Single-impulse push recovery is a binary chaotic quantity - cross-machine floating-point divergence can flip the outcome
single-impulse-recovery-is-chaotic.Never gate or compare single-event recovery outcomes across machines or domains: evaluate disturbances as survival distributions over phases and seeds, compare longitudinally on one machine, and treat any single-point cliff as unconfirmed until it survives the statistical protocol.
Symptom
Mac evaluation found a hard "0.8 N*s cliff" (0/3 survival) that the training machine flatly contradicted: the identical protocol (0.8 impulse at 8 s, cmd 0.2) survived 3/3 there, and a 0.6/0.8/2/4 cross sweep survived everything.
Context
The verdict became a named lesson ("跨机混沌课文"): whether one specific push at one specific phase is survived depends on a trajectory that diverges across machines from floating-point differences alone - "单次冲量恢复是二值混沌量, 跨机浮点发散可翻结局". The boundary was drawn precisely: the 20-seed statistical gates DO agree across machines (established precedent), but that agreement cannot be extrapolated to single-point recovery tests. Protocol amended: disturbance evaluation uses multiple push phases (8/10/12 s), >=10 seeds, and only same-machine longitudinal comparisons; the Mac-side recommendation built on the unreproducible cliff was not adopted, while its directionally-consistent small-impulse data was kept.
Change
Push evaluation redefined from single-event pass/fail to multi-phase multi-seed statistics, with cross-machine comparison banned for event-level results and allowed for distribution-level ones.
Outcome
A false hardware-relevant "cliff" was prevented from steering the ladder (the s2e push rung decisions were made on same-machine statistics); the chaos lesson was cited again when real push tests were restricted to qualitative cross-domain use.
Mechanism
Perturbation recovery near the viability boundary has sensitive dependence on initial conditions; different BLAS/GPU reduction orders yield different trajectories from identical configs, so a binary outcome at one phase is machine-specific noise. Averaging over phases and seeds restores a quantity whose expectation is machine-stable.
Applies when
- a push/disturbance result differs between machines or sim and real
- designing push-recovery acceptance tests
- a sharp pass/fail cliff appears in a chaotic-regime evaluation
“训练机上 Mac 原协议 (0.8 @8s cmd0.2) 3/3 全活 … 与 Mac 的 +0.8 0/3 直接矛盾。定性: 单次冲量恢复是二值混沌量, 跨机浮点发散可翻结局;统计门 (20-seed 八门) 跨机吻合的先例不能外推到单点恢复测试。协议改判: 抗推评测多相位 (push 时刻 8/10/12s) + ≥10 seed + 只做同机纵向比”