Harmonic Decompositions of Convolutional Networks
Authors: Meyer Scetbon, Zaid Harchaoui
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network expands into a sum involving elementary functions akin to spherical harmonics. This functional decomposition can be related to the functional ANOVA decomposition in nonparametric statistics. Building off our functional characterization of convolutional networks, we obtain statistical bounds highlighting an interesting trade-off between the approximation error and the estimation error. |
| Researcher Affiliation | Academia | 1CREST, ENSAE 2Department of Statistics, University of Washington. Correspondence to: Meyer Scetbon <meyer.scetbon@ensae.fr>, Zaid Harchaoui <zaid@uw.edu>. |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper refers to a 'longer version of the paper (Scetbon & Harchaoui, 2020)' and 'Co RR, abs/2003.12756, 2020', which is a reference to the arXiv version of the paper itself, not a statement about releasing source code for the methodology. |
| Open Datasets | No | The paper defines an 'Image Space' (I = (Sd 1)n) as a theoretical construct and references general applications of CNNs to 'image data' and specific datasets like CIFAR-10 and MNIST in the context of related works, but it does not provide concrete access information or state that any specific dataset is used for empirical evaluation within this paper. |
| Dataset Splits | No | This is a theoretical paper focused on mathematical analysis and does not describe any experimental setup involving dataset splits for training, validation, or testing. |
| Hardware Specification | No | This is a theoretical paper and does not mention any specific hardware used for experiments. |
| Software Dependencies | No | This is a theoretical paper and does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | This is a theoretical paper and does not provide details about an experimental setup, hyperparameters, or training configurations. |