Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
Authors: Alberto Bietti, Julien Mairal
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 3.4. Empirical Study of Stability In this section, we provide numerical experiments to demonstrate the stability properties of the kernel representations defined in Section 2 on discrete images. We consider images of handwritten digits from the Infinite MNIST dataset of Loosli et al. (2007), which consists of 28x28 grayscale MNIST digits augmented with small translations and deformations. [...] In Figure 3, we show average relative distance in representation space between a reference image and images from various sets of 20 images (either generated transformations, or images appearing in the training set). |
| Researcher Affiliation | Academia | Alberto Bietti EMAIL Julien Mairal EMAIL Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP , LJK, 38000 Grenoble, France |
| Pseudocode | No | The paper describes the methodology using mathematical formulations and textual descriptions rather than structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our C++ implementation for computing the full kernel given two images is available at https://github.com/albietz/ckn_kernel. |
| Open Datasets | Yes | We consider images of handwritten digits from the Infinite MNIST dataset of Loosli et al. (2007), which consists of 28x28 grayscale MNIST digits augmented with small translations and deformations. |
| Dataset Splits | No | The paper mentions using a "training set" in the context of numerical experiments (e.g., Figure 2, Figure 3), but it does not specify any particular percentages, counts, or methodology for splitting data into training, validation, or test sets. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run its experiments, such as GPU/CPU models or processor types. |
| Software Dependencies | No | The paper mentions a "C++ implementation" for the code release but does not specify any particular software dependencies with version numbers (e.g., C++ standard, compiler version, specific libraries, or frameworks). |
| Experiment Setup | Yes | We limit ourselves to 2 layers in order to make the computation of the full kernel tractable. Patch extraction is performed with zero padding in order to preserve the size of the previous feature map. We use a homogeneous dot-product kernel as in Eq. (2) with κ(z) = eρ(z 1), ρ = 1/(0.65)2. [...] For a subsampling factor s, we apply a Gaussian filter with scale σ = s/sqrt(2) before downsampling. [...] In Figure 3b, we vary the subsampling factor of the second layer, and in Figure 3c we vary the patch size of both layers. |