Define the two-layer XOR network data contract

Make malformed input fail before it reaches the interesting algorithm. The accepted contract is the four binary XOR examples, represented as two floats and one binary target. This boundary matters because dead ReLU paths, incompatible tensor shapes, exploding activations, and mistaking depth for guaranteed quality; allowing a bad value through makes later debugging look like an algorithm problem. Keep transformation functions separate from scoring or prediction so a test can identify which boundary changed the data.

The artifact's user-facing goal is specific: show why a hidden layer can solve XOR while a single straight decision boundary cannot. Its accepted input is the four binary XOR examples, represented as two floats and one binary target. Those statements are intentionally narrower than “build an AI system.” Narrow scope lets us inspect every input and expected result, and it prevents a toy result from being presented as a production claim. The example implements or probes the input boundary. Copy it into a fresh file and run it without extra packages.

Save this as lesson.py and run python3 lesson.py. It uses only the language standard library, so the example is reproducible offline.

def relu(x): return max(0,x)
def forward(x):
 h=[relu(x[0]-x[1]),relu(x[1]-x[0])]
 return h, h[0]+h[1]
print(forward((1,0)))

Expected output: hidden [1, 0] and score 1. Exact floating-point formatting may vary slightly, but the asserted behavior must not. Read the output as evidence about this stage, not merely proof that the interpreter started.

Print both hidden activations for all four XOR rows. A hidden unit that is zero for every row is dead and contributes nothing; revisit its weights before changing the output threshold. When a dot product fails, print both dimensions and repair the architecture, not the input by truncation. Keep the linear baseline visible: XOR's value is demonstrating representation, not merely obtaining four correct labels.

At the data contract stage, save the smallest failing fixture beside the expected result. Change one cause at a time and rerun the exact command printed above; that makes the repair reviewable and keeps this chapter's progressive artifact reproducible.

Assert the exact XOR truth table, then calculate hidden-unit activation coverage and prediction margin. Compare with the best single linear boundary, which cannot classify all four corners. Perturb each input slightly only if the declared domain permits non-binary values, and state that this fixed-weight demonstration explains a forward pass rather than proving a trained deep model will generalize.

For this data contract page, preserve the fixture and result as evidence for the next page. Label observations separately from conclusions: a passing assertion establishes the behavior it names, while broader usefulness requires the chapter's full evaluation set and stated operating limits.