# Fractionally-Strided-Convolution

## Understanding Fractionally-Strided Convolution

Fractionally-strided convolution, also known as deconvolution or transposed convolution, is a concept within the field of deep learning, particularly in the context of convolutional neural networks (CNNs). This type of convolution is used to upsample, or increase the spatial resolution of, feature maps. It is commonly employed in tasks such as image segmentation, super-resolution, and generative models like Generative Adversarial Networks (GANs).

## What is Fractionally-Strided Convolution?

Fractionally-strided convolution is essentially the reverse of a standard convolution operation. While standard convolutional layers reduce the spatial dimensions of the input data (downsampling), fractionally-strided convolutions aim to increase the spatial dimensions (upsampling). This is achieved by reversing the forward and backward passes of a convolution.

In a standard convolution, an input is convolved with a filter to produce an output feature map. In fractionally-strided convolution, the goal is to learn a convolution operation that, given an output feature map, can produce an input feature map of a larger spatial size. This is done by applying a stride in the input space that is a fraction of the convolutional filter size, hence the name "fractionally-strided."

## How Does It Work?

The process of fractionally-strided convolution involves inserting zeros between the entries of the input feature map, effectively increasing its dimensions. This expanded map is then convolved with a learned filter (or kernel), resulting in an output that is larger than the original input. The spacing between the input values is determined by the stride, which, in this case, is fractional. For example, a stride of 1/2 would double the spatial dimensions of the input.

It is important to note that the term "deconvolution" can be somewhat misleading. Deconvolution implies an exact reversal of the convolution process, which is not strictly what happens in fractionally-strided convolution. Instead, this operation should be thought of as a learnable upsampling that uses convolutional principles.

## Applications of Fractionally-Strided Convolution

Fractionally-strided convolution is widely used in various applications within deep learning:

• Image Segmentation:

In tasks where the goal is to classify each pixel of an image (semantic segmentation), fractionally-strided convolutions are used to upsample the feature maps to the original image size for pixel-wise classification.

• Super-Resolution: Super-resolution techniques use fractionally-strided convolutions to increase the resolution of images, enhancing details and improving visual quality.
• Generative Models:

In generative models like GANs, fractionally-strided convolutions are used in the generator network to transform a low-dimensional latent space into a high-dimensional data space, such as generating high-resolution images from random noise.

One of the main advantages of fractionally-strided convolution is its ability to learn upsampling. Unlike fixed upsampling techniques like bilinear or nearest-neighbor interpolation, fractionally-strided convolution allows the model to learn the most appropriate way to increase spatial resolution based on the data.

However, fractionally-strided convolution can introduce artifacts into the output, such as checkerboard patterns, due to the overlap in the convolution operation. Careful design of the network and training procedures is required to minimize these effects.

## Conclusion

Fractionally-strided convolution is a powerful tool in the deep learning toolkit, particularly for tasks that require upsampling of feature maps. Its learnable nature offers flexibility and adaptability to various applications, making it a popular choice for improving the resolution of outputs in CNNs. As with any technique, understanding its strengths and limitations is crucial for effectively applying it to solve real-world problems.

## References

For those interested in delving deeper into fractionally-strided convolution, the following references provide a starting point for further exploration:

• Dumoulin, V., & Visin, F. (2016). A guide to convolution arithmetic for deep learning.
• Zeiler, M. D., Taylor, G. W., & Fergus, R. (2010). Deconvolutional networks.
• Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., ... & Bengio, Y. (2014). Generative adversarial nets.

These resources provide both theoretical insights and practical guidance on the implementation and application of fractionally-strided convolutions in various deep learning contexts.