PYTHON · NUMPY

Two demonstrations against one hundred and twenty-eight

At kp=0 the clone gets sixty-four times more demonstrations, 2 to 128 episodes. How much operating region does that buy?

Clone the expert from camera observations at two data volumes on two bodies, and measure which axis moves the outcome: data or substrate.

01Challenge

A behaviour clone sees positions only, the way a camera does. Train it on 2 episodes and on 128, on the free body and the passively stable one. Fill the two-by-two table.

Predict firstAt kp=0 the clone gets sixty-four times more demonstrations, 2 to 128 episodes. How much operating region does that buy?

02Model

Now run the industry's experiment. A behaviour clone learns from demonstration frames, and like a camera it sees positions only: no velocities, no motor current, no efference. Give it a real function class, random Fourier features with ridge regression, so it can genuinely absorb more data. Then move the two levers separately: data from 2 episodes to 128, body from free to passively stable. The data thesis predicts the data axis matters. The two-operating-systems thesis predicts the body axis dominates, because most of what the stiff body contributes is not in the observations, so no amount of them can teach it, and most of what the free body needs is velocity feedback the camera never shows, so no amount of data can supply it. One of these predictions fails in this bench. The full research bench behind this lesson ran the same grid to 512 episodes at 256 seeds with the prediction registered before the run, and found the data axis worth minus 0.027 and the body axis worth plus 0.742.

03Guided practice

Run the grid. Compare within columns for the data effect and across columns for the body effect, then compare the kp=0 column against the expert's own 0.271 from the previous lesson.

04Feedback

PASS WHEN You measured the data axis flat and the body axis worth +0.729 region.

If your run fails, check:

At kp=0, two demonstrations and one hundred and twenty-eight score identically: 0.271. Sixty-four times the data bought nothing, because what is missing is velocity, and velocity is not in any frame.
The clone at kp=0 matches the expert's own region from the last lesson. The ceiling was never the policy or the data. It is the body's, and data cannot raise a ceiling the body owns.
On the stiff body two demonstrations already score 1.000. The observations barely matter because the behaviour barely lives in them. That is the thesis in one row.

05Retrieve & space

Why does more data fail at kp=0? Name the specific missing quantity.
Why do two demonstrations suffice at kp=1.00?
The research bench found 256 times more data worth minus 0.027 region. Why can that number be slightly negative rather than zero?

06Mastery & project

Predict, for a given observation set and body, whether the next order of magnitude of demonstrations will move competence, and say which axis would.

Estimate the cost of one order of magnitude more demonstration data for a robot you know, and the cost of raising its passive stability instead. Compare the two invoices against this lesson's table.

GO FURTHER · THE LIVE PLAYGROUND

Read the measurement section of TR-2026-43 ↗ · The registered predictions, the full grid to 512 episodes, and both falsifications.

← The demonstrator's secret The model that cannot exist →

PYTHON · NUMPY

Two demonstrations against one hundred and twenty-eight

Random Fourier clone, positions only. Two demo counts, two bodies, forty-eight test episodes per cell on seeds disjoint from the demonstrations.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you