Thanks for sharing this! It's been fascinating to try to piece together the story of subliminal learning, and it is very useful to have new experimental reports to help with this. A few quick comments: 1. The "Phantom transfer" paper reports positive results for subliminal effects with differently initialized models as well: arxiv.org/abs/2602.04899 (Cloud et al. also report a positive result in this space, for GPT-4.1 and GPT-4o, which are surely related models but which were not the same at the start of the SL experiments.) 2. It is easy to construct toy cases where different initializations lead to subliminal effects in the wrong direction for simple linear models, and it could be much worse for real LMs. Do you have any insights into how you have managed to avoid such situations? 3. Have you actually avoided such situations? The numbers for cross-model transfer seem pretty mixed. Are Figures 4B, A19B, and A26 really pictures of cross-model transfer? The effects seem weak at best to me. Maybe I am looking at this through the wrong lens? 4. Your results provide a clue that seems really valuable. You note that same-model transfer is generally early, as Cloud et al. would predict, whereas cross-model is generally late. This suggests different mechanisms in the two cases: gradient alignment for the same-model case, and, well, something else for cross-model. 5. For prompted subliminal learning, the generated dataset (in the limit) fully identifies the underlying prompt, and this goes a long way to explaining why the effects arise. This makes the results for generated sequences with no direct dependence on the prompt the most striking for me. That said, these seem to be results only for identical initializations, which makes them easier to rationalize, and I think the set-up is at least carrying over the teacher's bias for specific number tokens. 6. If we restrict to identical student and teacher initializations and focus on the prompted case, we have a principled reason to expect subliminal effects for OPD given @NathanHu12's work here: arxiv.org/abs/2609.16927 Nathan actually already conveyed to me that the insight behind his proof in Appendix A carries over to these objectives almost unchanged. However, in your settings (different models, fine-tuning), I am not sure how to get a toehold analytically.

A very interesting hypothesis, and clearly aligned with the findings from this cool paper ("Prompt Injection as Role Confusion"): arxiv.org/abs/2603.12277