Deriva — Derive the Algorithm

← Projectsclassifier-lab / L4Gradient Descent~22 min

one move: bound a failure

Implement the smallest learning loop. For f(x)=x², start at any x, repeatedly move against the gradient, and return the complete loss history so another engineer can inspect every update. In the Classifier Lab system, implement this level as a deterministic contract before composing it with the next service.

Required API

def gradient_descent(start, learning_rate, steps):
    return [[step, x, loss], ...]

Behavior

the returned history includes the starting point at step 0
each update uses the gradient of f(x)=x², which is 2*x
x moves against the gradient: x = x - learning_rate * 2*x
loss is x² and is recorded after every update
the input values are not mutated

Examples — tap to reveal

Constraints

return exactly steps + 1 rows
each row is [step_number, x_value, loss_value]
steps is a non-negative integer and learning_rate is a number

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