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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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CNN, “squared” or "non-squared image?

I'm working on a project about image recognition. In my dataset I have images of different size, all rectangular image (the most 640x480 and 1280x640). I would like to build my classifier to ...
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What is Supremal/Infimal Convolution

I'm currently reading a paper which mentions supremal and infimal convolutions. As I understood, they are upper and lower bounds for a joint distribution. One of the formulas in that paper is as ...
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Back propagation is done with each batch in a convolutional net, but is it also done with the validation set?

It's my understanding that the weights are updated in a convolutional neural network with each evaluation of a batch. But when the training data has been processed and it comes to predicting ...
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Convolution of two dependent distributions in MATLAB

Assume that I have two discrete random variables $X$ and $Y$. $X ∈ \{1,3,3,5,7,7,7,9,9,9,9,9\}$ and $Y ∈ \{5,5,9,9,10,12,13\}$ Where their empirical CDFs are given as: $F_x(1) = 0.0833, F_x(3) = ...
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is there a relationship between the determinant and the convolution

A long time ago, perhaps 13 or 16 years, I took a course called linear algebra. It has been a little while,so in parts that I don't use as much I was rusty. I possibly incorrectly remember having to ...
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Meaning of kernel size 1 for 1-D convolution in Keras

The kernel size is the window size for 1D convolution. Can anyone explain what is meant by kernel size $1$ in Keras/TensorFlow?
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Grad-CAM: Difference backprop modifier and grad modifier

I am using Grad-CAM to analyze my CNN. I want to apply a ReLU to the linear combination of feature maps because I am only interested in the features that have a positive influence on the class of ...
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What receptive field do we have after stacking $n \times n$ CONV layers with kernel size $k \times k$?

What receptive field do we have after stacking $n \times n$ convolutional layers with kernel size $k \times k$ and stride $1$? Layers numeration starts with $1$. The resulting receptive field will be ...
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Spectral graph convolutional network, re-assigning indices

This is a silly question for whom is familiar with the theory. I came across few papers that use a particular definition of convolution, designed to work with graphs, for example see section 2.1. of ...
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Compute $E(X_1|X_1+X_2)$ $X_1, X_2$ both iid $Exponential(1)$

I recently stumbled across this question on CV: Conditional expectation conditional on exponential random variable And really liked the answer provided by @Rush, but I wanted to try to compute this ...
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How to pass from {Probability density function, convolution} to {Probability density function, characteristic function}?

In Forsman, W.C. (1986) "Polymers in solution: theoretical considerations and newer methods of characterization", Springer, New York. https://www.springer.com/la/book/9780306421464 page 24, it states:...
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Why chomp in Temporal Convolutional Network?

In the code that accompanies the paper describing the TCN network, the activations of the temporal convolutions are "chomped", or sliced at the end by the number of zero-padding that was added. This ...
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Sum of two dependent random variables with copula

I'm trying to calculate sum of 2 random variables by using Copula Theory in R or Matlab. However, I have very limited knowledge about probability. Actually I read a lot of theoretical information ...
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What is the distribution of a sum of binomial distributions with the same parameter q but with the sample sizes following a Poisson distribution?

Let $\{a_1,a_2,\ldots,,a_n\}$ be a random sample of a Poisson distribution. Consider the following random variables $X_1=\mathrm{Binomial}(a_1,q), ~X_2=\mathrm{Binomial}(a_2,q),\ldots,~X_n=\mathrm{...
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Autoencoder - reconstructed image not matching the input image

I have trained a convolutional autoencoder on cifar10 dataset. The reconstruction loss on the test data is quite less (around 0.0225). However, the reconstructed training images do not look like ...
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Solving an equation that involves convolution and batch normalization

Basically the equation is $$ x = \mathrm{BN}(\mathrm{Conv}(z)) $$ where the convolution operation uses SAME padding with stride $1$ ensuring that the input and output have the same size. The ...
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CNN analysis help

http://scs.ryerson.ca/~aharley/vis/conv/ I'm trying to better understand the architecture in this CNN. After reading the paper here: http://scs.ryerson.ca/~aharley/vis/ the author says This ...
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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 ...
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Why use Convolution of probability function instead of cross-correlation? [duplicate]

First, let me quickly remind you of the two operations: convolution and cross-correlation between 2 function $f$ and $g$, assuming continuous domain. Cross-Correlation $f \star g$ : $\int f(\tau)g(\...
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Intuition behind product distribution pdf

Say we have two distributions $X$ and $Y$. I know that the pdf of the distribution $Z = X + Y$ is given by: $f_Z(z) = \int_{-\infty}^{\infty}f_X(x)f_Y(z-x)dx$ The intuition is that you sum up the ...
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What is the mode of the convoluted probability density function?

If I am aware of the distributions of both $V$ and $U$, is there general guiding principle in terms of the position of the mode of the distribution of $\varepsilon =V-U$. As I am not specifying the ...
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What might explain inferior performance in a LSTM featuring a convolution layer?

This is not a problem:solution scenario insofar that I am not attempting to find a way to improve the model, merely find a reason for its behaviour. Model using LSTM has accuracy of about 84-86% ...
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CNN training in bfloat16

Are there any efforts so far for training CNNs end-to-end with bfloat16 format? especially the convolution part, i.e. both multiplication and addition is done in bfloat16. Can this scale to large ...
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Why does each convolution layer require activation function and weight initialization?

