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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Mathematical representation of 1D convolution

How does one write the mathematical formula for conv1d used in PyTorch, including parameters like stride length and padding? For instance, I can write ...
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Spectral Graph Convolutions: What are the spectral filters functions

I am trying to understand the mathematical meaning of one of the steps that appear in the Convolution Theorem (Step 4 here). To give some context, this is related to applying the convolution theorem ...
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When is $\sum Z_i \sim \sqrt{n} Z_i$?

If $X_i$ are independently and identically distributed $N(0,\sigma^2)$ then $Y=\sum X_i \sim N(0,n\sigma^2)$, i.e. $\sum X_i \sim \sqrt{n}X_i$. That raises two questions: Is a zero-mean normal ...
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if i need a kernel to detect cones shape.. how to do so?

i'm working on a project of cones detection from lidar point cloud, I have got an idea to use Hough transform and I'm using convolution for voting principle for cone detection and I already ...
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A question about Convolutional Neural Networks, equivariance and parameter sharing

I have a couple of questions acbout Convolutional Neural Networks and I'm struggling to give an answer. Q1 Let's say I have $[3 \times 32 \times 32]$ image (with three channels) and I apply a first ...
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What is the best way to feed IMU data to CNN?

I took the Introduction to Embedded Machine Learning course, which is provided by Shawn Hymel, on Coursera. While talking about sensor fusion, he made the following statement for the following diagram:...
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Why CNN is suitable for time-series data? [duplicate]

I am confused by the statements that I came across in two different papers. The statement from the paper titled as "Detecting Cyber Attacks in Industrial Control Systems Using Convolutional ...
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Successor to Densenet, and Why Would My Resnet Model Peform Better Than My Densenet Model?

Currently, I'm modifying PoseNet, for use with camera localizaiton, with Resnet and Densenet. I modified both to have 2048 output classes, which feeds into dense layers to get the camera pose(like the ...
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Why does my loss decrease very slowing at the start of training, but picks up in the middle

I'm training S3D on my own dataset and uses a cosine learning rate decay. But the training loss doesn't decrease in the first 40 epochs, and than starts to decrease quickly, while the loss increased ...
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Do Convolutional Layers Pool data?

Sorry for the trivial question but considering this example in the image attached doesn't the conv layer pool data by summing them? What I am asking is if this images describes a subset where a conv ...
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Neural network to read short strings - translational invariance in CNNs

I have a series of short strings that each describe some item (one item per string). The people who write these strings can get pretty creative when it comes to spelling. For each string, I also have ...
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Recovering weights between neurons in a convolutional layer

Given a convolutional layer, I am interested in recovering the weight matrix $W$, where $w_{i,j}$ is the weight between neuron $i$ in the input layer and neuron $j$ in the output layer. I know that ...
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Calculating Convolution Only for a Certain Interval Using "conv()" in MATLAB

Below you can see the code for convolution of two continuous functions. There is a function called fx which I took as the square root of a Gaussian distribution. ...
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Convolution between two random variables

Given $X$ is a random variable which distributed uniformly in $[1,3]$ and $Y$ distributed uniformly in $[0,a]$. I need to calculate the value of the density function of: $$Z=X+Y,$$ at a point $b$ (i....
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CNN for images with different channel sizes

Assuming the channels of an image have different sizes. E.g.: red: 128x128, blue: 128x128, green: 256x256 Is it better to resize the green channel to a lower size, or would It be better to add a conv ...
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Does the sum of squared "dependent" Gaussian variables still exhibit a Chi-squared distribution?

Suppose we have $x_1,\cdots,x_n$, such that $x_i$ are i.i.d according to $x_i\sim N(0,1)$ for $i=1,\cdots,n$. Then we know that $Y=\sum_{i=1}^nx_i^2$ \begin{equation} Y\sim \chi^2(n) \end{equation} ...
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What is the resulting function to describe a log-normal function with Gaussian noise added?

