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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Is it acceptable to use pooling layers in variational autoencoders?
When training a model for image classification it is common to use pooling layers to reduce the dimensionality, as we only care about the final node values corresponding to the categorical ...
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what are the differences between receptive field (RF) and field-of-views (FOV) in DeepLab papers?
I am learning the deeplab models. However, some concepts in the papers made me confused. Receptive field (RF) and field-of-views (FOV) are two concepts mentioned in the Deeplabv1 paper. I know that ...
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Density of $|t_1 - t_2|$ where $t_1$ and $t_2$ are iid with $P(t) = \alpha e^{-t\alpha}$
I am trying to answer the following question from my quantum mechanics textbook and my probability theory is admittedly rusty (this is not schoolwork as should be clear from my post history on Phys ...
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Order Statistics - Percentile Range of Normal Mixture of Normals
Say I have draw N values from a normal distribution [$\mu_1$, $\sigma_1$]. Below are 10 sampled points compared to the normal distribution they're sampled from
I then create a normal mixture of ...
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How to calculate the maximum and minimum number of feature maps or filters in a CNN?
I programmed an Autoencoder to encode images, and I want to know what is the max and min number of feature maps in layers.Conv2D(?, (3, 3), activation='relu', padding='same')(input_img). The size of ...
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Distribution closed under convolution and truncation followed by convolution
Let $D(\theta)$ denote an absolutely continuous distribution on $\mathbb{R}$. (The finite dimensional vector $\theta$ collects the parameters of the distribution.) Assume that the p.d.f. of $D(\theta)$...
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How can I build a 6D Convolution Layer in a CNN, using R or Python? [closed]
As stated in the title, I would like to build an N-dimensional Convolutional Layer as part of a Convolution Neural Network, without doing dimensionality reduction on my data; because I have multiple ...
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Unclear Architecture of MNIST Neural Network
I am trying to reproduce a Neural Network trained to detect whether there is a 0-3 digit in an image with another confounding image. The paper I am following lists the corresponding architecture:
A ...
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What "Convolution filters along the time axis" means?
Suppose that I have a tensor of height:25 and width:50. Height is my temporal axis, therefore I have a window of 25 time steps. Therefore my input tensor is:
I want to extract temporal features / ...
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Calculating the receptive field of a CNN when stride > kernelsize
I am reading about how to calculate the receptive field on Araujo, et al., "Computing Receptive Fields of Convolutional Neural Networks", Distill, 2019. however there is one thing that ...
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Relationship between convolutions in neural nets and probabilistic convolution
In probability theory, convolution extends to produce the distribution of the sum of two independent random variables. I've only ever seen this in the context of univariate random variables.
However, ...
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Are Class Activated Maps an example of backpropagated Explainable AI?
Class Activated Maps (NOT GradCAM) is listed in van der Velden et al as a back-propagation approach in table 1, but that is not actually true, is it?
CAM doesn't use back-propagation in the method, ...
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How to calculate how much each error source contributes to an overall accuracy metric?
I am building a model of overall accuracy for a robotic system, I have various error sources from assembly, calibrations, measurements, imaging, for each error I have a PDF of the error it induces on ...
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How to average multiple non-normal distributions?
I have the following statistics of two independent random variables:
First random variable:
...
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Discovering alternative waveforms for Fourier transform (alternatives to sinusoidal waves)
I'm working on a classification algorithm that utilises a discrete Fourier transform on sensor data, as a means to detect the presence of an oscillating signal.
My issue is that the signal-generating ...
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Mean conditional on sum
Let $X$ and $Y$ be two random variables. I am interested in how $\mathrm{E}[X | X + Y = z]$ changes as $z$ changes.
Intuitively, if $X$ and $Y$ are independent, the conditional mean should be ...
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How to determine the no of multiplication operations in convolution operation?
Let's say We have an input of size 28×28×192. We apply 32, 5×5 convolution filters with padding "same". How many multiplication operations will be there in total?
I know there will be ...
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How to take 1000 samples from distribution X and then use MLE to prove they came from distribution X?
