Francesco Mori, Melanie Weber · 2026 · arXiv
DOI: 10.48550/arXiv.2610.30118 · open-access PDF
The success of convolutional neural networks is often attributed to locality and weight sharing. However, how these two properties separately shape learning, and how their effects depend on the spatial correlations of natural images, remain poorly understood. We address these questions in a teacher-student model with a convolutional teacher acting on $P$ input positions with correlation $c$ between positions. We compare convolutional and locally connected students trained by online stochastic gradient descent, and derive ordinary differential equations that describe their dynamics exactly in t
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