Neural Network Training With Levenberg-Marquardt and Adaptable Weight Compression.

Difficult experiments in training neural networks often fail to converge due to what is known as the flat-spot problem, where the gradient of hidden neurons in the network diminishes in value, rending the weight update process ineffective. Whereas a first-order algorithm can address this issue by learning parameters to normalize neuron activations, the second-order algorithms cannot afford additional parameters given that they include a large Jacobian matrix calculation. This paper proposes Levenberg-Marquardt with weight compression (LM-WC), which combats the flat-spot problem by compressing neuron weights to push neuron activation out of the saturated region and close to the linear region. The presented algorithm requires no additional learned parameters and contains an adaptable compression parameter, which is adjusted to avoid training failure and increase the probability of neural network convergence. Several experiments are presented and discussed to demonstrate the success of LM-WC against standard LM and LM with random restarts on benchmark data sets for varying network architectures. Our results suggest that the LM-WC algorithm can improve training success by 10 times or more compared with other methods.

A Hybrid Constructive Algorithm for Single-Layer Feedforward Networks Learning.

Single-layer feedforward networks (SLFNs) have been proven to be a universal approximator when all the parameters are allowed to be adjustable. It is widely used in classification and regression problems. The SLFN learning involves two tasks: determining network size and training the parameters. Most current algorithms could not be satisfactory to both sides. Some algorithms focused on construction and only tuned part of the parameters, which may not be able to achieve a compact network. Other gradient-based optimization algorithms focused on parameters tuning while the network size has to be preset by the user. Therefore, trial-and-error approach has to be used to search the optimal network size. Because results of each trial cannot be reused in another trial, it costs much computation. In this paper, a hybrid constructive (HC)algorithm is proposed for SLFN learning, which can train all the parameters and determine the network size simultaneously. At first, by combining Levenberg-Marquardt algorithm and least-square method, a hybrid algorithm is presented for training SLFN with fixed network size. Then,with the hybrid algorithm, an incremental constructive scheme is proposed. A new randomly initialized neuron is added each time when the training entrapped into local minima. Because the training continued on previous results after adding new neurons, the proposed HC algorithm works efficiently. Several practical problems were given for comparison with other popular algorithms. The experimental results demonstrated that the HC algorithm worked more efficiently than those optimization methods with trial and error, and could achieve much more compact SLFN than those construction algorithms.

An incremental design of radial basis function networks.

This paper proposes an offline algorithm for incrementally constructing and training radial basis function (RBF) networks. In each iteration of the error correction (ErrCor) algorithm, one RBF unit is added to fit and then eliminate the highest peak (or lowest valley) in the error surface. This process is repeated until a desired error level is reached. Experimental results on real world data sets show that the ErrCor algorithm designs very compact RBF networks compared with the other investigated algorithms. Several benchmark tests such as the duplicate patterns test and the two spiral problem were applied to show the robustness of the ErrCor algorithm. The proposed ErrCor algorithm generates very compact networks. This compactness leads to greatly reduced computation times of trained networks.

Neural network learning without backpropagation.

The method introduced in this paper allows for training arbitrarily connected neural networks, therefore, more powerful neural network architectures with connections across layers can be efficiently trained. The proposed method also simplifies neural network training, by using the forward-only computation instead of the traditionally used forward and backward computation.

Improved computation for Levenberg-Marquardt training.

The improved computation presented in this paper is aimed to optimize the neural networks learning process using Levenberg-Marquardt (LM) algorithm. Quasi-Hessian matrix and gradient vector are computed directly, without Jacobian matrix multiplication and storage. The memory limitation problem for LM training is solved. Considering the symmetry of quasi-Hessian matrix, only elements in its upper/lower triangular array need to be calculated. Therefore, training speed is improved significantly, not only because of the smaller array stored in memory, but also the reduced operations in quasi-Hessian matrix calculation. The improved memory and time efficiencies are especially true for large sized patterns training.