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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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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). ...
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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 (...
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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)...
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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 $s$ ...
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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: ...
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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 ...
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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 ...
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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 ...
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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. ...
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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,...
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39 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 ...
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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-...
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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) $\mu\equiv (\mu_1,..., \mu_J)$ ...
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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://...
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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 ...
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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 ...
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Intuitive explanation for spline convolution [duplicate]

What is spline convolution intuitively? When should use it? what is the motivation behind it?
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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 ...
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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-...
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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 ...
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Best practices: how to feed a set of long time series to a convolutional net for time series prediction

Let us assume we run N experiments. During the experiments we collect measurements. In these measurements we have features and labels. We want to predict the label Y(t) given a series of past ...
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Explaining results when changing kernel size in CNN

I trained a CNN on CIFAR10 (implemented in PyTorch) with the following architecture: INPUT: (3,32,32) --> Conv2d layer (kernel: 3x3, stride:1x1, filters: 64) --> Activation: ReLU --> Max pooling (...
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Does the following “theorem” have a name? [duplicate]

I am aware that if one has random variables, and sums them, then the result belongs to a distribution which is the convolution of the parent probability distributions of the initial random variables. ...
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Does feature detector(filter) has to be a sqaure matrix?

I am going through a course on Convolutional neural networks, where in the convolution step, the feature detector matrix was square shaped. Is there any mathematical significance that Feature ...
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Mixture or Convolution

tl;dr is final paragraph at the bottom. I have read the posts explaining the differences between mixture distributions and convolutions of distributions, but am having a hard time understanding which ...
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98 views

What is time complexity big O for 2D filters and 1D filters in image convolution Neural networks.?

I went through this link to understand, but was not able to grasp the concept. What is the computational complexity of a 1D convolutional layer? Consider a more general case: ...
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Problem with a factor in a convolution of two probability density functions

In a problem I'm working on I have analytical expression of two probability density functions $p_1(v_1),p_2(v_2)$ of two variables $v_1$ and $v_2$, which represent velocities of two particles. I wish ...
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Prove or disprove the Linearity of Expectiles used in Expectile Regression

For expectation (mean), there are many useful properties such as Linearity of Expectation: $\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$ $\mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]$ (The 2 equations ...
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91 views

Temporal Convolutional Networks (TCNs): Possibility to provide general information for each sample?

In my task it is important to provide general information for each sample. A sample consists of a time sequence and there is a channel with n values for each time t of the sequence. This results in a ...
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Clarified a previous question. How to evaluate the following probability? [duplicate]

I would kindly ask you not to close this prematurely. I have tried to give an elaborate explanation to the best of my ability and could really use some advice as how to go about this. The first ...
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Combine normal distribution and Rayleigh distribution

I am trying to find the maximum wave for a given time span based on a given measured wave height. In the top image the measured wave height is 2m and indicated with the black line. The probability ...
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46 views

Does a CNN have to be Fully Connected?

So I am trying to implement a specific CNN called a U-net. It states in page 3 that it doesn't have a fully connected layer. Till then I understood CNN to have two stages; 1. Convolution, where the ...
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PDF of sum of stationary processes

I would like to obtain formulas for the sum of random processes $U(\omega,t), V(\omega,t)$: Sum of two signals: $G(\omega,t) = U(\omega,t) + V(\omega,t)$ Case 1: $U,V$ are also jointly stationary $...
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324 views

Sum of Exponential and Gamma Distributions [duplicate]

I have been learning sums of distributions and understand that the sum of exponential distributions with parameter B is a gamma distribution with parameters a=1 and B. However, I need to figure out: ...
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How can I evaluate the following bivariate distribution?

Say $A$ and $B$ and $C$ and $D$ are four random variables, such that $A\not\!\perp\!\!\!\perp B$ and $C\not\!\perp\!\!\!\perp D$. How can I evaluate a bivariate CDF of the form? \begin{equation} P(A+B&...
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What is the convolution of the distribution function of sum of dependent variables?

Say $Z=X+Y$ and where $X\not\!\perp\!\!\!\perp Y$. Would we have? \begin{equation} F_{X+Y}(z)=\int_0^zF_{X,Y}(x,z-x)dx \end{equation}
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Derivation of winograd filter transform matrices

For http://web.archive.org/web/20190509195948/https://www.intel.ai/winograd-2/ , how to derive the winograd filter transform matrices ?
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How can we evaluate the following CDF?

First let us consider the following regression \begin{equation} y_t=\beta'x_t+\varepsilon_t,\quad t=1,...,n \end{equation} where $x_t$ is a $k\times 1$ vector of "fixed" regressors and $\beta$ is ...

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