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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6 views

Inconsistent and ambiguous dimensions of matrices used in the Attention layer in GNMT or text-to-speech synthesis?

Attention-scoring mechanism seems to be a commonly-used component in various seq2seq models, and I was reading about the original "Location-based Attention" in Bahadanau well-known paper at https://...
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How exactly does conv1d filter work when operating on a sequence of characters?

I understand convolution filters when applied to an image (e.g. an 224x224 image with 3 in-channels transformed by 56 total filters of 5x5 conv to a 224x224 image with 56 out-channels). The key is ...
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What is the difference between a class activation map and a saliency map for convolutional neural networks?

I am researching attribution methods in computer vision literature to better understand how a CNN model arrives at its predictions. I have come across the terms ...
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Intuitive explanation for spline convolution [duplicate]

What is spline convolution intuitively? When should use it? what is the motivation behind it?
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Can we derive the standard normal distribution function from specification of convolution?

In this article, the following is said: Why is the normal distribution so important? Because it is its own convolution with itself, is why. If you average many similar things, what you get has ...
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Let N be the number of times you roll a 6-sided die until you roll a 1. Let M be the sum of rolling N six-sided dice. What is the pdf of M?

I understand that a geometric distribution can be used to determine the pmf for N, but am lost on finding the distribution for M. Also, if done in reverse order: Let N be the result of rolling a 6-...
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Why does R have a different definition on convolution?

I found convolution in R works differently from Python. In Python, it will flip the input and run the convolution. In the R documentation, it says Note that the usual definition of convolution of ...
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Is there a way to figure out using filter sizes (manually) how many operations Batchnorm, Conv, and Relu layers take during backprop? [duplicate]

I'm working with a basic resnet model. I want to understand how to compute by-hand the number of ops for a specific layer during backward pass (backprop) during Training (not inference). This involves ...
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Best practices: how to feed a set of long time series to a convolutional net for time series prediction

Let us assume we run N experiments. During the experiments we collect measurements. In these measurements we have features and labels. We want to predict the label Y(t) given a series of past ...
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Explaining results when changing kernel size in CNN

I trained a CNN on CIFAR10 (implemented in PyTorch) with the following architecture: INPUT: (3,32,32) --> Conv2d layer (kernel: 3x3, stride:1x1, filters: 64) --> Activation: ReLU --> Max pooling (...
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Does the following “theorem” have a name? [duplicate]

I am aware that if one has random variables, and sums them, then the result belongs to a distribution which is the convolution of the parent probability distributions of the initial random variables. ...
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Bottleneck block in pytorch ResNet

I was trying to understand the output the pytorch resnet model and can't seem to figure out the following issue with what printing the model shows. Why is the following only there in Bottleneck-0 and ...
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Does feature detector(filter) has to be a sqaure matrix?

I am going through a course on Convolutional neural networks, where in the convolution step, the feature detector matrix was square shaped. Is there any mathematical significance that Feature ...
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Mixture or Convolution

tl;dr is final paragraph at the bottom. I have read the posts explaining the differences between mixture distributions and convolutions of distributions, but am having a hard time understanding which ...
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What is time complexity big O for 2D filters and 1D filters in image convolution Neural networks.?

I went through this link to understand, but was not able to grasp the concept. What is the computational complexity of a 1D convolutional layer? Consider a more general case: ...
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Problem with a factor in a convolution of two probability density functions

In a problem I'm working on I have analytical expression of two probability density functions $p_1(v_1),p_2(v_2)$ of two variables $v_1$ and $v_2$, which represent velocities of two particles. I wish ...
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Prove or disprove the Linearity of Expectiles used in Expectile Regression

For expectation (mean), there are many useful properties such as Linearity of Expectation: $\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$ $\mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]$ (The 2 equations ...
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Temporal Convolutional Networks (TCNs): Possibility to provide general information for each sample?

