Deriva — Derive the Algorithm

← ProjectBuild Everything / A1Gradient Descent: The Engine of All Learning~30 min

A1descend the loss15 lines · Nothing

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.

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

Optional design question

Think through the mechanism first if you want the extra reasoning step. It never blocks the editor.

Visible contract tests

•
two updatesgradient_descent(2.0, 0.25, 2)
the update must move downhill and record both the start and each new point
•
zero stepsgradient_descent(3.0, 0.1, 0)
zero iterations still expose the initial loss
•
zero startgradient_descent(0.0, 0.5, 2)
the optimum is stable under further updates

3 hidden edge tests run after the visible contract passes.

def gradient_descent(start, learning_rate, steps):
    # Return [step, x, loss] for the starting point and every update.
    # f(x) = x ** 2, so its gradient is 2 * x.
    # Keep the history observable: it becomes the evidence for every later lab.
    pass

Run Tests to see the contract verdicts here.

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