Newest papers

The role of locality and weight sharing in convolutional neural networks

Francesco Mori, Melanie Weber · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30118 · cited by 0 works (OpenAlex) · open-access PDF

German

Der Erfolg von konvolutionären neuronalen Netzwerken ist oft an Ort und Gewichtszuweisung zurückzuführen. Jedoch, wie diese beiden Eigenschaften lokales Lernen trennen, und wie ihre Auswirkungen auf die späten räumlichen Korrelationen derselben natürlichen Bilder abhängen, bleibt schlecht verstanden. Wir behandeln diese Fragen in einem Lehrer-Student-Modell mit einem konvolutionären Lehrer, der auf $P$ Eingangspositionen mit Korrelation $C$ zwischen Positionen handelt. Wir vergleichen konvolutionäre und lokal verbundene Studenten, die von online-stochastischen gradient-Descent-Distributionen geschult werden, und ergeben gewöhnliche Differentialgleichungen, die ihre Dynamik genau in der Grenze der großen Feature-Dimension $D$ beschreiben. Für un

Machine translation (Meta M2M100); the English original follows.

Abstract

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 the limit of large feature dimension $D$. For uncorrelated positions ($c = 0$), the two students follow the same learning trajectory, with the convolutional student learning exactly $P$ times faster. We also find that locality affects the sample complexity: a student that matches the kernel size of the teacher recovers it from $\mathcal{O}_{D}(D)$ samples, whereas $\mathcal{O}_{D}(D\log(D))$ samples are needed with a larger kernel. For $c > 0$, spatial correlations can reduce the advantage of weight sharing. The asymptotic error of the convolutional student grows with $c$, whereas that of the locally connected student is independent of $c$ and overall lower when evaluated at the same learning rate. When the learning rate is instead tuned to the training horizon, however, the locally connected student wins at early times and the convolutional student at late times, with a transition that we predict analytically.

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Topics: Convolutional neural network, Locality, Limit (mathematics), Computer science, Uncorrelated, Dimension (graph theory)

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