Covert Trait Propagation Is Representation Alignment: Mechanistic Evidence from Hidden-Channel Distillation
A student model trained on pure uniform noise can still inherit its teacher's digit-classification ability, provided the two share initialization. Previous work proves this transfer is guaranteed when the teacher's learning rate is small enough, but does not explain where in the network the channel lives or what sets its capacity. Working in an MLP distillation setting on MNIST, we show these channels are not purely informational: geometric alignment gates access to the information the channel carries. Shared initialization makes the output projection W_2 a common coordinate key, and KL gradients reshape the student's input projection W_0 until its hidden representations align with the te...
| Authors | Kargi Chauhan, Aditya Shah |
|---|---|
| Primary category | cs.LG |
| Published | 5 July 2026 |
| Last updated at source | 5 July 2026 |
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