Continuous Function

Learning with agents · public prototype

When does a gradient step go too far?

Make a prediction, ask for a hint, and inspect the calculation. Then carry the same example into your own Codex or Claude session.

Working now: local calculation and authored guidance. Hosted AI assistance is planned. See the direction →

01 / Try the mechanism

Downhill is a direction. Step size still matters.

Imagine adjusting two model parameters, x and y, to reduce an error. This small example uses L(x, y) = x² + 2y². A gradient gives the local uphill direction; a gradient step subtracts a chosen multiple of it.

One step, two dimensionless parameters, no trained model. New to gradients? Open the full lesson.

Start at (2, 1) with loss 6.

After one step, will the loss…
One step on a quadratic lossContours of L(x,y) = x squared plus 2 y squared. A starts at (2, 1) with loss 6. The endpoint will appear after you check the step.L=1L=2L=6L=12xy0-2-2-1-11122A (2, 1)
A is the starting point. B stays hidden until you check the step. Each ellipse joins points with equal loss; smaller contours have lower loss.

02 / Carry the example forward

Give your agent the calculation, not just the question.

A useful learning partner should know which example you tried, what you predicted, and what the calculation supports. Export that context for your own Codex, Claude or another assistant.

Check a prediction or inspect a worked example above to prepare your task.

Your selections stay in this page's memory and clear on refresh. Download a packet to keep them. No account or API key is needed.

03 / The direction

Assistance that helps you reason, and work you can inspect.

We are building toward a learning environment where an assistant can explain a selected step, suggest a useful comparison and help reproduce a calculation. You keep control of the question, the evidence and the next move.

  1. Available here

    A checked learning object

    Local hints, predictions, exact calculations and a portable task packet. The guidance is authored; no model is connected.

  2. Next · qualification required

    Grounded model explanations

    Help attached to the current example and validated calculations, with clear sources, assistance records and an option to try without help. Before launch: sign-in, usage limits, cost controls and tests for incorrect or answer-revealing guidance.

  3. Later · separate approval

    Isolated coding workers

    Codex or Claude Agent SDK could draft a code witness or inspect a bounded experiment in a separate workspace. Each job would need explicit permissions, a spending limit, constrained tools and checked outputs. A person decides what is accepted or published.

Current interface research: Codex SDK, OpenAI Agents SDK, and Claude Agent SDK. These are implementation options, not integrations active on this page.

This prototype has technical checks, not an independent human security audit or a measured learning-effectiveness result. Hosted assistance remains unavailable while its safeguards are being qualified.

Continue with the gradient descent lesson →