This chapter is more mathematically involved than the rest of the book. If you're not crazy about mathematics you may be tempted to skip the chapter, and to treat backpropagation as a black box whose details you're willing to ignore. Why take the time to study those details? The reason,...
the relevant question is how to compute the gradient of a loss function for spiking neural networks, preferably with the computational efficiency afforded by the backpropagation algorithm and retaining any potential advantages of event-based communication. Backpropagation in discrete-time artificial...
First of all, I would like to start with defining what the backpropagation algorithm really is. If this definition will not make much sense at the beginning, it should make much more sense later on. 1. What is the backpropagation algorithm? Given a neural network, the parameters that the ...
In the backward() function like we have in the derivation, first calculate the dA,dW,db for the L'th layer and then in the loop find all the derivatives for remaining layers. The below code is the same as the derivations we went through earlier. We keep all ...
The main contribution of this letter is the derivation of a steepest gradient descent learning rule for a multilayer network of theta neurons, a one-dimens... McKennoch,Sam,Voegtlin,... - 《Neural Computation》 被引量: 41发表: 2009年 Hyperbolic Gradient Operator and Hyperbolic Back-Propagation...
derivation of the back-propagation method: trainrx. Neural network training The back-propagation algorithm consists of error-back propagation that allows supervised training of multi-layers of nodes =-=[29]-=-. This method is a ... Rahim,G Mazin - 《Journal of the Acoustical Society of Ameri...
The reason for this result is the small number of data selected for training and the limited derivation of thresholds and weights by the BP neural network. It is worth noting that the BP neural network also performs well after optimizing the thresholds and weights by GA (as shown in Figure ...
where 𝑥𝑑xd is a given signal, 𝑥1x1 is the state variable of the system; derivation of 𝑒2e2 can be obtained in the following way: 𝑒˙2=𝑥˙𝑑−𝑥˙1=𝑥˙𝑑−𝑥2.e˙2=x˙d−x˙1=x˙d−x2. (28) The input of BP neural network can be expressed as...
When calculating partial derivatives, any variable that isn’t the one you care about, you just treat as a constant and do normal derivation. If you put both of those values together into a vector you have what is called the gradient vector. The gradient vector has an interesting property,...
where\(\tilde{\mathbf {b}}_{l}\)is the derivation of non-linear activation function of thelth layer,\(\tilde{\mathbf {b}}_{l} = \frac{\partial \sigma (\mathbf {z}_l)}{\partial {\mathbf {z}_l}}\). Since bp-DNN has an inverted structure, showing in Fig.1, we use an ...