Abstract
This study explores which properties of a partially trained network are causally portable to a different, independently trained network. Single-trajectory interventions show necessity within one run but lack 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.
In 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 out of 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, perfectly separating all 20 pairs by norm class (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.
Blogger's Review: This research utilizes the innovative approach of cross-trajectory chimera interventions to delve into the distinct roles of weight direction and magnitude, revealing the complexities of training processes in deep learning and providing valuable insights for future model design and optimization.