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For ResNets under depth-$\\mu$P scaling, prior work treats the layer index $\\ell$ as a continuous time $t_\\ell = \\ell/L$, yielding SDE descriptions of the training dynamics. A key unresolved issue is that backpropagation reuses each forward weight matrix $W_\\ell$ through its transpose $W_\\ell^\\top$, creating correlations between forward features and backward gradients whose behavior and role in feature learning remain unclear. We study this reused-weight forward--backward coupling in one-layer ResNets under depth-$\\mu$P. Using conditional Gaussian representations, we explicitly separate the coupling terms induced by weight reuse from decoupled Gaussian fluctuations before taking any network limit. At initialization, we prove that the cou","title":"Feature Learning Dynamics in Infinite-Depth Neural Networks","url":"https://arxiv.org/abs/2512.21075","vendor":"arxiv_cs_ai"},"summary":"arXiv:2512.21075v3 Announce Type: replace-cross \nAbstract: Deep neural networks have achieved remarkable success in practice, yet a mechanistic understanding of how features evolve during training remains incomplete, especially in the large-depth limit. For ResNets under depth-$\\mu$P scaling, prior work treats the layer index $\\ell$ as a continuous time $t_\\ell = \\ell/L$, yielding SDE descriptions of the training dynamics. A key unresolved issue is that backpropagation reuses each forward weight matrix $W_\\ell$ through its transpose $W_\\ell^\\top$, creating correlations between forward features and backward gradients whose behavior and role in feature learning remain unclear. We study this reused-weight forward--backward coupling in one-layer ResNets under depth-$\\mu$P. Using conditional Gaussian representations, we explicitly separate the coupling terms induced by weight reuse from decoupled Gaussian fluctuations before taking any network limit. 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