PYTHON · NUMPY

The observer's physics

The observer reconstructs actions with textbook physics that has no spring. Its label error, plotted against pole angle, has slope:

Reconstruct actions from observed motion the way video pipelines do, and measure the systematic error the missing substrate leaves in the labels.

01Challenge

Invert the textbook cart-pole, no spring, no damper, no wind, on each observed transition of the real plant. Plot the label error against pole angle, per stiffness.

Predict firstThe observer reconstructs actions with textbook physics that has no spring. Its label error, plotted against pole angle, has slope:

02Model

Human video has no motor port. Every large-scale egocentric pipeline gets its action labels by reconstruction: watch the motion, invert a model of the body, call the result the action. The catch fits in one sentence. The observer's model has no substrate in it, and from outside, the substrate's torque and the motor's torque are physically indistinguishable, so whatever the spring did gets booked to the motor. This bench does the reconstruction honestly on our plant and then does what a pipeline cannot: compares against the true logged action, because in simulation we have it. The error is not noise. Plotted against pole angle it is a line, and the line's slope is the spring showing through: near zero on the free body, four and a half at soft stiffness, sixteen at the passive threshold's double, thirty-five on the stiffest. And note the trap in the last column: the mean absolute error barely grows, because a stiff body holds its angle small. A large systematic slope hides inside a small average, waiting for the first situation that holds the angle away from zero.

03Guided practice

Run the regression per body. Read the slope column as the substrate leaking into the labels and the flat mean column as why nobody notices.

04Feedback

PASS WHEN You measured the label error's slope growing from zero to thirty-five with stiffness.

If your run fails, check:

On the free body the observer's model is right and the slope sits at noise. The slope is not a flaw of inverse dynamics; it is precisely the unmodelled substrate.
The mean absolute error moves only from 0.084 to 0.120 newtons across a sixty-fold slope change, because stiff bodies keep their angles tiny. Averages hide structure that slopes reveal.
The flat part of the error is the unseen disturbance, which the observer also hands to the motor. Everything the camera cannot see ends up in the label, and the label is what the policy will imitate.

05Retrieve & space

Why are spring torque and motor torque indistinguishable from outside the body?
Why does a sixty-fold change in slope barely change the mean absolute error?
Name the two distinct contributions this bench found inside the reconstructed labels.

06Mastery & project

Given a body model used for label reconstruction and the true plant, predict the sign, the scaling, and the hiding place of the induced label error.

Look up how one hand-pose or inverse-dynamics labelling pipeline you know models the hand or body. List the compliances it omits, and state where its label error will concentrate.

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PYTHON · NUMPY

The observer's physics

Sixteen expert episodes per stiffness, every transition reconstructed and differenced against the logged action, then one linear fit per body.

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