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.

Filter by
Sorted by
Tagged with
2
votes
0answers
8 views

Question about the distribution of the average of Dirichlet-distributed random variables

Suppose that each in a set of $n$ random variables $\boldsymbol{X}_1, .., \boldsymbol{X}_n$ are Dirichlet-distributed with parameters $\boldsymbol{\alpha}_i$, where $i$ is an index for the random ...
1
vote
0answers
8 views

Reusing Weights in Transposed Convolution

As far as I know it's possible to reuse the weights of a convolution in a transposed convolution to upsample an image. However when reusing the weights, the resulting restored images aren't even close ...
0
votes
1answer
37 views

How to insert a normal distribution into another function?

I am struggling with the following problem. TLDR: I want to merge the uncertainty of the normal distribution into another function. Imagine a certain significant wave height (Hs) of 2 metres in a sea ...
1
vote
1answer
22 views

Step change detection in signal by convolving with step vector

I am facing the following problem in signal processing and I have run into a wall. I am trying to detect abrupt changes (step changes) in a constantly decreasing signal by convoluting the signal with ...
2
votes
1answer
73 views

What are “Grids” and Detection at different scales" in YOLOV3?

I've recently started working with Yolov3 and the more I go in depth, the more confused I get. In the simplest terms what I think about YOLOV3 ...
2
votes
1answer
11 views

It is always necessary to include a Flatten layer after a set of 2D convolutional layers for convolutional neural networks in Keras?

It is no clear for me when to use the flatten operation for building convnets. It is always necessary to include a flatten operation after a set of 2D convolutions (and pooling)? For example, let us ...
0
votes
0answers
14 views

Taking into account padding during backward pass for convolutional layers

I know there exists several threads on this matter but I could not find a satisfying answer so far. During backpropagation in a convolutional layer, we compute the gradient of the loss with respect to ...
1
vote
1answer
27 views

Is it possible to generate an 1D dimensional output of a 2D convolutional layer in Keras?

I'm trying to apply convolutional neural networks for dealing with a 2D input, which is a 2X300 matrix. It is basically a matrix with 2 lines, where each line is a vector of 300 positions. I would ...
0
votes
0answers
9 views

Do I need to use the complex conjugate when convolving two functions with the FFT?

I know that, due to the convolution theorem, two densities $f$ and $g$ can be convolved by (i) applying the FFT to both of them, (ii) multiplying the results, (iii) applying an inverse FFT. Since I ...
1
vote
1answer
27 views

Probability of sum of 2 variables - Convolution

Let say $A$ and $B$ are two uniform random variables independent over $[0,10]$ and: $X = max(A-1, 0)$ $Y = max(B-2, 0)$ So that $X$ and $Y$ have their density function respectively: $F_{X}(x) = \frac{...
10
votes
1answer
920 views

Why the sum of two absolutely-continuous random variables isn't necessarily absolutely continuous?

Why "a sum of two absolutely-continuous random variables does not need to be absolutely continuous"? See problem 6.4 on page 6 in https://web.ma.utexas.edu/users/gordanz/notes/...
2
votes
0answers
122 views

On random variables made up of independent random digits

Some random variables can be expressed as a binary expansion whose digits are chosen independently at random; this is called a convolution. One example of this kind of random variable is the one for ...
2
votes
0answers
55 views

What is the distribution of $(X−Y)^2+(Z−Y)^2$, where $X$,$Y$ and $Z$ are independent normal distributions with their own means and variance? [duplicate]

I came up with a question: What is the distribution of $(X−Y)^2+(Z−Y)^2$, where $X$,$Y$ and $Z$ are independent normal distributions with their own means and variance? The common part is $Y$ in both ...
2
votes
0answers
28 views

Why does fast graph convolution need Chebyshev polynomials?

I'm reading the paper Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering and find it difficult to understand the motivation for using Chebyshev polynomials. With localized ...
1
vote
0answers
34 views

Convolution kernels

Below are two different convolution kernel formulas, h and H, written in Python which I think are both symmetric. What is the ...
1
vote
0answers
31 views

Convolution: PDF of difference of uniform random variables [closed]

PDF of $X$: PDF of $Y$: $Z=X-Y$, $T=X+2Y$, how to find the PDF of $Z$ and $T$ and plot them?
3
votes
1answer
35 views

difference between the “Kernel Convolution” and “Kernel PCA”

Can anybody explain the difference between the "Kernel Convolution" and "Kernel PCA" to me, please?
0
votes
0answers
24 views

Why are point-wise nonlinearities equivariant to any permutation of the input and output indices of a network layer?