I am trying to do:
find 1000 points that represent samples from distribution X with parameters $(a,b,c,\ldots, d)$
be guaranteed that the MLEs for those 1000 points are $(a,b,c,\ldots, d)$ with $99\%$...
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What is difference between the joint probability distribution and the sum/convolution, of 2 dists? [duplicate]
Google is coming up a bit short when I searched for "joint vs sum random variables".
Perhaps someone can provide an authoritative answer to compare and contrast the sum/convolution of 2 ...
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Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease (such as in a CNN?)
The function np.convolve is a 1D convolution (e.g. when both inputs are 1D). It results in a larger output size.
...
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Convolution of two multivariate guassian distribution for the posterior predictive distribution
To find the full conditional distribution of $\eta$ for a Gibbs sampling algorithm , I have to show that
$$
p(\eta|-) \propto \int N(\eta;\Omega(\Lambda+\Delta^{-1}\mu),\Omega) N(\mu;\hat{\mu},\Delta/\...
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How to incorporate prior knowledge into a CNN?
I'm pretty new to Bayesian inference and machine learning, so I think I'm just lacking the right words to search for a paper that addresses this topic, so here goes:
I'm trying to do image ...
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Numerical Solution of two convoluted stable paretian random variables
I am trying to numerically compute the joint density of X and Y, where both are stable paretian distributed random variables with different alphas (1.4 and 1.7).
I can compute the PDF via inversion ...
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What kind of architecture to use for non-binary output multi-label image clasification
I want to make a network for making multi-label attribute classifications on images of clothing.
This is a simplified case of what I want to do, I have 9 different attribute categories that I wish to ...
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Why does my network not learn a single image perfectly?
I have a convolutional neural network that uses Resnet(18,34 or 50 doesn't matter) as the backbone and pretrained weights from ImageNet.When I try training it with a single image for 50 or so epochs, ...
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How to calculate the Transposed Convolution?
Studying for my finals in Deep learning. I'm trying to solve the following question:
Calculate the Transposed Convolution of input $A$ with kernel $K$:
$$
A=\begin{pmatrix}1 & 0 & 1\\
0 & ...
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Sparsity of connections in a CNN - why is it beneficial?
In his CNN video, Andrew Ng explains the benefits of convolutions over FC, and he mentions sparsity of connections as being one of them. Can someone please explain what is the benefit of sparsity when ...
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How to explain the high accuracy and F1 score on the test set with a huge binary crossentropy loss?
I'll provide a little of introduction based on my example. I have a small collection of RGB (but 'gray-looking') brain MRI photos, divided into 2 classes: healthy and tumor. My data split looks like ...
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does kernel or filter update through backpropagation , is require fully connected layers?
does CNN itself without FC has the ability to make backpropagation to update its filters, after comparing them with the output and calculating the loss, and then pass them through the FCC?
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GAN artifacts on borders
not quite a math-question, but I have a doubt.
I'm trying to build from scratch the Pix2pix network, on the facades dataset, and I think I finally got a good model (from the paper I borrowed just the ...
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Why not using Convolutional pooling instead of MaxPooling to avoid invariance
I was reading the paper of [Geoffrey Hinton: Capsule network], and I watch it's talk on Youtube about the problem of Conv Network is actually the (max) pooling layer, since we don't want to be ...
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How does fix-up initialization avoid prevent the neurons from updating in the exact same direction?
We know zero initialization is bad:
Pitfall: all zero initialization. Lets start with what we should not do. Note that we do not know what the final value of every weight should be in the trained ...
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Validation loss is stuck at certain loss [duplicate]
I am trying to implement 1D-CNN to time-series data. Here is my data.
Here is my dataframe:
I am trying to forecast each of these futures. I am following the TensorFlow forecasting guide.
Based on ...
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Sum of iid Exponential observations then subtracting the minimum of the observations [duplicate]
Consider $n$ iid $X_1,...,X_n \sim Exp(1)$. My goal is to find the density of $\sum (X_i - X_{(1)})$.
My attempt
If we write out the entire summation in order statistics, we get
$X_{(1)}-X_{(1)} + X_{(...
