Manifold-Constrained Hyper-Connections for Parameter-Efficient Finetuning

Finetuning methods for foundation models usually change weights, prompts, or hidden states, while leaving the residual topology fixed. We ask whether residual topology itself can become a finetuning object. To study this, we adapt manifold-constrained hyper-connections (mHC), recently introduced for pre-training, to frozen-backbone finetuning. mHC turns a Transformer into an input-dependent multi-stream residual architecture, routing representations through multiple streams at every sub-layer. Across mHC variants, we find that dynamic residual routing can finetune Transformers, but that its role differs from pre-training: by preserving stream mixing and learning only how sub-layers access streams, loss is improved and trainable parameters are reduced. Overall, our results identify residual routing as a promising architectural axis for efficient finetuning of foundation models.