I have a log-normal distribution: $\frac{1}{x} Ae^{-\frac{(ln(x)-\mu)^2}{2\sigma^2}}$ And I draw from it (1000 times) and plot the draws in a histogram: The log-normal function from which the draws ...
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Sum of Equally Interval Censored Normal Random Variables

Suppose a standard normal random variable $Z\sim N(0,1)$ is interval censored at $[-a,a]$, $a >0$, so that the new censored variate $x$ is $$ x = \begin{cases} -a &z\leq-a \\ z & -a< z&...
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Maximum likelihood estimate for multivariate sum of normal distributions

For each $j = 1,\dots,N$, let $\mu_j \in \mathbb{R}^N$ denote a known column vector, $\Sigma_j \in \mathbb{R}^{N\times N}$ a known covariance matrix, and $\theta_j \in \mathbb{R}$ an unknown parameter,...
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Why convolution output size is different using Toeplitz matrix?

From CNN, 2D Convolution output size is (Input height - Kernel height + 1) * (Input width - Kernel width + 1), where padding = 0 and stride = 1. I was trying to find how to compute a convolution ...
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What is the significance behind having small kernel sizes over having one large kernel size that covers the entire input in a CNN?

I have hardly ever seen anyone cover the entire input image with a filter of the same dimensions. I was wondering why that is the case, and if the performance in say, an image detection application ...
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Decompound a Compound Probability Distribution

I am trying to figure out how to deconvolve or decompound a compound probability density function - knowing one of the distributions and having samples from the compound distribution. Assume I only ...
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Is a convolution with $n$ input channels, $n$ filters and $n$ groups the same as depthwise convolution?

Let's say we have an input tensor $X$ with $n$ channels and a grouped convolution with $n$ groups and $n$ filters which produces an output tensor $Y$ with $n$ channels. Will this convolution ...
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Why does strict translation invariance get destroyed after doing zero padding in the images?

While reading the paper on the Siamese Visual Tracking approach, I stumbled on this concept of Strict Translation Invariance in CNNs. The paper quotes: "Concretely speaking, one reason is that ...
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Is increasing the number of channels with 1x1 convolutions a good idea?

Everywhere that I have seen 1x1 convolutions being used is towards reducing the dimensionality (number of channels) of features. However, I was trying to reduce the number of parameters of my model ...
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Using convolution formula

I would like your help to solve the following exercise. I have also reported below my attempt, but I'm not sure I'm properly manipulating the various integrals involved (in particular the switching ...
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How Convolutional layer work exaclty in RGB image processing?

I'm studying convolutional layers and I'm pretty confused. Supposing that I give to my network (CNN) an RGB image, so an image with three channels. Since the image has 3 channels, then the kernels ...
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Reason behind performing dot product on Convolutional Neural networks

I was recently exploring CNNs and came to know that initial step consists of multiplying pixels of the input image with the corresponding value in the kernel(dot product of kernel and input image). ...
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The convolution of a Poisson Distribution and Scaled Poisson Distribution

I am trying to do a likelihood analysis on a variable, $Z$, which is defined as $(1)$ $Z = X - cY$ where $X$ and $Y$ are both independent Poisson distributions with rate parameters $\lambda_{x}, \...
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Why does the bottleneck layer in densenet increase the number of feature maps

Hi I'm working with a modified version of the keras densenet (https://arxiv.org/abs/1608.06993) model and I have a question about the denseblock they propose i understand the idea behind having all ...
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Explanation of effect of bias in deconvolution

I've been reading the deconvolution article on distill. I am not able to figure out the meaning of the text These artifacts tend to be most prominent when outputting unusual colors. Since neural ...
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What is the output dimension of a a filter with stride and pad?

