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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71 views

What are the gamma-Pareto convolutions and how have they been used?

The Pareto distributions, i.e., density functions (pdf), are types I through IV and the type II variant; the Lomax distribution. This makes for a number of possible gamma-Pareto convolutions (GPC; ...
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CNN: Details of Zeiler Fergus Net

I want to replicate the modified AlexNet by Zeiler and Fergus from 2013 (Visualizing and Understanding Convolutional Networks) but they spare some details. Hope someone here knows more about it. What ...
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How to handle even and odd convolutional filter sizes and images

Is there a rule of thumb for determining the size of a convolutional filter given the shape of the input? Specifically, if you want to do a 1D convolution over an even-length vector, does the kernel ...
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Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll ...
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Siamese Network: validation accuracy highly fluctuating

I am trying to train a Siamese Network with 1D CNN, where I calculate the absolute difference between the two latent vectors, and then pass it to a sigmoid neuron to determine if the two inputs belong ...
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1answer
181 views

AutoEncoder Reconstruction error for Anomaly Detection

I'm building a convolutional autoencoder as a means of Anomaly Detection for semiconductor machine sensor data - so every wafer processed is treated like an image (rows are time series values, columns ...
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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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78 views

Convolve Gamma distribution with Triangle distribution?

I am working on the use of distributed delay applied to pharmacometric models. Specifically, the delay kernel I am interested in is the Gamma distribution, with non-integer shape. The historical ...
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689 views

CNN convolutional layer backpropagation formulas

I tried to implement a CNN in Java but I am stuck at updating the weights in my convolution layer. I tried to create the following image that shows how I calculate each weight delta and error signals:...
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702 views

What do the dimensions of a convolutional layer represent?

My understanding is that the width and the height represents a kernel (convolution matrix) that is convolved over the image. The depth is the number of these kernels. If that is the case, how would ...
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What does 1x1 convolution mean in a neural network?

I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what ...
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Can one image be used for training cnn

Is it possible to train neural network with only one image data so it can recognize this only one image? For example i want to develop a facial recognition software using cnn where their will be ...
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Visualine Node Importance in Graph Convolution

I am quite new to the concept of attention. I am working with graph data and running graph convolution on it to learn node level embedding first. Then an attention layer to aggregate the nodes to ...
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convolution and deconvolution of random variables of different dimensions

Preliminary: Let's say we have $Y=X+Z$ ($Y$ is data, $X$ is latent variable and $Z$ is noise), where the random variables are all in $\mathbb{R}$. Then an inverse Fourier transform leads to \begin{...
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When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X $ and $Y$, you know $$ X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p) $$ I am interested in what if anything can be said about the ...
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Convolutional roots of mixture of exponential distributions

In the reference book on infinite divisibility and generalised gamma convolution, BONDESSON, Lennart. Generalized gamma convolutions and related classes of distributions and densities. Springer ...
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Convolution with multiple input channel and multiple filters which have depth

How does the convolution work for an input which has multiple channels convolving with filters that also have depth. For example, assume somewhere in the network we have a ...
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1answer
32 views

Neural networks assume continuity, what does this mean?

I encountered the following paragraph by Pedro Domingos (mentioned in Gary F. Marcus paper): ANNs assume continuity, graphical models assume conditional independence, and instance-based learning ...
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171 views

Convolution equality

If $k$ is an squared or absolutely integrable kernel are the belo equalities true ? $$z(s)=\int_{R}^{} \! k(u-d) x(u).du \ \ =\int_{R}^{} \! k(u+d) x(u).du \ \ $$ and $$\int_{R}^{} \! k(u-d) k(u-d^{...
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Does replacing a random variable in a sum with it's expectation shift the mass of the expectation towards the mean?

Assume any two positive, independent random variables $X$, $Y$ with pmf's $f_X$ and $f_Y$, as well as a third (degenerate) random variable $Z$ that is defined to be equal to the expectation of $Y$, i....
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Cropping input images Neural Networks

I'm creating a simple neural network for image classification,I had some doubts about the input images. Let's suppose i'm trying to classify (for example) a bear and i have an input image like this: ...
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How do I learn one time signal given another?

I conducted an experiment which led me to believe that two sensors were time correlated somehow. Their signals do not show any obvious correlation, however their spectrograms show a strong similarity ...
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More efficient way to calculate convolution of Weibull distribution

Hi I was trying to compute the convolution of Weibull distribution as follows with parameter t, lambda(scale parameter) and k: ...
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Convolution of two indicator functions [duplicate]

I am experiencing difficulties understanding the concept of convolution and especially convolution of 2 independent indicator functions. I would be really thankful if someone can help understand the ...
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Convolutions of joint random variables

I have two discrete dependent random variables $X,Y$, where both $X$ and $Y$ can take values either $0$ or $1$. Furthermore, I know their joint distribution $f_{X,Y}(X,Y)$. Now let's say I have an ...
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What is the purpose of the last 1x1 convolution layer in segmentation networks providing a linear transformation of the features?