The statement from [1] says that: Pointwise nonlinearities such as ReLU and sigmoid are already equivariant to any permutation of the input and output indices (of a network layer), which includes ...
1
vote
1answer
33 views

Graph convolution network for variable number of nodes

Is it possible to train a graph convolutional network on graphs with a varying number of nodes? I have a dataset of graphs with a range of 400-1000 nodes, though I could see a higher number of nodes ...
0
votes
0answers
36 views

Projection shortcuts in Resnets implemented as 2D convolutions

I'm currently preparing for a presentation on the well-known Resnet ("Deep Residual Learning for Image Recognition") paper and couldn't find a satisfying answer to my question yet. My ...
0
votes
0answers
27 views

Normalization and Standardization of color channels for Convolutional Neural Networks

I have created 2D heat maps with 3 color channels. On these heat maps, I will train CNN networks. The range of values in the three colors channels is very different. In the first channel the values ...
0
votes
1answer
18 views

X axis scale for convoluted function in Matlab

I convoluted gamma distributed having x axis range from 1 to 100 (m=100) and normal distribution with x axis range from -25 to 24 (n=50). By using conv function in MATLAB I got m+n-1 = 149 values. How ...
0
votes
0answers
42 views

Max Absolute Value Pooling and Tanh in CNNs?

I am trying to build my first convolutional neural network from scratch. I haven't wrote the back propagation algorithm yet, but just looking at the result of convolving the input images, max pooling, ...
1
vote
0answers
66 views

Should convolutions or transposed convolutions be used in the decoder part of a Conv-based autoencoder?

I am implementing a convolutional autoencoder. For the decoder part of the model, some examples (such as this one from Francois Chollet) use standard convolutional layers (Conv2D in keras) in the ...
2
votes
0answers
27 views

Unexpected results when applying convolution to variables created using rnorm?

I create two variables $x$ and $eps$ using the norm function and then convolve them to obtain a new variable $y$. When I plot the densities of $x, eps$, and $y$, however, there seems to be a problem ...
0
votes
0answers
12 views

How to construct input dependent convolutional filter (kernel)?

I am constructing a convolutional variational autoencoder for images, starting out with mnist digits. Typically I would specify convolutional layers in the following way: ...
0
votes
0answers
42 views

CNN: Using multiple smaller convolutions or few larger kernels?

In Google's inception network paper under section 3.1. Factorization into smaller convolutions, I saw that the team decided to use multiple smaller 3x3 kernels instead of larger 5x5 or 7x7. This ...
0
votes
0answers
17 views

Why is a Residual Block in (dilated) convolutional network comprised of 2 layers?

In my previous question, I thought that each dilated convolution layer in a Residual Block corresponds to a separate layer in the convolutional network. After reading these papers (here and here), I ...
2
votes
0answers
27 views

How to deconvolve normally distributed errors

I have a random variable which is has some unknown distribution (I have some priors for what it may be but the less assumptions the better). I'm then measuring it with some normally distributed error ...
1
vote
1answer
85 views

What's the expression for convolution of a uniform[a,b] density and a normal(0,d^2) density?

Suppose I have $X\sim Uniform[a,b]$ and $Y\sim normal(0,d^2)$, what's the expression for the density of $Z=X+Y$? Let $F_{Z}(z)$ be the cdf of $Z$ evaluated at $z$, and let $\Phi(\cdot)$ and $\phi$ be ...
2
votes
1answer
37 views

Weighted sum of negative binomial distributions - approximate fast parameter calculation

Let's suppose we have a convolution (weighted sum) of three negative binomials (parameterised as mean and overdispersion). ...
2
votes
0answers
14 views

Why do tied weights in Autoencoders *force* divergence in the features?

Imagine the following scenario: Given a signal x, you pass it through a bank of convolutional filters to get a feature map z (...
1
vote
2answers
176 views

How do you get the double sum or integral from $E(X+Y)$ (expected value)?

