direction-method-of-multipliers with decentralized average consensus. This helps us to establish decentralized learning with centralized equivalence. For the underlying communication network topology, we use a doubly-stochastic network policy matrix and synchronous communications. Experiments with nine benchmark datasets show that the five neural networks provide good performance while requiring low computational and communication complexity for decentralized learning. The performance rankings of five neural networks using Friedman rank are also enclosed in the results, which are ELM < RVFL< dRVFL < edRVFL < SSFN.

We propose a greedy algorithm to select N important features among P input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural networks as predictors in the algorithm to compute the loss and hence, we refer to our method as neural greedy pursuit (NGP). NGP is efficient in selecting N features when N << P, and it provides a notion of feature importance in a descending order following the sequential selection procedure. We experimentally show that NGP provides better performance than several feature selection methods such as DeepLIFT and Drop-one-out loss. In addition, we experimentally show a phase transition behavior in which perfect selection of all N features without false positives is possible when the training data size exceeds a threshold.

We propose ReDense as a simple and low complexity way to improve the performance of trained neural networks. We use a combination of random weights and rectified linear unit (ReLU) activation function to add a ReLU dense (ReDense) layer to the trained neural network such that it can achieve a lower training loss. The lossless flow property (LFP) of ReLU is the key to achieve the lower training loss while keeping the generalization error small. ReDense does not suffer from vanishing gradient problem in the training due to having a shallow structure. We experimentally show that ReDense can improve the training and testing performance of various neural network architectures with different optimization loss and activation functions. Finally, we test ReDense on some of the state-of-the-art architectures and show the performance improvement on benchmark.

In a communication network, decentralized learning refers to the knowledge collaboration between the different local agents (processing nodes) to improve the local estimation performance without sharing private data. The ideal case is that the decentralized solution approximates the centralized solution, as if all the data are available at a single node, and requires low computational power and communication overhead. In this work, we propose a decentralized learning of randomization-based neural networks with asynchronous communication and achieve centralized equivalent performance. We propose an ARock-based alternating-direction-method-of-multipliers (ADMM) algorithm that enables individual node activation and one-sided communication in an undirected connected network, characterized by a doubly-stochastic network policy matrix. Besides, the proposed algorithm reduces the computational cost and communication overhead due to its asynchronous nature. We study the proposed algorithm on different randomization-based neural networks, including ELM, SSFN, RVFL, and its variants, to achieve the centralized equivalent performance under efficient computation and communication costs. We also show that the proposed asynchronous decentralized learning algorithm can outperform a synchronous learning algorithm regarding computational complexity, especially when the network connections are sparse.

We consider the problem of training a neural net over a decentralized scenario with a low communication over-head. The problem is addressed by adapting a recently proposed incremental learning approach, called `learning without forgetting'. While an incremental learning approach assumes data availability in a sequence, nodes of the decentralized scenario can not share data between them and there is no master node. Nodes can communicate information about model parameters among neighbors. Communication of model parameters is the key to adapt the `learning without forgetting' approach to the decentralized scenario. We use random walk based communication to handle a highly limited communication resource.

Self size-estimating feedforward network (SSFN) is a feedforward multilayer network. For the existing SSFN, a part of each weight matrix is trained using a layer-wise convex optimization approach (a supervised training), while the other part is chosen as a random matrix instance (an unsupervised training). In this article, the use of deterministic transforms instead of random matrix instances for the SSFN weight matrices is explored. The use of deterministic transforms provides a reduction in computational complexity. The use of several deterministic transforms is investigated, such as discrete cosine transform, Hadamard transform, Hartley transform, and wavelet transforms. The choice of a deterministic transform among a set of transforms is made in an unsupervised manner. To this end, two methods based on features' statistical parameters are developed. The proposed methods help to design a neural net where deterministic transforms can vary across its layers' weight matrices. The effectiveness of the proposed approach vis-a-vis the SSFN is illustrated for object classification tasks using several benchmark datasets.

We design a low complexity decentralized learning algorithm to train a recently proposed large neural network in distributed processing nodes (workers). We assume the communication network between the workers is synchronized and can be modeled as a doubly-stochastic mixing matrix without having any master node. In our setup, the training data is distributed among the workers but is not shared in the training process due to privacy and security concerns. Using altemating-direction-method-of-multipliers (ADMM) along with a layer-wise convex optimization approach, we propose a decentralized learning algorithm which enjoys low computational complexity and communication cost among the workers. We show that it is possible to achieve equivalent learning performance as if the data is available in a single place. Finally, we experimentally illustrate the time complexity and convergence behavior of the algorithm.

We study the problem of learning without forgetting (LwF) in which a deep learning model learns new tasks without a significant drop in the classification performance on the previously learned tasks. We propose an LwF algorithm for multilayer feedforward neural networks in which we can adapt the number of layers of the network from the old task to the new task. To this end, we limit ourselves to convex loss functions in order to train the network in a layer-wise manner. Layer-wise convex optimization leads to low-computational complexity and provides a more interpretable understanding of the network. We compare the effectiveness of the proposed adaptive LwF algorithm with the standard LwF over image classification datasets.

In this work, we exploit an asynchronous computing framework namely ARock to learn a deep neural network called self-size estimating feedforward neural network (SSFN) in a decentralized scenario. Using this algorithm namely asynchronous decentralized SSFN (dSSFN), we provide the centralized equivalent solution under certain technical assumptions. Asynchronous dSSFN relaxes the communication bottleneck by allowing one node activation and one side communication, which reduces the communication overhead significantly, consequently increasing the learning speed. We compare asynchronous dSSFN with traditional synchronous dSSFN in the experimental results, which shows the competitive performance of asynchronous dSSFN, especially when the communication network is sparse.

For prediction of a non-negative target signal using a non-negative input, we design a feed-forward neural network to achieve a better performance than a non-negative matrix factorization (NMF) algorithm. We provide a mathematical relation between the neural network and NMF. The architecture of the neural network is built on a property of rectified-linearunit (ReLU) activation function and a convex optimization layerwise training approach. For an illustrative example, we choose a speech enhancement application where a clean speech spectrum is estimated from a noisy spectrum.