This paper proposes a novel framework for deep learning on non-Euclidean domains such as graphs and manifolds, called MoNet. The framework generalizes convolutional neural networks (CNNs) to non-Euclidean data by formulating convolution-like operations as template matching with local intrinsic 'patches' on graphs or manifolds. The key innovation is the use of parametric construction for patch extraction, allowing for a flexible and learnable approach to convolution on non-Euclidean domains. The paper demonstrates that various existing non-Euclidean CNN methods can be considered as particular instances of this framework. The authors test their approach on standard tasks in image, graph, and 3D shape analysis, showing that their method consistently outperforms previous approaches. In image analysis, they apply the method to handwritten digit classification on the MNIST dataset, demonstrating superior performance compared to spectral CNN methods. In graph analysis, they perform vertex classification on citation networks, achieving better results than existing methods. In 3D shape analysis, they learn dense intrinsic correspondence between 3D shapes, showing significant improvements over other approaches. The paper also discusses various existing methods for deep learning on graphs and manifolds, including spectral CNNs, diffusion CNNs, and anisotropic CNNs. It highlights the limitations of spectral methods, such as their dependence on the Fourier basis and the difficulty of transferring models between different domains. The proposed MoNet framework addresses these limitations by using a spatial-domain approach that is more general and flexible. The authors show that their approach can be applied to a wide range of tasks, including image, graph, and 3D shape analysis, and that it achieves state-of-the-art results. The framework is particularly effective for deformable 3D shape analysis, as it is intrinsic and thus deformation-invariant by construction. The paper concludes that the proposed framework has significant potential for future applications in computational social sciences and other domains.This paper proposes a novel framework for deep learning on non-Euclidean domains such as graphs and manifolds, called MoNet. The framework generalizes convolutional neural networks (CNNs) to non-Euclidean data by formulating convolution-like operations as template matching with local intrinsic 'patches' on graphs or manifolds. The key innovation is the use of parametric construction for patch extraction, allowing for a flexible and learnable approach to convolution on non-Euclidean domains. The paper demonstrates that various existing non-Euclidean CNN methods can be considered as particular instances of this framework. The authors test their approach on standard tasks in image, graph, and 3D shape analysis, showing that their method consistently outperforms previous approaches. In image analysis, they apply the method to handwritten digit classification on the MNIST dataset, demonstrating superior performance compared to spectral CNN methods. In graph analysis, they perform vertex classification on citation networks, achieving better results than existing methods. In 3D shape analysis, they learn dense intrinsic correspondence between 3D shapes, showing significant improvements over other approaches. The paper also discusses various existing methods for deep learning on graphs and manifolds, including spectral CNNs, diffusion CNNs, and anisotropic CNNs. It highlights the limitations of spectral methods, such as their dependence on the Fourier basis and the difficulty of transferring models between different domains. The proposed MoNet framework addresses these limitations by using a spatial-domain approach that is more general and flexible. The authors show that their approach can be applied to a wide range of tasks, including image, graph, and 3D shape analysis, and that it achieves state-of-the-art results. The framework is particularly effective for deformable 3D shape analysis, as it is intrinsic and thus deformation-invariant by construction. The paper concludes that the proposed framework has significant potential for future applications in computational social sciences and other domains.