04 · Demonstrations, behavior cloning and ACT

Assumptions, implementation & acceptance

Action chunks are supervised sequences; temporal ensembling blends overlapping predictions for the same execution time. A low offline regression loss does not eliminate closed-loop distribution shift.

Formula conditions, units and worked arithmetic reviewed. The implementation isolates one numerical mechanism; it does not train a policy or control real hardware.

Before running: predict a boundary case

Predictions must refer to the same execution time; normalized nonnegative weights form a convex combination.

Minimal executable example

Save the example and linked modules in one folder. Use Node.js 22 or newer, then run node imitation-and-act.mjs. No third-party runtime dependencies.

const solve=()=>{
const predictions=[1,3], weights=[.75,.25];
return predictions.reduce((s,x,i)=>s+weights[i]*x,0);
};
const actual=solve();
const expected=1.5;
if(JSON.stringify(actual)===JSON.stringify(expected)){console.log('PASS',actual)}else{
const a=[actual].flat(), b=[expected].flat();
if(a.length!==b.length||a.some((v,i)=>!Number.isFinite(v)||Math.abs(v-b[i])>1e-10))throw Error('Numerical mismatch');
console.log('PASS within 1e-10',actual);
}

1.5

Test and transfer

Predictions must refer to the same execution time; normalized nonnegative weights form a convex combination.

Record input, code version, expected result and observed result in the notebook below. Then construct a counterexample that violates the assumption above and explain why the original conclusion no longer follows.