A Hybrid Recursive Implementation of Broad Learning With Incremental Features

Dynamic Neural Network Structure: A Review for its Theories and Applications

The dynamic neural network (DNN), in contrast to the static counterpart, offers numerous advantages, such as improved accuracy, efficiency, and interpretability. These benefits stem from the network's flexible structures and parameters, making it highly attractive and applicable across various domains. As the broad learning system (BLS) continues to evolve, DNNs have expanded beyond deep learning (DL), orienting a more comprehensive range of domains. Therefore, this comprehensive review article focuses on two prominent areas where DNN structures have rapidly developed: 1) DL and 2) broad learning. This article provides an in-depth exploration of the techniques related to dynamic construction and inference. Furthermore, it discusses the applications of DNNs in diverse domains while also addressing open issues and highlighting promising research directions. By offering a comprehensive understanding of DNNs, this article serves as a valuable resource for researchers, guiding them toward future investigations.

Bidimensionally partitioned online sequential broad learning system for large-scale data stream modeling

Incremental broad learning system (IBLS) is an effective and efficient incremental learning method based on broad learning paradigm. Owing to its streamlined network architecture and flexible dynamic update scheme, IBLS can achieve rapid incremental reconstruction on the basis of the previous model without the entire retraining from scratch, which enables it adept at handling streaming data. However, two prominent deficiencies still persist in IBLS and constrain its further promotion in large-scale data stream scenarios. Firstly, IBLS needs to retain all historical data and perform associated calculations in the incremental learning process, which causes its computational overhead and storage burden to increase over time and as such puts the efficacy of the algorithm at risk for massive or unlimited data streams. Additionally, due to the random generation rule of hidden nodes, IBLS generally necessitates a large network size to guarantee approximation accuracy, and the resulting high-dimensional matrix calculation poses a greater challenge to the updating efficiency of the model. To address these issues, we propose a novel bidimensionally partitioned online sequential broad learning system (BPOSBLS) in this paper. The core idea of BPOSBLS is to partition the high-dimensional broad feature matrix bidimensionally from the aspects of instance dimension and feature dimension, and consequently decompose a large least squares problem into multiple smaller ones, which can then be solved individually. By doing so, the scale and computational complexity of the original high-order model are substantially diminished, thus significantly improving its learning efficiency and usability for large-scale complex learning tasks. Meanwhile, an ingenious recursive computation method called partitioned recursive least squares is devised to solve the BPOSBLS. This method exclusively utilizes the current online samples for iterative updating, while disregarding the previous historical samples, thereby rendering BPOSBLS a lightweight online sequential learning algorithm with consistently low computational costs and storage requirements. Theoretical analyses and simulation experiments demonstrate the effectiveness and superiority of the proposed algorithm.

Class-Incremental Learning Method With Fast Update and High Retainability Based on Broad Learning System

Machine learning aims to generate a predictive model from a training dataset of a fixed number of known classes. However, many real-world applications (such as health monitoring and elderly care) are data streams in which new data arrive continually in a short time. Such new data may even belong to previously unknown classes. Hence, class-incremental learning (CIL) is necessary, which incrementally and rapidly updates an existing model with the data of new classes while retaining the existing knowledge of old classes. However, most current CIL methods are designed based on deep models that require a computationally expensive training and update process. In addition, deep learning based CIL (DCIL) methods typically employ stochastic gradient descent (SGD) as an optimizer that forgets the old knowledge to a certain extent. In this article, a broad learning system-based CIL (BLS-CIL) method with fast update and high retainability of old class knowledge is proposed. Traditional BLS is a fast and effective shallow neural network, but it does not work well on CIL tasks. However, our proposed BLS-CIL can overcome these issues and provide the following: 1) high accuracy due to our novel class-correlation loss function that considers the correlations between old and new classes; 2) significantly short training/update time due to the newly derived closed-form solution for our class-correlation loss without iterative optimization; and 3) high retainability of old class knowledge due to our newly derived recursive update rule for CIL (RULL) that does not replay the exemplars of all old classes, as contrasted to the exemplars-replaying methods with the SGD optimizer. The proposed BLS-CIL has been evaluated over 12 real-world datasets, including seven tabular/numerical datasets and six image datasets, and the compared methods include one shallow network and seven classical or state-of-the-art DCIL methods. Experimental results show that our BIL-CIL can significantly improve the classification performance over a shallow network by a large margin (8.80%-48.42%). It also achieves comparable or even higher accuracy than DCIL methods, but greatly reduces the training time from hours to minutes and the update time from minutes to seconds.

Minibatch Recursive Least Squares Q-Learning

The deep Q-network (DQN) is one of the most successful reinforcement learning algorithms, but it has some drawbacks such as slow convergence and instability. In contrast, the traditional reinforcement learning algorithms with linear function approximation usually have faster convergence and better stability, although they easily suffer from the curse of dimensionality. In recent years, many improvements to DQN have been made, but they seldom make use of the advantage of traditional algorithms to improve DQN. In this paper, we propose a novel Q-learning algorithm with linear function approximation, called the minibatch recursive least squares Q-learning (MRLS-Q). Different from the traditional Q-learning algorithm with linear function approximation, the learning mechanism and model structure of MRLS-Q are more similar to those of DQNs with only one input layer and one linear output layer. It uses the experience replay and the minibatch training mode and uses the agent's states rather than the agent's state-action pairs as the inputs. As a result, it can be used alone for low-dimensional problems and can be seamlessly integrated into DQN as the last layer for high-dimensional problems as well. In addition, MRLS-Q uses our proposed average RLS optimization technique, so that it can achieve better convergence performance whether it is used alone or integrated with DQN. At the end of this paper, we demonstrate the effectiveness of MRLS-Q on the CartPole problem and four Atari games and investigate the influences of its hyperparameters experimentally.