I have an input dimension of 32x32x3 and 10 filters of 5x5 with stride 1 and pad 2. What is the according output dimension? Stride represents the number of pixel to shift the filter and pad is the ...
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Error Propagation through Iterated Functions (variable star data)

I'm an astronomer trying to smooth variable star data, and one way I'm doing this is using a 7-point, second-order Savitzky-Golay filter. I iteratively apply the filter 51 times (i.e. I apply the ...
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Can padding values in CNN model be not equal to zero

I found this animation in the cnn model article. https://towardsdatascience.com/detecting-pneumonia-from-chest-x-rays-with-deep-learning-6b83b4a77ee8 The animation link is the following: https://...
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CNNs Scale/Rotation Invariance

CNNs are translation-invariant due to the pooling layer. How can we make them scale/rotation invariant? I have beginner-level knowledge of Deep Learning so please help me understand.
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Summation of median and quantiles of multiple forecasted variables

Assume that I have Y1_hat with its P10_1 and P90_1 and Y2_hat with its P10_2 and P90_2. Is it valid to sum Y1_hat and Y2_hat, sum P10_1 and P10_2, and sum P90_1 and P90_2? and would that present any ...
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understanding transfer learning for mobileNet

I am trying to visualise how transfer learning (feature extraction in particular) works with mobileNet using ml5.js. With ml5.js, you can extract a part of the pre-trained model (the features). Those ...
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Trying to understand WaveNet CTC for speech recognition

So I just understood how dilated convolutions work. Now I found this model on github. The "red" part is supposed to be the the dilated CNN, but after checking this explanation it looks like ...
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When comparing CNN architectures, should I use the same learning rate?

I am doing a report that compares the performance of ResNet50, VGG16 and EfficientNetB0 on a certain multi-class classification problem. Should I use the same learning rate for each of them or should ...
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What image filter is used in max pooling in image processing

I am curious to know which filter is used in to do max pooling? I am aware that it is a Deconvolution layer. As it takes the maximum value across all pixels - would it use an nonlinear area filter? As ...
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What is pixel shifting problem in even-sized kernel?

I've got to know that there is a pixel shift problem with an even-sized kernel which is one of the reasons even-sized kernels are not use much. I've tried to search a lot about what exactly is pixel ...
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Help with computing convolution of gaussian and dirac delta

I'm trying to calculate message passing in Trueskill factor, Trueskill paper. Given only two players competing, the message from difference factor to winner team node t1 would be $$ \begin{align} m_{...
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What is the difference between the receptive field and a patch?

In this question and answer it is beautifully described what a patch is. What's a "patch" in CNN? However, for me, following the explanation in the link, it seems like a patch and the ...
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How to prove the tail behavior of the sum of random variables with one dominating?

Assume I have given independent, continous random variables $X_1, \ldots, X_n$ and assume that they all have support $[-\infty, \infty]$. If $X_1$ asymptotically dominates all others, i.e. $$f_{X_i}(\...
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Variance of DFT of filtered noise

I am struggling with the following question: Let v(t) be a stationary stochastic process with Gaussian probability distribution and power spectral density $S(\omega)$. Let the DFT of $v(t)$ be $V(k)=\...
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What could possibly be the reason why my CNN achieves abnormally high validation loss for some epochs?

I am training a CNN for a simple binary classification problem and for some reason, I am getting abnormally high validation_loss at some epochs while still achieving good validation_accuracy. What am ...
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Autoencoder with feature maps as latent representation in TensorFlow - 3D voxel model reconstruction

I am working on a 3D voxel model reconstruction network based on autoencoder architecture. I am using ResNet152v2 as encoder and then transposed 3D convolutional layers with stride = 2 and padding = &...
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Convolution formulation with central element of the Kernel matrix is superimposed on the pixel

Suppose we perform the convolution operation with a Kernel of odd size. Suppose that the central element of the Kernel matrix is superimposed on the p-th pixel of the image being processed. Suppose: ...
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Can convolutional neural network learn integral operator?

Given a function $$ u(x), x\in [0,1] $$ Say 1D convolutional neural network, we all know it can learn the differential operator. $$ \partial u/ \partial x \approx D u $$ But what about the integral ...
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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 ...

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