# Understanding Mean Squared Error in Neural Networks

• hisham.i
In summary: The mean squared error is a measure of how consistent the error values are over time, and is used in many different areas of machine learning including neural networks. In a neural network, the learning algorithm will stop when the mean squared error is less than a certain value.

#### hisham.i

In neural network the learning algorithm ends when the mean squared error value is less than or equal to a value we have precised.
But i don't understand why we are comparing with the mean squared error and not the mean error?
What does the mean squared error represent?

I'm not sure of the exact answer you require, but if it's anything like using RMS values it's pretty straight forward.

Let's say you have two error values: -1 and 1

The mean error value is 0.
The mean squared error is 1.

If I remember correctly, it is because you have alternating positive and negative values and no matter what you do you end up with 0 as the mean if you simply take the average of the exact values.

For example, with alternating current of 230V (UK standard supply) you have a sin wave with a maximum of +320V and a minimum of -320V. If you average these values you get an average voltage out of your wall socket of 0V - this is of no use to you.

So you use an RMS (Root Mean Squared) value to get a useful value.

In this case you have +320V and -320V. So you square them (+3202 and -320V-2).
Add the squared values together (+320V2+-320V2).
Square root them and then take the mean (Sqrt(+320V2+-320V2))/2.

This then gives you the RMS voltage. For the UK this is ~230V.

So by using a value such as your "squared error" you get a useful answer instead of 0 every time.

hisham.i said:
In neural network the learning algorithm ends when the mean squared error value is less than or equal to a value we have precised.
But i don't understand why we are comparing with the mean squared error and not the mean error?
What does the mean squared error represent?

I'm sure you mean the root mean squared error meaning the root of the averaged sum of the squared differences from the averaged value.

## 1. What is Mean Squared Error (MSE)?

Mean Squared Error (MSE) is a metric used to evaluate the performance of a neural network. It measures the average squared difference between the predicted and actual values of the output variables. A lower MSE indicates a better fit of the model to the data.

## 2. How is MSE calculated in a neural network?

In a neural network, MSE is calculated by taking the average of the squared differences between the predicted and actual values of the output variables for each data point in the training set. This value is then used as a measure of the network's performance and is used to update the network's parameters during the training process.

## 3. What is the significance of MSE in neural networks?

MSE is an important metric in neural networks as it allows us to quantitatively evaluate the performance of the model. It helps us to identify how well the network is able to predict the output variables and adjust the model accordingly to improve its performance.

## 4. What are some factors that can affect the MSE in a neural network?

The MSE in a neural network can be affected by a variety of factors, such as the complexity of the network, the amount and quality of the training data, the selection of input features, and the choice of activation functions and optimization algorithms.

## 5. How can MSE be used for model selection in neural networks?

MSE can be used as a criterion for model selection in neural networks. By comparing the MSE values of different models, we can determine which one performs better on the given dataset. However, it is important to note that MSE should not be the sole criterion for model selection, as other factors such as interpretability and generalization ability should also be considered.