From a course on convolutional neural network, my understanding is basically that the convolutional layer does a convolution with a filter across your image, and generates some output (and maybe a ...
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Wavenet joint probability

As presented in the first article of Google Wavenet (https://arxiv.org/pdf/1609.03499.pdf) the model can approximate the joint probability of the whole sequence (raw audio waveform) using the chain ...
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Dimensions and implementation of the Convolution step in CNN

I am trying to write my own convolutional neural network from scratch (Python) and after reading several articles and watching tutorials (on CNN) there are still a couple of issues that I am unable to ...
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How are convolution layer/max-pool layer operations carried out

I understand the concept behind why convolution layers / max pool operations work, but I cannot conceptualize how they are applied in typical neural network model. For example if I had a NN model ...
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Why does fully convolutional network plateau first and then learns?

Im training a fully convolutional network to classify handwriting Chinese characters. The dev dataset I am using has 250 classes with 200 - 300 samples in each class. And I found out no matter how I ...
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Why resolution is not important for pre-trained models

As far as I understand (and even successfully applied in Kaggle competition), it's possible to feed images of any resolution into the pre-trained model (e.g. ResNet34). But I do not understand, why it ...
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1answer
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Joint cumulative distribution of independent random variables

X,Y,Z are non negative random variables which are independent and uniformly distributed in [0,1] and let $\alpha$ be a given number in [0.1]. Now how to compute $\text{Pr}(X+Y+Z>\alpha \;\;\; \&...
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Why is the convolution of two box kernels a triangle kernel? [duplicate]

Can anyone show the mathematical steps proving $K_{box}*K_{box} = K_{triangle}$
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Histogram of Subtraction of Underlying Values

I have histograms produced from two sets of data recording. One of background noise of values $X$ and another $Z$ with a signal of values $Y$ present such that $Z = X + Y$. How can I estimate a ...
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Understanding TensorFlow' conv2d for multiple output channels

I'm trying to understand the convolution process better by applying conv2d to different inputs. However I get unexpected result by transforming 3x3 matrix from 1 to ...
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How do convolutional neural networks deal with many filters during convolution?

I am unsure of how convolutional neural networks treat several filters. Many of the examples I have seen only have filter at a time, and that is intuitive for me. Look at the nice visual tutorial here:...
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Difference between two random variables

Consider the case of two jointly continuous random variables. Assume that $G$ (generation process) and $L$ (load process) are jointly continuous random variables, with joint PDF given by $f_{G, L}(g, ...
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Is there a function that combines correlation and convolution?

I'm actually trying to find some correlations between functions, and i was wondering if there is a function that quantifies the amount of time we need to shift a curve to have a high correlation with ...
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1answer
166 views

Convolutional network - how to choose output channels number, stride and padding?

I am trying to create a convolutional network for image classification problem. I am using PyTorch but I have troubles in understending the implementation of their 2D convolutional layer. I understand ...
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Is convolution in CNNs a similarity measure

Is it correct to say that convolution in CNNs is a similarity measure between filter and receptive field? and what is the difference between correlation and convolution?
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Sums of degenerate quadratic forms

I am searching for an analogue of the fact: let $\Sigma_1 , \Sigma_2> 0$ in $\mathbb R^{m \times m}$ and let $x,c_1, c_2 \in \mathbb R^m$ be arbitrary. Let $\Sigma_3^{-1} = \Sigma_1^{-1} + \Sigma_2^...
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CNN Flower recognition (5 classes) accuracy improvement

I have created a CNN for image recognition (Flower types - 5 classes) and am now considering model parameter changes to improve accuracy. The model (5 3*3conv + 4 2*2max pooling layers) attains ~60% ...
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Keras TimeSeries - Regression with negative values

I am trying to make regression tasks for time series, my data is like the below, i make window size of 10, and input feature as below, and target is the 5th column. as you see it has data of {70, 110, ...
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Recurrent convolution evaluation in R [closed]

I want to compute the convolution of order 3 which is defined as follows: So first I compute the convolution of order 2 (this I can do properly). My problem is: how can I keep the convolution of ...
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t-sne V CNN extracted features

If one were to visualise images (say MNIST) with t-sne we get great separation in the t-sne lower dimensional space. However what would happen if one where to run a CNN on MNIST, then remove the ...
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Distribution of sum of exponentials

Let $X_1$ and $X_2$ be independent and identically distributed exponential random variables with rate $\lambda$. Let $S_2 = X_1 + X_2$. Q: Show that $S_2$ has PDF $f_{S_2}(x) = \lambda^2 x \text{e}^{-...
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Estimate Convolution Filter Formula from Noisy Input and Output

When I learned signal processing, I learned how to calculate the output with given input and given convolution filter. However, if now I have the noisy input and output, assuming the system is linear ...
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193 views

Siamese Networks Pytorch

I have 2 images as input, x1 and x2 and try to use convolution as a similarity measure. The idea is that the learned weights substitute more traditional measure of similarity (cross correlation, NN, ....
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RGB images as input to CNN

Considering a 32*32*3 RGB image, would there be filters/kernels for each color channel? I haven't found examples explaining how CNN works for RGB images and whether each filter is a 3D. If I decide to ...
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Why researchers use conv1d for embeddings instead of dense layers?

In some papers (like Reinforcement learning for Vehicle Routing Problem), researchers use conv1d to embed the problem input into a hyperspace; for example, in solving TSP, they use conv1d on the (x,y) ...
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Distribution of 'DFSTAT'

Apart from the commonly applied "influence measures" in linear regression, i.e. dfbeta(s) / Cook's distance / covratio / dffit(s) / studentized residuals / leverage, there is one not so famous, ...
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Convolution for uniform distribution and standard normal distribution

Consider a random variable $U$ that has a uniform distribution on $(0,1)$ and a random variable $X$ that has a standard normal distribution. Assume that $U$ and $X$ are independent. Determine an ...