# Questions tagged [convolution]

Convolution is a function-valued operation on two functions $f$ and $g$: $\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau$. Often used for obtaining the density of a sum of independent random variables. This tag should also be used for the inverse operation of deconvolution. DO NOT use this tag for convolutional neural networks.

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### What is the Identity of a convolution layer in a Neural Network?

I wanted to know what the identity of a convolutional layer of a neural network was. For standard convolution operation in mathematics the identity is the delta function, however, convolutions in ...
178 views

### How to add bias in convolution transpose?

My question is regarding the transposed convolution operation (also commonly called deconvolution or upconvolution). In TensorFlow, for instance, I refer to this layer. My question is, how / when do ...
914 views

### Padding and stride in backpropagation of a conv net

I am trying to implement the back-propagation of a simple convolutional network. Specifically I understand that one of the steps is the convolution of the gradients coming from the next layer, with ...
2k views

### Wouldn't multiple filters in a convolutional layer learn the same parameter during training?

Based from what I have learned, we use multiple filters in a Conv Layer of a CNN to learn different feature detectors. But since these filters are applied similarly (i.e. slided and multiplied to ...
52 views

### When is the convolution of symmetric bimodal densities unimodal?

Let $X$ and $Y$ be real valued random variables with densities $f_X$ and $f_Y$. It is well known that if $f_X$ and $f_Y$ are symmetric about zero and unimodal then their convolution $f_X \ast f_Y$ is ...
50 views

### The Application of Convolution and Delta Functions

$$K=Z-(X+Y)$$ $Z$ is any discrete value. I applied convolution for PDF of two exponential random variables: $X$ and $Y$. Which is like that here. Now I need to compute PDF and expected value of $K$? ...
116 views

### Solve a linear equation system of convolutions

For linear systems of equations, like Ax = b, the solution that minimizes the mean squared error and the norm is given as ...
199 views

### What is the differennce between invariance to translation, covariance to translation and equivariance to translation?

I get stuck at understanding the difference between invariance to translation, covariance to translation and equivariance to translation in the context of of convolutional neural network. What does ...
112 views

### Finite sum of beta prime iid random variables

The beta prime distribution is infinitely divisible, as proved in Steutel and van Harn, 2003 (Appendix B). Sadly, in this book, there is no espression of the parameters of the distribution of n ...
818 views

### Concatentation of feature maps in U-net

I am looking at the following snippet of code: ...
50 views

### What does the matrix $M = [diag(m_{:,1}),\ldots,diag(m_{:,m})]$ look like?

I'm reading this paper about a convolutional neural network (CNN) to model sentences. I think I understand the paper reasonably well until section 3.4. Please consider the following text taken from ...
91 views

### How to insert feature vectors as additional channels in conditional DCGANs

I understand that in a fully-connected GAN you can simply concatenate the flattened image and feature vector as input for the network. For convolutional GANs I've read that you should add the feature ...
2k views

### Sum of normal independent random variables with coefficients

I'm trying to wrap my head around linear transformations to random variables (with coefficients > 1). Consider the two random and independent variables $X$ and $Y$ where: X \sim \mathcal{N}(0,1)\...
136 views

### convolution and deconvolution of random variables of different dimensions

Preliminary: Let's say we have $Y=X+Z$ ($Y$ is data, $X$ is latent variable and $Z$ is noise), where the random variables are all in $\mathbb{R}$. Then an inverse Fourier transform leads to \begin{...
132 views

### How to create a wave-net-like CNN?

I would like to create a CNN in a similar way to WaveNet architecture. i.e. on the first layer it takes convolves 3x3 areas. In the next layer it also convolves 9 pixels but spaced out like this: <...
60 views

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### Intuition for why sum of gaussian RVs is different from gaussian mixture

I know that in the case of Gaussian mixture, the "intuition" is that you're drawing from a PDF which itself is just a sum of weighted Gaussian PDFs. I don't understand the intuition behind how the ...
165 views

### Training a Convolution Neural Network with Statistical Data (Features Extracted from the Medical Image)

I'm currently working on a project to classify the medical images as normal and abnormal using convolution neural network with input as feature data (Statistical feature values extracted from medical ...
4k views

### What should regularization loss look like?

New to ML and Deep Learning. I am trying my hands on some image classification using resnet50. Here are some of the graphs I see on tensorboard: As you can see, my total loss is mostly being ...
253 views

### How do I model a pixel-wise regression convnet? What kind of loss should I use?

Given an input of (HxWxD), I want to output a confidence map of size (HxW) where each value is a probability. I'll try to be concise. I have 2 inputs: input_image of size (HxWx3) input_map of size (...
2k views

### Showing prediction output in Keras [closed]

I am doing a image classification with CNN using Keras. The training process was so far so good. But when it comes to the prediction, I couldn't figure out to extract correct prediction results out of ...
206 views

### sum product algorithm and Convolution Neural Network

I'm trying to understand the sum-product algorithm implemented using Convolution Neural Network by the paper [1,2] to solve the problem of human pose estimation. Human pose estimation is formulated ...
662 views

### convolution of two probability densities in MatLab

I am considering two exponential probability distribution functions with mean equal to 5 and 3. pdf1=@(x)exppdf(x,5); pdf2=@(x)exppdf(x,3); I want to compute the ...
5k views

### Batch normalisation at the end of each layer and not the input?

I am currently studying the paper of network implementation RCNN. The core module inside RCNN is the Recurrent Convolutional Layer (RCL), whose state evolves over discrete time steps. The ...
The problem and some of my thought are as followed, could you help check if I'm wrong. Suppose $X∼Bin(n_1,1/2)$ and $Z∼Bin(n_2,p)$, $0<p<1$ being an unknown parameter; $X$ and $Z$ are assumed ...