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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61 views

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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Question about log-concave random variables

Can anybody help me with this question? Suppose $\xi_i \sim_{iid} G(x)$, where $G(x)$ is log-concave. Define then: $$s_i(v_1,..,v_n) = \ln\Big(\mathbb{P}\big(v_i-\xi_i \ge \max_{j \neq i}\{ v_j-\xi_j \...
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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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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 ...
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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 ...
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1answer
24 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 ...
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179 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 ...
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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 ...
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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 ...
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1answer
79 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 ...
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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 ...
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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{...
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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/...
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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 ...
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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 ...
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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 ...
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Convolution kernels

Below are two different convolution kernel formulas, h and H, written in Python which I think are both symmetric. What is the ...
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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?
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difference between the “Kernel Convolution” and “Kernel PCA”

Can anybody explain the difference between the "Kernel Convolution" and "Kernel PCA" to me, please?
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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 ...
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1answer
94 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 ...
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53 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 ...
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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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1answer
28 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 ...
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73 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, ...
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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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120 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 ...
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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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