The following is a simple neural network I made for demonstration purposes. The network trains on a subset of the famous iris dataset found here.
Use the Initialize button to give random values to the neural net matrices' entries, and to reset the step-size for RMSProp gradient descent. The Next Sample button proceeds to the next x-y* pair, and the Predict button lets us see what the neural net, with its current parameters, would predict for the current x. After making a prediction for a given sample, the Adjust button should be used to utilize back-propagation to adjust the neural net matrices' entries appropriately. Finally, the Train button lets us iterate through 1000 cycles of Next Sample, Predict, and Adjust.
After training the desired network, switch the Mode to Validation. Then, press the Validate button to obtain the validation accuracy of the network on a subset of the iris-dataset that was withheld during training.