Semantic segmentation networks make use of a final 1x1 convolution layer at the very end of their network which brings the feature maps equal to the number of classes in the dataset. Since this 1x1 ...
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ResNet Reduce Block

I am building a ResNet. I have two separate blocks: Cnn block, Reduce block. Cnn block - 1 cnn layer, activation, Batch Normal -> 1 cnn, activation, Batch Normal, so 2 CNN in this block. In Reduce ...
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CNN models comparison [duplicate]

I coded a 38 layer CNN and 8 layer CNN but there's something wrong in my 38 layer CNN, which doesn't learn anything. Not able to fugure out what's wrong. They were trained on CIFAR.
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Does max-pooling increase the receptive field? [duplicate]

I'm new in deep learning. when applying convolution on the image , the receptive field is increased but when applying max pooling on the image, I don't know the receptive field is increasing or keep ...
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Do convolutional neural networks flip the kernel?

After reading various examples of CNNs it doesn't look like the kernel used for convolution is flipped. Can anybody explain why?
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How many input pixels influence output pixel in an FCN type architecture?

Let's say I have 8 back to back convolutional layers with zero padding such that the input and output dimensions are the same. There are no max-pooling layers between the layers. All the layers use a ...
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Question about the log-normal distribution

The main object of my question is this: if $X$ has a log-normal distribution, $Y = X + Z$ and $Y$ has the same distribution as that of $Z^2$ (in other words, $F_{Z^2} = F_{X+Z}$) and $X, Z$ are ...
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Unlearning Neural Network? Prevent learning from a specific feature

Is it possible to train a NN to avoid the features that a different neural network finds? For example, let's train a simple 1 layer CNN with 1x1 kernels on a supervised binary classification problem. ...
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163 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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How can a Keras convolutional network be defined such that it outputs images of the same dimensions as the input?

I wanna train a convolutional neural network to convert an input image to an output image, where the input and output images are of the same dimensions (50 pixels wide, 300 pixels high and greyscale). ...
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Why is the sum of two random variables a convolution?

For long time I did not understand why the "sum" of two random variables is their convolution, whereas a mixture density function sum of $f(x)$ and $g(x)$ is $p\,f(x)+(1-p)g(x)$; the arithmetic sum ...
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1answer
984 views

How to implement 1D Convolutional Autoencoder with multiple channels? [closed]

I want to build a 1D convolution autoencoder with 4 channels in Keras. Instead of images with RGB channels, I am working with triaxial sensor data + magnitude which calls for 4 channels. I haven't ...
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1answer
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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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1answer
319 views

Sampling from a Convolutional Restricted Boltzmann Machine's Visible Gaussian Real-valued Units

I am trying to confirm whether or not I am understanding the process described in the title. I am implementing a CRMB (with Real Valued Gaussian Visible units and Binary hidden units) as outlined in ...
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1answer
879 views

Padding and stride in backpropagation of a conv net

I am trying to implement the back-propagation of a simple convolutional network. Specifically I understand that one of the steps is the convolution of the gradients coming from the next layer, with ...
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1answer
189 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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1answer
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Does the model architecture of a CNN depend on the dimension of your input images?

By model architecture, I'm interested in knowing the following: Number of nodes in input layer Number of nodes in subsequent layers Number of layers in the architecture Number of filters and ...
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1answer
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What is the difference between 1x1 convolutions and convolutions with “SAME” padding?

In general, 1x1 convolutions are used to reduce the dimensionality of filter space. I referred this answer. But we can also reduce the dimensionality of filter ...
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1answer
21 views

Deleting and repairing a Convolution Neural Network

Let's say that I have a convolutional neural network with multiple blocks, each consisting of multiple filters. If we have something along the lines of Input -> Block1 -> Block2 -> Block3 -> Max ...
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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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1answer
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Cannot overfit Mobilenet with one example

I am trying to do a single object detection. Since the problem is much simpler than multibox object localization I decided to try using a simple CNN that predicts the object class and its location. ...
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CNN Feature Extraction Time

I have a dataset consist of 260 thousands images that are extracted from several videos. I want to extract features of these images and use them for frame retrieval. I used VGG16 (pretrained on ...
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1answer
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What is E[X|X+Y < z] with X, Y independent Normals?

Let $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$ and $Cov(X,Y)=\sigma_{XY}$. Define $Z=X+Y$. I know that $E[X|Z=z]=\mu_X + \frac{\sigma_X^2+\sigma_{XY}}{\sigma_X^2+2\sigma_{XY}+\...
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How does the weight affect the sum of two Normals?

Question Take two independent, non-degenerate Normals, $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$. Define $Z=aX + Y$ with $a>0$. This implies $Z \sim N(a\mu_X+\mu_Y,a^2\sigma_X^...
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Why do we connect convolution layers in sequence instead of applying them separately on input image?

I am already aware of the convolution function, CNN and all. I have already implemented a few. But this question strucks my mind every time. Most of the networks I have seen, use a stack of ...