Convolutional neural network: Difference between revisions
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though they can be used anywhere you have a rectangular grid with spatial relationship among your data. | though they can be used anywhere you have a rectangular grid with spatial relationship among your data. | ||
==Motivation== | |||
[https://arxiv.org/pdf/1611.08097.pdf Geometric Deep Learning]<br> | |||
Convolutional neural networks leverage the following properties of images: | |||
* ''Stationarity'' or shift-invariance - objects in an image should be recognized regardless of their position | |||
* ''Locality'' or local-connectivity - nearby pixels are more relevant than distant pixels | |||
* ''Compositionality'' - objects in images have a multi-resolution structure. | |||
==Convolutions== | ==Convolutions== |
Revision as of 20:48, 11 March 2020
Convolutional Neural Network
Primarily used for image tasks such as computer vision or image generation,
though they can be used anywhere you have a rectangular grid with spatial relationship among your data.
Motivation
Convolutional neural networks leverage the following properties of images:
- Stationarity or shift-invariance - objects in an image should be recognized regardless of their position
- Locality or local-connectivity - nearby pixels are more relevant than distant pixels
- Compositionality - objects in images have a multi-resolution structure.
Convolutions
Pytorch Convolution Layers
Types of convolutions animations
Here, we will explain 2d convolutions.
Suppose we have the following input image:
1 2 3 4 5 6 7 8 2 3 2 5 9 9 5 4 8 8 2 1
and the following 3x3 kernel:
For each possible position of the 3x3 kernel over the input image, we perform an element-wise multiplication (\(\displaystyle \odot\)) and sum over all entries to get a single value.
Stride
How much the kernel moves along. Typically 1 or 2.
Padding
Convolutional layers yield an output smaller than the input size. We can use padding to increase the input size.
- Types of padding
- Zero
- Mirror
Dilation
Space between pixels in the kernel
A dilation of 1 will apply a 3x3 kernel over a 5x5 region. This would be equivalent to a 5x5 kernel with odd index weights (\(\displaystyle i \% 2 == 1\)) set to 0.
Groups
Other Types of Convolutions
Transpose Convolution
See Medium Post
Instead of your 3x3 kernel taking 9 values as input and returning 1 value (</math>\sum_i \sum_j w_{ij} * i_{i+x,j+y}</math>), the kernel now takes 1 value and returns 9 (</math>w_{ij} * i_{x,y}</math>).
Gated Convolution
See Gated Convolution (ICCV 2019)
Given an image, we have two convolution layers \(\displaystyle k_{feature}\) and \(\displaystyle k_{gate}\).
The output is \(\displaystyle O = \phi(k_{feature}(I)) \odot \sigma(k_{gate}(I))\)
Pooling
Unpooling
![](/img_auth.php/thumb/7/76/Unpooling_deeppainter_2016.png/500px-Unpooling_deeppainter_2016.png)
During max pooling, remember the indices where you pulled from in "switch variables".
Then when unpooling, save the max value into those indices. Other indices get values of 0.