AbstractIn this paper, we propose a generalization of convolutional neural networks (CNN) to non‐Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the local behavior of some dense intrinsic descriptor, roughly acting as an analogy to patches in images. The resulting local frequency representations are then passed through a bank of filters whose coefficient are determined by a learning procedure minimizing a task‐specific cost. Our approach generalizes several previous methods such as HKS, WKS, spectral CNN, and GPS embeddings. Experimental results show that the proposed approach allows learning class‐specific shape descriptors significantly outperforming recent state‐of‐the‐art methods on standard benchmarks.