Lab: Build a Two-Layer XOR Network

Mission

Build a hand-checkable layered calculation that matches all four XOR cases. You will not hide a failed row or claim that four binary cases prove anything about a deployed neural network.

Network specification

Use the step function step(z) = 1 when z ≥ 0; otherwise it returns 0.

h1 = step(x1 + x2 - 0.5)       # OR-like hidden feature
h2 = step(x1 + x2 - 1.5)       # AND-like hidden feature
y  = step(h1 - 2h2 - 0.5)      # combine the hidden features

The hidden layer changes the representation. Instead of asking one line to separate the original four points, the output unit receives two intermediate features.

Completed guided row

For x1 = 1 and x2 = 1:

h1 score = 1 + 1 - 0.5 = 1.5  → h1 = 1
h2 score = 1 + 1 - 1.5 = 0.5  → h2 = 1
y score  = 1 - (2 × 1) - 0.5 = -1.5 → y = 0

The XOR target for 1,1 is 0, so this row passes.

Procedure

1. Copy the four XOR input rows into a Layered Network Test Record.
2. For each row, calculate the raw score and output of h1.
3. Calculate the raw score and output of h2.
4. Use those hidden outputs to calculate y.
5. Compare y with the XOR target. Mark pass or fail without editing the target.
6. Change only the output weight on h2 from -2 to -1.
7. Rerun all four rows and identify the first exact counterexample.
8. Restore -2 and write a bounded conclusion.

Record template

Success criteria

• every raw score can be independently recalculated;
• the baseline network passes all four supplied XOR cases;
• the changed-weight run preserves at least one exact failure;
• the explanation identifies the hidden layer as a representation change; and
• the limitation rejects claims about learning quality, generalization, safety, biological brains, or larger neural networks.

Troubleshooting

If step(0) differs between group members, return to the declared rule: this Lab defines it as 1. If the changed run still appears to pass, inspect the 1,1 row and show the raw output score. If a value changes unexpectedly, recalculate one unit at a time instead of carrying the entire network mentally.

Safety and runtime boundary

Use only the four supplied binary cases. This deterministic paper-or-local calculation sends no data over a network, trains no model, and makes no real decision. Submit the complete table and both conclusions; a photograph of an incomplete table is not equivalent evidence.

robotnix-ai-lab :: local deterministic XOR network
Target mapping: 00→0 · 01→1 · 10→1 · 11→0
Predict both hidden clues, then run the forward pass.