{"ID":6138650,"CreatedAt":"2026-07-09T01:07:32.349475501Z","UpdatedAt":"2026-07-10T11:58:56.339151614Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06628","arxiv_id":"2607.06628","title":"Cross-Trajectory Chimera Interventions Reveal Dissociable Roles of Weight Magnitude and Direction in Grokking","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2607.06628","url_pdf":"https://arxiv.org/pdf/2607.06628v1","authors":"[\"Truong Xuan Khanh\"]","published":"2026-07-07T12:12:43Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}