What does it cost to send only a fraction of the outer update, and does error feedback help?

What it found

Each worker transmits a random fraction p of its pseudo-gradient. Rescaling the subset (unbiased) inflates the stationary noise floor by exactly 1/p. Adding a per-worker error-feedback memory gives an exact closed form from a four-dimensional second-moment recursion and costs only 1 + αs(1/p − 1) at small steps, for any number of workers, because the virtual iterate follows uncompressed SGD. The price is speed: the mean dynamics have determinant 1 − p, so the contraction cannot beat √(1 − p) per round; over a 400-round horizon error feedback reaches 0.39, 0.24 and 0.17 of the unbiased loss at p = 0.25, 0.1, 0.03, and the advantage disappears when the horizon is shorter than about 1/p. Stylised: diagonal quadratics, Bernoulli masks, no top-k.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

• Can a DiLoCo-style run hide its synchronisation by applying the outer update rounds late?Overlapping the DiLoCo sync by applying the outer step τ rounds late does not pay: stable iff αs < 2 sin(π/(4τ+2)), best rate 1−2 sin(π/(4τ+2))/κ_H (exactly κ_H/(κ_H+1) at τ=1), momentum is useless once τ≥1 (69 → 1388 rounds at κ_H=100), hidden-sync gain ≤ (τ+1) sin(π/(4τ+2)) ≤ 1 (search: 1.5–4.9× slower than blocking averaging), fixed if the fresh pseudo-gradient has weight >½.
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• A free-space radar twin ignores ground-bounce lobing: how wrong is it, and can a two-ray twin with a slightly wrong target height be worse?Free-space radar twin vs two-ray ground-bounce lobing: detection fraction exactly 2/3 at the free-space range edge, real detects 44% beyond it, a two-ray twin with height error δh disagrees ≈4h_rδh/(λr) and is worse than free space at short range, a height-jitter ensemble scores Brier 0.119 vs 0.197 deterministic. Stylised.
• A point-target radar twin of two unresolved scatterers: it has the right median, so what does it get wrong, and does averaging looks converge where it says?Point-target radar twin of two unresolved scatterers under ideal monopulse: real mean is exactly the strong scatterer and median exactly the power centroid, outside-span probability arccos(r)/π, a variance-matched Gaussian twin is 27× too optimistic at a 3σ gate (r=0.9), averaging looks floors at bias 2r²/(1+r²) where the twin predicts √(var/N), and the median beats the mean for r≥0.477. Stylised.
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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.