I was given a proof for $E(X+Y)$ = $E(X)+E(Y)$ for cases where both variables are either discrete or continuous: Discrete: $$ \begin{align*} E(X+Y) &=\sum_{x\in\mathcal X}\sum_{y\in\mathcal Y}(x+y)...
0
votes
0answers
18 views

backword propagation of convolutional neural network layer

Consider a convolutional layer of a convolutional Neural network with a single window applied to a single channel image of size $m\times n$. Considering a window of size $f \times f$ with a stride $s$ ...
1
vote
1answer
21 views

Is there any relationshipe between image input dimension, filter/kernal size and feature map?

Is there any relation between image input dimension (height, width), filter/kernal size and feature map? if for example I have this code: ...
1
vote
0answers
71 views

What is wrong with my approach on a custom way of creating Gabor-filter convolution kernels?

Disclosure: I am not a prominent mathematician (current bachelor student) like others on this website and my approach has been mostly pragmatic. Please do tell me if I can improve the formulation of ...
0
votes
0answers
31 views

Contextual Attention method and dilated convolution

When do image inpainting project, I have a question about the role of dilated convolution and contextual attention maybe overlap. Below image, I have 2 brands, which is try to get more information ...
0
votes
0answers
43 views

Creating CNN-Autoencoder From CNN With Non-Square Kernels

I'm attempting to create a CNN-Autoencoder model for an unsupervised clustering problem on adjacency matrix data. The CNN I'm working with, BrainNetCNN, is unconventional in that its filters aren't ...
0
votes
1answer
91 views

Layer Normalization for neural networks

Below is the description for the implementation of layer normalization from Stanford's CS 231n def layernorm_forward(x, gamma, beta, ln_param): """ Forward pass for layer normalization. ...
0
votes
0answers
33 views

Most efficient way to apply many 2d convolutions

I have two $4$ dimensional tensors, where the first two indices correspond to some fixed values in my problem, and the last two specify a 2D distribution. For each fixed value of the first two indices,...
0
votes
0answers
78 views

Inverse of Global Average Pooling?

I am working with a project where I want to upsample some parameters to create an electrical signal (shape: input=(3) output=(50,19)) The first part of my ...
0
votes
0answers
122 views

How to understand the dilated conv1d layers dimensions in this model?

I was trying to see the layers used in a Wavenet model for speech generation and I can't seem to make sense of the output layers printed by the TF model. Model is this: https://github.com/Rayhane-...
1
vote
1answer
73 views

Show that the sum of two random variables is a mixture

Take any $({\lambda},{\mu},F,G)$ such that 1) $\lambda\equiv (\lambda_1,..., \lambda_J)$, $\lambda_j\in (0,1)$ for each $j=1,...,J$ and $\sum_{j=1}^J \lambda_j=1$ 2) $\mu\equiv (\mu_1,..., \mu_J)$ ...
0
votes
0answers
11 views

Inconsistent and ambiguous dimensions of matrices used in the Attention layer in GNMT or text-to-speech synthesis?

Attention-scoring mechanism seems to be a commonly-used component in various seq2seq models, and I was reading about the original "Location-based Attention" in Bahadanau well-known paper at https://...
1
vote
0answers
126 views

How exactly does conv1d filter work when operating on a sequence of characters?

I understand convolution filters when applied to an image (e.g. an 224x224 image with 3 in-channels transformed by 56 total filters of 5x5 conv to a 224x224 image with 56 out-channels). The key is ...
1
vote
0answers
165 views

What is the difference between a class activation map and a saliency map for convolutional neural networks?

I am researching attribution methods in computer vision literature to better understand how a CNN model arrives at its predictions. I have come across the terms ...
0
votes
0answers
20 views

Intuitive explanation for spline convolution [duplicate]

What is spline convolution intuitively? When should use it? what is the motivation behind it?
1
vote
0answers
21 views

Can we derive the standard normal distribution function from specification of convolution?

In this article, the following is said: Why is the normal distribution so important? Because it is its own convolution with itself, is why. If you average many similar things, what you get has ...
0
votes
0answers
34 views

Let N be the number of times you roll a 6-sided die until you roll a 1. Let M be the sum of rolling N six-sided dice. What is the pdf of M?

I understand that a geometric distribution can be used to determine the pmf for N, but am lost on finding the distribution for M. Also, if done in reverse order: Let N be the result of rolling a 6-...
11
votes
1answer
553 views

Why does R have a different definition on convolution?

I found convolution in R works differently from Python. In Python, it will flip the input and run the convolution. In the R documentation, it says Note that the usual definition of convolution of ...

1
2 3 4 5
8