Training BP Networks Using Momentum Gradient Descent Algorithm

In neural network training, the momentum gradient descent algorithm serves as a widely-used optimization method that effectively accelerates convergence and reduces oscillations. When applied to BP networks, this approach adjusts weight updates by introducing a momentum term, enabling the network to better escape local minima. Code implementation typically involves storing previous weight updates and combining them with current gradients using a momentum coefficient (usually set between 0.5-0.9).

The Levenberg-Marquardt (L-M) optimization algorithm is a hybrid method combining gradient descent and Gauss-Newton approaches. Particularly suitable for small to medium-sized BP networks, it achieves rapid convergence to optimal solutions. The algorithm dynamically switches between gradient descent and Gauss-Newton methods by adjusting a damping parameter, leveraging advantages from both techniques. Implementation requires calculating the Jacobian matrix and using a trust-region strategy for parameter updates.

Bayesian regularization algorithm improves BP network training from a different perspective by treating network weights and biases as random variables within a Bayesian framework. This method automatically determines optimal model complexity while effectively preventing overfitting. During training, the algorithm balances training error and network complexity, resulting in networks with superior generalization capabilities. Implementation involves estimating hyperparameters through evidence approximation or Markov Chain Monte Carlo methods.

These training methods possess distinct characteristics: L-M optimization offers fast convergence suitable for high-precision scenarios, while Bayesian regularization, despite higher computational demands, produces more robust network models. Practical applications allow selection of appropriate training strategies based on specific requirements, or combined usage for enhanced performance. Code examples often include early stopping criteria and cross-validation techniques to optimize algorithm parameters.