Neural Networks: A Forward Pass You Can Check

Artificial Intelligence and Data Science · CHAPTER 4 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Compute one neuron and understand the role of activation.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

A neuron combines inputs using weights and a bias, then applies an activation. Stacking neurons builds nonlinear functions. Training adjusts parameters to reduce an objective; the forward pass alone does not learn. Architecture size is not evidence of generalisation.

2. Write the model

z = wx+b; ReLU(z) = max(0,z)

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

For w=2 and b=−1, inputs 0,1,2 give z=−1,1,3 and ReLU outputs 0,1,3. The kink at zero creates a nonlinear response.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Input x	z=2x−1	ReLU(z)
0	-1	0
1	1	1
2	3	3

Sweep x through the activation boundary at 0.5. Compare the linear pre-activation with the clipped output.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What output follows for x=0.25?

Reveal the answer and check your work

0, because z=−0.5.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

This forward calculation is not a trained deep-learning experiment.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.