匿名共享是成对相位盲
Anonymous sharing is pairwise phase-blind
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中文总结 AI 辅助
该研究通过积分-点火振荡器模型证明匿名共享资源下作业间成对相位耦合消失，同步为非吸引子不动点，随机作业群无锁定但仍有I/O突发，仅异构作业在绑定上限时产生成对耦合。
中文摘要 AI 辅助
独立训练作业共享存储系统时，会通过相同的有限带宽写入检查点，由此产生的相关I/O突发通常被描述为自我强化的“检查点风暴”。我们将这种自我强化形式化为通过共享资源耦合的积分-点火振荡器群体中的相位锁定，并在该模型中证明其不成立。若资源对活跃用户的交付速率仅取决于活跃用户数量而非具体用户，则称该资源是匿名的。对于写入时间短于计算间隔的相同作业，匿名资源完全不会产生成对耦合：在存储竞争、共享功率上限以及两者同时存在的情况下，两作业相位差的返回映射均为恒等映射，因此Kuramoto和Mirollo-Strogatz框架所基于的两体相互作用在此处并非弱耦合，而是完全不存在。对于任意规模的作业群和任意上限，匿名性还会冻结点火顺序，因此没有轨迹能从外部达到同步状态。残留的是三阶效应：当所有N个写入窗口重叠且上限未绑定时，连续写入起始时间间隔的映射为a_j ↦ ((N-j)/j)a_j，具有倒数谱和单位行列式，使得同步是具有⌈N/2⌉-1个膨胀方向的不动点，而非吸引子。该行列式源于匿名性而非公平性：对于满足f(n)≤n的任意匿名吞吐量f，谱变为(N-j)f(j)/(j f(N-j))，其乘积仍为1。数值模拟显示，随机启动的作业群既不会锁定也不会聚类，且无锁定并非无突发：并发写入者数量的上尾始终高于独立相位值。绑定上限后的异构作业确实会产生真实的成对耦合，这是该结论不再通用的地方。
英文摘要
Independent training jobs sharing a storage system write their checkpoints through the same finite bandwidth, and the resulting bursts of correlated I/O are commonly described as a self-reinforcing "checkpoint storm". We formalise the self-reinforcement as phase locking in a population of integrate-and-fire oscillators coupled through a shared resource, and show that within that model it fails. Call a resource anonymous if the rate it delivers to an active user depends on how many users are active and not on which. For identical jobs whose write is shorter than their compute interval, an anonymous resource produces no pairwise coupling at all: the two-job return map of the phase gap is the identity, under storage contention, under a shared power cap and under both, so the two-body interaction on which the Kuramoto and Mirollo-Strogatz frameworks are built is not weak here but absent. Anonymity also freezes the firing order, for any fleet size and any cap, so no trajectory reaches the synchronous state from outside it. What survives is a third-order effect: where all $N$ write windows overlap and the cap does not bind, the map is diagonal in the intervals between consecutive write starts, $a_j \mapsto ((N-j)/j)a_j$, with reciprocal spectrum and unit determinant, making synchrony a fixed point with $\lceil N/2\rceil-1$ expanding directions rather than an attractor. That determinant follows from anonymity and not from fairness: for any anonymous throughput $f$ with $f(n)\le n$ the spectrum becomes $(N-j)f(j)/(j f(N-j))$, whose product is still one. Numerically, a fleet launched at random neither locks nor clusters, and absence of locking is not absence of bursts: the upper tail of the number of concurrent writers stays above its independent-phase value. Heterogeneous jobs behind a binding cap do acquire a genuine pairwise coupling, which is where the statement stops generalising.
