How many skipped training steps hide in the loss noise?

research/compute-shirking

Detecting skipped training steps from the loss alone: hidden compute is the loss curve inverted at the noise band (f* = 1−(1+(e^q−1)/r)^{−1/β}), grows as reducible loss falls, seed noise sets a floor no eval size removes, simulation matches within 1.5 points, and the loss test is worth ≈4.4 step audits at best.

14 tests

What it found

If a worker paid for T steps runs only (1−f)T, the verifier’s log-loss test (null sd σ′, level α) hides exactly the compute at which the loss curve, inverted, crosses the noise band: L((1−f*)T) = L(T)e^{σ′(z_α+z_P). For a power law with a loss floor this is closed form and grows as the reducible share r falls (6% at r=1 but 64% at r=0.05 for σ′=0.02). Run-to-run seed noise is a floor that no evaluation size removes: with 2% seed noise a 5% cap is unreachable for r ≥ 0.05, while without it 10⁴ to 4×10⁶ eval samples suffice. On exactly solvable quadratic GD the predicted detection probability matches simulation within 1.5 points, and the loss test is worth only about 4.4 random step audits at best (0.16 once training is floor-dominated). Stylised: one statistic, normal approximation, known curve family.}

A figure from its own output

Figure produced by research/compute-shirking: hidden_fraction — compute-shirking/experiments/hidden_fraction.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.