Name
Abstract | ||
|---|---|---|
We prove that linear rectifiers act as phase transformations on complex analytic extensions of convolutional network coefficients. These phase transformations are linearized over a set of phase harmonics, computed with a Fourier transform. The correlation matrix of one-layer convolutional network coefficients is a translation invariant representation, which is used to build statistical models of stationary processes. We prove that it is Lipschitz continuous and that it has a sparse representation over phase harmonics. When network filters are wavelets, phase harmonic correlations provide important information about phase alignments across scales. We demonstrate numerically that large classes of one-dimensional signals and images are precisely reconstructed with a small fraction of phase harmonic correlations. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Signal Processing | Mathematical analysis,Convolutional neural network,Sparse approximation,Harmonic,Fourier transform,Harmonics,Invariant (mathematics),Lipschitz continuity,Mathematics,Wavelet |
DocType | Volume | Citations |
Journal | abs/1810.12136 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stéphane Mallat | 1 | 4107 | 718.30 |
| Sixin Zhang | 2 | 0 | 0.68 |
| Gaspar Rochette | 3 | 0 | 0.68 |