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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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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28 views

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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60 views

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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151 views

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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47 views

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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188 views

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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40 views

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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107 views

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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55 views

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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64 views

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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53 views

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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78 views

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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381 views

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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30 views

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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139 views

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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109 views

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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1answer
33 views

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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84 views

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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92 views

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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28 views

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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345 views

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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31 views

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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37 views

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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394 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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160 views

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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946 views

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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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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1k views

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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255 views

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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422 views

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 ...
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2answers
721 views

CNN and kernel sizes: is upsampling useful?

I am playing with Deep Recurrent Q-Network in Reinforcement learning. The architecture I am currently using is similar to the one presented in "Human-level control through deep reinforcement learning"...
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2answers
61 views

Convolution of a less typical distribution

$X_1$ and $X_2$ are independent and identically distributed (i.i.d) random variables defined on R+ each with pdf of the form $f_X(x) = \sqrt\frac{1}{2\pi x}exp[\frac{-x}{2}]\quad ,\quad x>0, \quad ...
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349 views

1x1 convolution for inception module

When understanding inception module, I once saw the following statement from an online post. What's the calculation underline the "...
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42 views

Deep learning evaluation result

A CNN model in Keras gave me the following result. Code: ...
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856 views

Normalization of convolution kernel

I am trying to smooth a noisy one-dimensional physical signal, y, while retaining correspondence between the signal's amplitude and its units. I'm applying a ...
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411 views

What is the Identity of a convolution layer in a Neural Network?

I wanted to know what the identity of a convolutional layer of a neural network was. For standard convolution operation in mathematics the identity is the delta function, however, convolutions in ...
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162 views

How to add bias in convolution transpose?

My question is regarding the transposed convolution operation (also commonly called deconvolution or upconvolution). In TensorFlow, for instance, I refer to this layer. My question is, how / when do ...