Neural networks: Interactive exercises
In the interactive exercises below, you'll further explore the inner workings ofneural networks. First, you'll see how parameter and hyperparameter changesaffect the network's predictions. Then you'll use what you've learned to train aneural network to fit nonlinear data.
Exercise 1
The following widget sets up a neural network with the following configuration:
- Input layer with 3 neurons containing the values
0.00,0.00, and0.00 - Hidden layer with 4 neurons
- Output layer with 1 neuron
- ReLU activation function applied toall hidden layer nodes and the output node
Review the initial setup of the network (note:do not click the▶️ or>| buttons yet), and then complete the tasks below the widget.
Task 1
The values for the three input features to the neural network model are all0.00. Click each of the nodes in the network to see all the initializedvalues. Before hitting the Play (▶️) button, answer this question:
Now click the Play (▶️) button above the network, and watch all the hidden-layerand output node values populate. Was your answer above correct?
Click here for an explanation
The exact output value you get will vary based on how the weight and bias parameters are randomly initialized. However, since each neuron in the input layer has a value of 0, the weights used to calculate the hidden-layer node values will all be zeroed out. For example, the first hidden layer node calculation will be:
y = ReLU(w11* 0.00 + w21* 0.00 + w31* 0.00 + b)
y = ReLU(b)
So each hidden-layer node's value will be equal to the ReLU value of the bias (b), which will be 0 if b is negative and b itself if b is 0 or positive.
The value of the output node will then be calculated as follows:
y = ReLU(w11* x11 + w21* x21 + w31* x31 + w41* x41 + b)
Task 2
Before modifying the neural network, answer the following question:
Now modify the neural network to add a new hidden layer with 3 nodes as follows:
- Click the+ button to the left of the text1 hidden layer to add a newhidden layer before the output layer.
- Click the+ button above the new hidden layer twice to add 2 more nodesto the layer.
Was your answer above correct?
Click here for an explanation
Only the output node changes. Because inference for this neural network is "feed-forward" (calculations progress from start to finish), the addition of a new layer to the network will only affect nodesafter the new layer, not those that precede it.
Task 3
Click the second node (from the top) in the first hidden layer of the networkgraph. Before making any changes to the network configuration, answer thefollowing question:
Now, click in the text field for the weight w12 (displayed below thefirst input node, x1), change its value to5.00, and hit Enter.Observe the updates to the graph.
Was your answer correct? Be careful when verifying your answer: if a nodevalue doesn't change, does that mean the underlying calculation didn't change?
Click here for an explanation
The only node affected in the first hidden layer is the second node (the one you clicked). The value calculations for the other nodes in the first hidden layer do not contain w12 as a parameter, so they are not affected. All the nodes in the second hidden layer are affected, as their calculations depend on the value of the second node in the first hidden layer. Similarly, the output node value is affected because its calculations depend on the values of the nodes in the second hidden layer.
Did you think the answer was "none" because none of the node values in the network changed when you changed the weight value? Note that an underlying calculation for a node may change without changing the node's value (e.g., ReLU(0) and ReLU(–5) both produce an output of 0). Don't make assumptions about how the network was affected just by looking at the node values; make sure to review the calculations as well.
Exercise 2
In theFeature cross exercisesin theCategorical data module,you manually constructed feature crosses to fit nonlinear data.Now, you'll see if you can build a neural network that can automatically learnhow to fit nonlinear data during training.
Your task: configure a neural network that can separate the orange dots fromthe blue dots in the diagram below, achieving a loss of less than 0.2 on boththe training and test data.
Instructions:
In the interactive widget below:
- Modify the neural network hyperparameters by experimenting with someof the following config settings:
- Add or remove hidden layers by clicking the+ and- buttons to theleft of theHIDDEN LAYERS heading in the network diagram.
- Add or remove neurons from a hidden layer by clicking the+ and-buttons above a hidden-layer column.
- Change the learning rate by choosing a new value from theLearning ratedrop-down above the diagram.
- Change the activation function by choosing a new value from theActivation drop-down above the diagram.
- Click the Play (▶️) button above the diagram to train the neural networkmodel using the specified parameters.
- Observe the visualization of the model fitting the data as trainingprogresses, as well as theTest loss andTraining loss values intheOutput section.
- If the model does not achieve loss below 0.2 on the test and training data,click reset, and repeat steps 1–3 with a different set of configurationsettings. Repeat this process until you achieve the preferred results.
Click here for our solution
We were able to achieve both test and training loss below 0.2 by:
- Adding 1 hidden layer containing 3 neurons.
- Choosing a learning rate of 0.01.
- Choosing an activation function of ReLU.
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Last updated 2025-08-25 UTC.