In my task it is important to provide general information for each sample. A sample consists of a time sequence and there is a channel with n values for each time t of the sequence. This results in a ...
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Clarified a previous question. How to evaluate the following probability? [duplicate]

I would kindly ask you not to close this prematurely. I have tried to give an elaborate explanation to the best of my ability and could really use some advice as how to go about this. The first ...
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Combine normal distribution and Rayleigh distribution

I am trying to find the maximum wave for a given time span based on a given measured wave height. In the top image the measured wave height is 2m and indicated with the black line. The probability ...
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30 views

Does a CNN have to be Fully Connected?

So I am trying to implement a specific CNN called a U-net. It states in page 3 that it doesn't have a fully connected layer. Till then I understood CNN to have two stages; 1. Convolution, where the ...
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PDF of sum of stationary processes

I would like to obtain formulas for the sum of random processes $U(\omega,t), V(\omega,t)$: Sum of two signals: $G(\omega,t) = U(\omega,t) + V(\omega,t)$ Case 1: $U,V$ are also jointly stationary $...
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Sum of Exponential and Gamma Distributions [duplicate]

I have been learning sums of distributions and understand that the sum of exponential distributions with parameter B is a gamma distribution with parameters a=1 and B. However, I need to figure out: ...
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How can I evaluate the following bivariate distribution?

Say $A$ and $B$ and $C$ and $D$ are four random variables, such that $A\not\!\perp\!\!\!\perp B$ and $C\not\!\perp\!\!\!\perp D$. How can I evaluate a bivariate CDF of the form? \begin{equation} P(A+B&...
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What is the convolution of the distribution function of sum of dependent variables?

Say $Z=X+Y$ and where $X\not\!\perp\!\!\!\perp Y$. Would we have? \begin{equation} F_{X+Y}(z)=\int_0^zF_{X,Y}(x,z-x)dx \end{equation}
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Derivation of winograd filter transform matrices

For http://web.archive.org/web/20190509195948/https://www.intel.ai/winograd-2/ , how to derive the winograd filter transform matrices ?
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How can we evaluate the following CDF?

First let us consider the following regression \begin{equation} y_t=\beta'x_t+\varepsilon_t,\quad t=1,...,n \end{equation} where $x_t$ is a $k\times 1$ vector of "fixed" regressors and $\beta$ is ...
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winograd convolution output size

For http://web.archive.org/web/20190509195948/https://www.intel.ai/winograd-2/ , why is winograd convolution between 4x4 matrix and 3x3 kernel giving an output matrix of size 2x2 instead of (4+3-1, 4+...
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The receptive field of a stack of dilated convolution layers with exponentially increasing dilation

In the paper that describes the multi-scale context aggregation by dilated convolutions, the authors state that their proposed architecture is motivated by the fact that dilated convolutions support ...
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Deriving skew t density function through convolution representation?

I am studying on skew t distribution, so i need its density function. I want to derive that via, integral of convolution representation. Could you please help me and introduce a good source?
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25 views

How to properly upscale images using deconvolutions

I have a dataset that has 32x32x3 images. However, I want to use models that were developed for 224x224x3 images, e.g. resnet. A common theme I see is that people resize 32x32x3 to 224x224x3, but this ...
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How to go about designing a program that identifies corn fields on a map?

I am working on a project that identifies corn fields on a map (satellite imagery), given the latitude/longitude coordinates of known corn fields. My plan is to use a deep learning convolutional ...
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Is there any benefit for using 1x1 convolution over FC?

I see several authors describe their deep learning models with fully connected layer, but when they implement it, they use 1 by 1 convolution with stride 1 instead, I understand that, mathematically ...
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What is the purpose of rotating filters while building convolutions with scipy signal?

I recently came across a bit of python code (here) which does 2d convolution with scipy signal. But before the convolve2d operation, the filter was rotated. What is the purpose of that?
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Possible to work backward from Convolution of Distributions?

So, having discovered distribution convolution, which is a method for deriving the density of a sum of individual probability distribution densities, $$S = X_{first\_distribution} + Y_{second\...
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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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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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42 views

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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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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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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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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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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1answer
61 views

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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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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26 views

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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