Neural networks and the derivatives of the cost function

In summary, the conversation is about the derivation of the derivatives of the quadratic cost function in an artificial neural network. The person is having trouble finding the derivative of the cost function with respect to the weight matrix and is looking for resources for a thorough derivation or linear algebra resources that could help with their question. A helpful derivation from stats.stackexchange is also mentioned, which focuses on the chain rule for derivatives.
  • #1
2sin54
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Hello. I need some guidance on the derivation of the derivatives of the quadratic cost function (CF) in an artificial neural network. I can derive the equations for the forward propagation with no trouble but when it comes to finding the derivative of the CF with respect to the weight matrix (matrices) I struggle to distinguish where to use the Hadamar product, where to use the dot matrix product and the order of the multiples. Does anyone know some good resources where I could see a thorough derivation of this OR linear algebra resource relevant to my question?
 
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  • #2

1. What is a neural network and how does it work?

A neural network is a type of machine learning algorithm inspired by the structure and function of the human brain. It consists of interconnected nodes, or neurons, that process and transmit information. The network learns by adjusting the strength of connections between neurons based on the data it is trained on.

2. What is the cost function in a neural network?

The cost function in a neural network is a mathematical expression that measures the difference between the predicted output of the network and the actual output. It is used to evaluate the performance of the network and guide the learning process by minimizing the cost through the adjustment of parameters.

3. Why do we need to calculate the derivatives of the cost function in a neural network?

The derivatives of the cost function are used to update the parameters of the neural network during the learning process. By calculating the derivatives, we can determine the direction and magnitude of the change needed to minimize the cost function and improve the performance of the network.

4. How are the derivatives of the cost function calculated in a neural network?

The derivatives of the cost function are typically calculated using the chain rule, which involves taking the partial derivative of the cost function with respect to each parameter in the network. This process is repeated for each layer in the network, starting from the output layer and working backwards.

5. What is the role of backpropagation in calculating the derivatives of the cost function?

Backpropagation is an algorithm used to efficiently calculate the derivatives of the cost function in a neural network. It works by propagating the error from the output layer back through the network, using the chain rule to determine the contribution of each layer to the overall error. This allows for faster and more accurate calculation of the derivatives compared to other methods.

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