Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds.

This supplementary document is organized as follows: Section 1 shows the proof that the formula of FRFT degrades to that of FT when α = π/ 2. Section 2 shows the discrete implementation of 2D FRFT. Section 4 shows the experimental results with single branch. Section 5 shows the architecture design of SFC and example usage of SFC and MFRFC. Section 6 introduces the periodicity of FRFT. Section 7 introduces the energy distribution of FRFT.

This paper focuses on the methods that explain what neurons learn during the training process.

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We introduce a hierarchy of expressiveness classes connecting the global approximability property to the weaker property of infinite VC dimension, and prove a series of classification results for several increasingly complex functional families.