Module 8 · Neural and language models

Module 8: guided construction and mastery

Start with the foundation bridge and applied concept sequence. This is the worked stage; the next stage removes implementation support. Use the existing environment for this module.

Predict before running

The actual label is 1. Predict whether this small update raises or lowers its probability and loss. Write what each array dimension represents. This demonstrates one logistic-output update; the hidden-layer derivatives are computed by the framework.

Follow a small worked implementation

import numpy as np
x = np.array([[1., 2.]])
w = np.array([[.5], [-1.]])
bias = .5
before = 1 / (1 + np.exp(-(x @ w + bias)))
gradient = (before - 1) * x   # one positive label; illustrative output-layer gradient
updated = w - .1 * gradient.T
after = 1 / (1 + np.exp(-(x @ updated + bias)))
print("Probability before/after:", before.item(), after.item())
print("Positive-label loss before/after:", -np.log(before.item()), -np.log(after.item()))

Change one thing and explain

Use a negative label instead: replace the target 1 by 0 in the gradient, then compare the negative-label loss -log(1-p) before and after. Reset before independent practice. Explain why a very large step might behave differently.

Record the prediction, actual output and explanation. If they differ, identify the line or assumption responsible instead of simply replacing your answer.

Reconstruct with less support

Open independent practice. Implement the three functions in its starter notebook. Visible checks give actionable feedback; solutions are separate. Preserve your attempted code and reasoning before inspecting a solution.

Connect to the complete study

After practice, use the complete reference walkthrough. Its real-data protocol, baseline comparison, final evaluation and artifacts remain the module reference. The small sandbox is development practice and does not replace that evidence.

Use practice solutions for misconception-specific feedback and recorded-study feedback to interpret the complete study. The pilot guide distinguishes technical verification from observed learner mastery.