# 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 does 1x1 convolution mean in a neural network?

I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what ...
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### Importance of local response normalization in CNN

I've found that Imagenet and other large CNN makes use of local response normalization layers. However, I cannot find that much information about them. How important are they and when should they be ...
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### What is translation invariance in computer vision and convolutional neural network?

I don't have computer vision background, yet when I read some image processing and convolutional neural networks related articles and papers, I constantly face the term, ...
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### Why is the sum of two random variables a convolution?

For long time I did not understand why the "sum" of two random variables is their convolution, whereas a mixture density function sum of $f(x)$ and $g(x)$ is $p\,f(x)+(1-p)g(x)$; the arithmetic sum ...
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### Convolutional neural networks: Aren't the central neurons over-represented in the output?

[This question was also posed at stack overflow] The question in short I'm studying convolutional neural networks, and I believe that these networks do not treat every input neuron (pixel/parameter) ...
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### How does Max Pooling handle Odd Image Dimensions? [closed]

For the even image dimension case, max pooling is simple to understand - it simply performs convolution over the image with the max operator with a $x$-by-$x$ kernel with a stride of $x$. However for ...
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### Why does multiplication in the frequency domain equal convolution in the time domain?

This question came in the context of understanding how to get a distribution of a sum of two iid random variables. I'm working through the top answer to this question Consider the sum of $n$ uniform ...
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### In convolutional neural network, what does fully-connected layer mean?

There are convolution layers, pooling layers, and possibly a classifier layer (e.g. softmax layer) in a convolutional neural network (CNN). I heard that there is also a fully-connected layer. What ...
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### Difference between Conv and FC layers?

What is the difference between conv layers and FC layers? Why cannot I use conv layers instead of FC layers?
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### Proving the Convolution of PDFs gives a PDF

I am struggling with a question about the convolution of PDFs, in particular, proving that given two PDFs $f$ and $g$, then their convolution $f*g$, will also be a PDF. Proving non negativity is easy ...
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### Training a convolutional neural network

Based on my research on convolution neural networks, every other layer in such a network has a subsampling operation, in which the resolution of the image is reduced so as to improve generalization of ...
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### Why do people use Zero-Padding in Convolutional Neural Networks?

I am wondering why people usually pad with zeros instead of e.g., using the min-value. Zero-padding, in my opinion, makes sense if you have input images with a pixel range [0, 255] or [0, 1] (after ...
462 views

### Sum of absolute values of T random variables

Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$. I am looking for the distribution of the n-summed variable $\sum_{1 \leq i \leq n}|x_i|$. $Y=|X|$ ...
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### Is output of Deamer deconvolution not a density?

I have a Model Y= X+e and need the density of X. The deamer package deconvolves the density for X, but if I use the simpsons rule to integrate this density, I get values which are above 1. The ...
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### Convolutional neural networks backpropagation

My question is regarding the answer to this question: Training a convolution neural network It seems like the answer is saying to change all the weights in a given filter by the same amount in the ...
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### Sum of truncated Gammas

I have a set of i.i.d. variables $X_i$ that are distributed according to a truncated $\text{Gamma}(\alpha,\beta)$ distribution, with support on $[0,w)$ where $w$ is a known constant. What's the ...
909 views

### Does the property of equivariance to translation of convolution layers help to learn translation-invariant features?

In some texts, people mention that the reason why convolutional neural networks are able to learn translation-invariant features are related to the property that convolution layers are equivariant to ...
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### Two-sample bootstrap?

I have two independent samples of observations. From each sample I produce a statistic. Let's denote these as $\theta_1$ and $\theta_2$. I'd like to test the hypothesis that $H_0: \Theta_1=\Theta_2$, ...
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### general solution sum of two uniform random variables aY+bX=Z?

is there a general solution to that? I have seen simple examples for Y+X=Z but I was wondering how this would be with rescaling?
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### In convolutional neural networks, how to prevent the overfitting?

Given certain amount of labeled data, we define the net structure, such as number of layers, types of layers, the number of convolutional layers, the number of pooling layers, etc. And train the ...
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### How does local connection implied in the CNN algorithm

I am trying to understand the process of Convolutional Neural Networks. Basically, I am trying to understand how does the local connection works. The first step of CNN is a convolution layer where ...
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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 ...
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### CNN vs RNN for time series classification

I am new to neural networks and after some research i read about CNN and RNN neural networks. The data that i am having is multiple different time series of numbers. So for example instead of input 1 ...
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### Is there a nice way to visualize the convolution of two random variables?

It is easy for me to visualize the distribution of a random variable by drawing its density function. Suppose I have two independent random variables now. I can plot the densities and visualize how ...
364 views

### Placement of earlier features in more complex features in CNN

I'm trying to understand convolutional neural networks better. I've been doing different tutorials, but there are some basics concerning how the hidden units represents features that I really would ...