An illustrative studio note. This is an exploratory direction, not a published research result.
The question
Machine learning often feels opaque because the interesting activity happens between the input and the output. Making an individual update visible gives us a smaller, more approachable unit of explanation.
The exploration
The gradient descent experiment starts with f(x) = x². That deliberate simplicity lets the learning rate, derivative, and sequence of guesses remain visible at the same time. A learner can watch a small rate approach the minimum, then compare it with oscillation or divergence.
What comes next
The next direction would be to introduce a two-dimensional surface and noisy gradients while preserving the ability to inspect each update. This is an illustrative notebook and proposed design exploration, not a published evaluation.