拆解神经网络权重的大小与方向，发现方向决定解决方案，大小影响稳定性。
Cross-Trajectory Chimera Interventions Reveal Dissociable Roles of Weight Magnitude and Direction in Grokking
- 将不同训练路径的权重分解为大小和方向，交叉重组后继续训练。
- 方向可迁移并决定最终解，40/40次实验中成功引导至捐赠者解。
- 适合研究模型内部机制或可解释性的研究人员阅读。
部分训练的神经网络中哪些属性具有因果可移植性？单轨迹干预仅显示某次运行内的必要性，而非跨运行可移植性。我们提出跨轨迹嵌合体干预：给定两个不同随机种子的训练结果，将每个权重向量拆分为模长和单位方向，将一个运行的模长与另一个的单位方向重组后继续训练。在两个发生‘领悟’（grokking）的模运算任务上，这两者可分离。方向携带可移植、捐赠者特异的电路身份：将捐赠者的方向植入接收者的模长，40/40次实验均引导该运行走向捐赠者的电路；而角度匹配的随机控制组无此效果。该转移呈阈值特性，其位置由接收者的模长预测，在全部20对组合中按模长类别完全分离（联合置换概率1.9e-4）。模长仅带来微弱、分布式的延迟效应，无身份信号。自适应二分法将阈值定位至±1/64范围内。方向决定轨迹趋近哪个解，模长则控制该身份被覆盖的敏感程度。
原文摘要 · Abstract (English)
Which properties of a partially trained network are causally portable to a different, independently trained network? Single-trajectory interventions show necessity within one run, not portability across runs. We introduce cross-trajectory chimera interventions: given two runs from different seeds, we split each weight vector into a norm and a unit direction, recombine one run's norm with the other's direction, and continue training. On two modular-arithmetic tasks that grok, the components dissociate. Direction carries a transferable, donor-specific circuit identity: implanting a donor's direction at the recipient's norm drives the run to the donor's circuit in 40/40 cases, while an angle-matched random control yields no shift. The transfer is threshold-like, and its location is predicted by the recipient's norm, separating perfectly by norm class over all 20 pairs (joint permutation probability 1.9e-4). Norm carries only a modest, distributed delay effect and no identity signal. An adaptive bisection procedure localizes the threshold to +/-1/64. Direction indexes which solution a trajectory approaches; norm governs how susceptible that identity is to being overwritten.
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