How much smoothing does a differentiable twin of a hard contact event need, and what does it cost?

research/smooth-twin

Smoothing a hard contact edge to make a twin trainable: real gradient is zero, twin ascent is trapped below τ_c=0.105 and misses the edge above R/(8cm), annealing crosses the trap, and the overshoot ≈τ ln(R/(2cmτ)) is an implicit safety margin capped at 0.168.

11 tests

What it found

A hard success edge has zero real gradient, so a smoothed twin is the only learning signal. The twin optimum overshoots the edge, θ ≈ τln(R/(2cmτ)) (within 5% at τ=0.02), and gradient ascent from the nominal pose is trapped below τ_c=0.105 (real regret 0.75) while above τ_u=R/(8cm)=0.25 the twin optimum falls below the real edge and regret jumps to 0.98. Annealing τ from 0.2 crosses the trap (regret 0.08 at τ=0.02; the real plant alone needs 161 to 3.5×10⁶ evaluations). With an uncertain real edge the overshoot is a safety margin: the best trainable width is within 0.0014 expected regret of the Bayes-best pose, but reachable margins are capped at 0.168 and annealing to zero width discards the margin. Stylised (one parameter, logistic smoother, deterministic ascent, simulated “real” plant).

A figure from its own output

Figure produced by research/smooth-twin: optimum_vs_tau — smooth-twin/experiments/optimum_vs_tau.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.