发表机构
University of Puerto Rico（波多黎各大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过 64 个种子网络的副本重叠探针检验 grokking 转变，发现注册探针因对齐缺陷失效，仅标准差比率具有统计功效，结论为未确定。
AI 中文摘要
我们在四种配置下训练了 64 个独立种子的网络，并将每个网络持续训练至稳定收敛或 40,000 轮的上限。随后，我们探究了受 RSB 启发的成对权重重叠分布在 grokking 转变过程中是否发生变化。决定这一注册探针能报告何种结果的是对齐步骤，而非重叠统计量本身。注册实现仅对隐藏单元进行置换，而未相应置换偏置和头部内部置换，因此并未保持网络函数不变。通过这种对齐计算出的每个 q_wt 值都继承了该缺陷；而 q_fn 则不受影响，因为它基于未置换模型的预测计算。数值精度要求也未满足，审计发现了协议偏差。因此，预注册规则无法给出判定：注册结果为“未确定”（原因代码 C0_INSTRUMENT_INVALID）。这些数据既不能提供验证性的零结果，也不能提供对 Parisi 序参数的有效解读。只有 frac40 配置满足了 12/16 的检查点完整性要求。对于该配置，对相同数据应用的事后标准给出的 Hartigan-dip 区间包含零（Delta dip 的 95% CI = [-0.017, 0.034]），而重叠标准差增大了约 5.6 倍。事后校准表明，在模拟分离度下 dip 检验的功效为零；因此该区间不具信息量，而非无变化的证据。标准差比率是唯一在观测效应下具有功效的统计量。仅在预设的 1% 阈值下，集成损失接近平坦。最后，grokking 率 0/16、11/16 和 16/16 仍仅为描述性结果，因为训练比例与分割身份混杂。
英文摘要
We trained 64 independently seeded networks in four configurations, continuing each to sustained convergence or a 40,000-epoch ceiling. We then asked whether an RSB-inspired distribution of pairwise weight overlaps changes across the grokking transition. It is the alignment step, not the overlap statistic, that determines what this registered probe can report. The registered implementation permutes hidden units without the corresponding bias and head-internal permutations and therefore does not preserve the network function. Every q_wt value computed through this alignment inherits the defect; q_fn does not, because it is computed from predictions of the unpermuted models. The numerical-precision requirement also failed, and an audit found protocol deviations. Consequently, the pre-registered rule gives no verdict: registered outcome UNDETERMINED (reason code C0_INSTRUMENT_INVALID). These data provide neither a confirmatory null nor a validated reading of the Parisi order parameter. Only frac40 cleared the 12/16 checkpoint-completeness requirement. For this configuration, a post-hoc criterion applied to the same data gave a Hartigan-dip interval containing zero (95% CI for Delta dip = [-0.017, 0.034]), whereas the overlap standard deviation increased by a factor of about 5.6. A post-hoc calibration assigns the dip test zero power at the simulated separations; the interval is therefore uninformative, not evidence of no change. The standard-deviation ratio is the only statistic here with power at the observed effect. Ensemble loss was near-flat only under the pre-specified 1% threshold. Finally, grokking rates of 0/16, 11/16 and 16/16 remain descriptive because train fraction is confounded with split identity.
Comments13 pages, 5 figures. Pre-registered study; the registered decision rule returns UNDETERMINED (reason code C0_INSTRUMENT_INVALID) because the registered alignment implementation is not function-preserving. Reported as an honest negative/instrument-invalid result