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Deformable Convolution implementation in tensorflow2
Is there any good implementation of Deformable Convolution in tensorflow2?
Deformable Convolutional Networks
Deformable ConvNets v2: More Deformable, Better Results
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Find pdf of X+Y [duplicate]
Let X ∼ Exp(λ) and Y ∼ Exp(μ) be two independent exponential random variables,
where λ, μ > 0.
Find the probability density function of X + Y if λ ̸= μ.
I have successfully find ans if λ = μ, but ...
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When does the sum of two $t$-distributed random variables follow a $t$ distribution?
In the scope of a project, I need to find the sum of two independent $t$-distributions.
I know that in the general case, the sum of two $t$-distributed random variables is not $t$-distributed. However,...
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How general is this property about correlation and the sum of two normal RVs?
(Cross-posted from math stack exchange as I didn't get any responses there)
Given a random vector $(X_1,X_2)$ that is jointly normal with means / sd's $\mu_1,\mu_2, \sigma_1,\sigma_2$ and correlation ...
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Covariance of a convolution between a gaussian random walk and white noise [closed]
I want to compute the covariance of $$U_t:=\sum_{l=-L}^{l=L} (X_l-X_{l-1})X_{l-t}$$
with $X_t$ defined as : \begin{align*}
X_0&=0
\\
X_t&=X_{t-1}+\epsilon_t
\end{align*}
$t=1,2,...$...
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Issue about both results in agreement with 2 different ways to compute variance of a random variable : weighted chisquared vs Gamma distributions
1.) I am interested in computing the variance of this observable $O$ involving the coefficients of spherical harmonics $a_{\ell m}$ and the $C_{\ell}$ which is the variance of an $a_{\ell m}$ :
$$O=\...
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3D convolutions and jitter
I want to process a sequence of cropped and aligned face images from a video with a neural network. I am considering a use of 3D convolutions in order to capture the spatiotemporal dependency. However,...
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Why does MobileNet Architecture start with a Standard Convolution?
I am trying to understand the design choices behind the MobileNet architecture. (pdf available on the right).
The authors use Depthwise Separable Convolutions as a replacement for Classical ...
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How to count the parameters in a convolution layer?
I'm preparing for an exam in Computer Vision. I came across with the following question from one of the exams:
What is the number of parameters of a convolution layer in a neural network, when the ...
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How to obtain the density of a sum of independent discrete random variables?
Let's $X_1, X_2, ..., X_n$, $n=1,2,...$ are independent discrete random variables.
It is necessary to find the distribution law of the their sum:
$p(k) =P(X_1 + X_2 + ... + X_n = k), k=0, 1, 2, ... $
...
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CNN model accuracy is increasing really slowly [duplicate]
I am training a CNN model from scratch on the Caltech101 dataset. The accuracy of the model is increasing very slowly after the 5th epoch. Shown below is the accuracy and loss curves of the model for ...
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Why my cdf of the convolution of n exponential distribution is not in the range(0,1)?
I assume that there are n exponential distribution that $x_i$ ~ $Exp(\lambda_i)$, i=1..n, and I want to calculate the cumulative distribution of $S=x_1+x_2+...+x_n$, the convolution of n exponential ...
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Training accuracy growing way faster than validation accuracy?
i've been trying to solve this classification problem using a convolutional neural network for some days but no matter what I do I can't seem to find the correct hyperparameters and configuration to ...
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What prevents my PyTorch convolutional auto-encoder to converge on some initializations? [duplicate]
I built a small auto-encoder for greyscale images. It is there to make some tests, so I train it often, and I have a strange behavior.
On some initialisations, it does not converge. I mean, the MSE ...
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Convolution of a conditional PDF with itself [duplicate]
Let's say that $x$ is a random variable which follows a conditional probability density function $f(x|N)$, where $N$ is an integer parameter. If the functional form of $f(x|N=1)$ is known, then one ...
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convolving a conditional pdf with itself
Let's say that x is a random variable which follows a conditional probability density function $f(x|N)$, where $N$ is an integer parameter. If the functional form of $f(x|N=1)$ is known, then one can ...
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