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Questions tagged [convolution]

For questions related to the convolution operation in mathematics, convolutional neural networks, image processing and computer vision.

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What's the best criterion for evaluating activation maps in a CNN?

I'm currently studying CNNs and I had the idea of building a model without a fully connected layer at the end. I think this could be beneficial, if one can somehow model the desired outputs as a ...
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What is the matrix representation of a dilated convolution?

I am delving into the matrix representation of dilated convolutions, especially after understanding standard 1D convolutions as Toeplitz matrix-vector multiplications. My specific focus is on Dilated ...
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Why are convolutions and pooling described as layers in a network?

Whenever I look at resources on convolutions and max-pooling in CNNs they always seem to describe these algorithms as being part of the network - a preliminary set of layers before the main ...
Gamaray's user avatar
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Difference in quantization regarding transpose_conv2d / conv2d

I'm trying to implement a transpose_conv2d function using padding/dilation of the input and calling a regular conv2d function. My approach is calculating the new input shape, padding and dilating the ...
punktphil's user avatar
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How does Conv2Plus1D reduces the number of paramateres?

Based on this tutorial, and the An advantage of this approach is that factorizing the convolutions into spatial and temporal dimensions saves parameters. statement, the Conv2Plus1D must have fewer ...
Ali Khalili's user avatar
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Do all CNNs learn to detect edges in the first layer?

I was looking at 3D CNNs that process volumetric data, e.g. for MRI images of brain, where the input is a 4D tensor, and I couldn't find images from the filters of the first layer. Suppose that ...
ado sar's user avatar
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Is there a correct order of "conv2d", "batchnorm2d", "ReLU/LeakyReLU", "MaxPool2d" for UNet like architectures?

Context I'm investigating the UNet architecture for a little while now. After investigating the structure of the official UNet architecture as proposed in the official paper I noticed a recurrent ...
timu vlad's user avatar
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3 answers
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2D convolution with channels versus 3D convolution for layers of a map?

Introduction I am considering to use a convolutional neural network in implementing Monte Carlo control with function approximation. I am using a Monte Carlo estimate as it is unbiased and has nice ...
Dylan Solms's user avatar
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Can a convolution learn to generate fine details? [closed]

I'm trying to get a convolutional autoencoder to reconstruct images of a dataset with crisp details. I've read in a couple places that convolutional autoencoders "naturally produce blurry images&...
Soltius's user avatar
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2 answers
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How Does Convolution Backpropagation Work?

Assume in a convolutional layer's forward pass we have a $10\times10\times3$ image and five $3\times3\times3$ kernels, then $(10\times10\times3) *( 3\times3\times3\times5)$ has the output of ...
rkuang25's user avatar
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Is there a best practice for creating multiple convolutional layers from small image inputs?

With all the work being done on larger and larger images, I'd like to ask if a best practice(s) has arisen for allowing multiple convolutional layers on small image inputs? For instance, in my case I ...
Josh's user avatar
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ML model giving rank errors on 3D layers on converting 2D images to 3D models

i am currently working on a model to convert 2d images to 3d models through a ml model. For this i have taken into reference a research paper which had this diagrammatical flow of layers & i have ...
quest1001's user avatar
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Combining Different Inputs in a Neural Network for Numerical Integration

I am building a NN that numerically integrates a non-linear differential equation. Given a DE: $$ \frac{d}{dt}x(t) = f(x, p) $$ with solution $x \in \mathbb{R}^n$ and parameters $p \in \mathbb{R}^m$, ...
Yoni Maltsman's user avatar
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What are the benefits of using multiple convolutions, as opposed to one, before the pooling layer in a U-Net?

I have seen U-Nets that use a single convolution before the pooling operator and some that use two or more. My question is, what is better? Or what are the benefits of using more or less convolutions?
Lukas Pezzei's user avatar
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Implement 4D convolution as matrix-matrix multiplication - paper is confusing!

I am confused by this paper https://arxiv.org/pdf/1410.0759.pdf which displays on page 4 how to model a 3D convolution (input has more than 1 channel and filter has more than one output). In this ...
binaryBigInt's user avatar
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1 answer
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How are CNN kernels trained when using FFT for convolutions?

CNNs (convolutional neural networks) are adept at processing images, as their construction is based on the biological neural networks found in the human eye. "Kernels", sometimes called &...
Steve Mucci's user avatar
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1 answer
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Is down-sampling the only purpose of using stride?

Stride is used in at least two operations: convolution and pooling. Both operations can be viewed as applying a kernel function on input using a kernel (filter). Stride determines the amount of "...
hanugm's user avatar
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What is a filter in the context of graph convolutional networks?

In Section 2.1 of the research paper titled Semi-Supervised Classification with Graph Convolutional Networks by Thomas N. Kipf et al., Spectral convolution on graphs defined as The multiplication of ...
JAEMTO's user avatar
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In this paper, if region $R_{2}$ moves in a sliding window manner, won't the saliency map have a smaller size than the original image?

In the paper Salient Region Detection and Segmentation, I have a question pertaining to section 3 on the convolution-like operation being performed. I had already asked a few questions about the paper ...
user avatar
3 votes
1 answer
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How do I choose the hyper-parameters for a model to detect different guitar chords?

I need to build a hand detector that recognizes the chord played by a hand on a guitar. I read this article Static Hand Gesture Recognition using Convolutional Neural Network with Data Augmentation ...
Deffo's user avatar
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Is it possible to apply 2D convolution to 1D data?

Suppose that I have a 1D dataset with 6 features. Can I apply a 2D convolutional neural net to this dataset?
user366312's user avatar
1 vote
1 answer
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Why does $I_N + D^{-\frac{1}{2}}AD^{-\frac{1}{2}}$ have eigenvalues in the range [0, 2]?

In Semi-supervised classification with Graph Convolutional Networks, I am unable to understand a few things. Given an undirected graph having adjacency matrix $A$, degree matrix $D_{ii} = \sum_j A_{...
willtryagain's user avatar
1 vote
0 answers
154 views

Couldn't the self-attention mechanism be replaced with a global depth-wise convolution?

The main advantages of the self-attention mechanism are: Ability to capture long-range dependencies Ease to parallelize on GPU or TPU However, I wonder why the same goals cannot be achieved by ...
spiridon_the_sun_rotator's user avatar
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2 answers
180 views

Why do we lose detail of an image as we go deeper into a ConvNet?

I was reading this research paper titled 'Image Style Transfer using Convolutional Neural Networks' which as the title suggests was based on Neural Style Transfer. I came across this line which didn't ...
HarshDarji's user avatar
2 votes
1 answer
858 views

Why do we add 1 in the formula to calculate the shape of the output of the convolution?

In the formula to calculate output shape of tensor after convolution operation $$ W_2 = (W_1-F+2P)/S + 1, $$ where: $W_2$ is the output shape of the tensor $W_1$ is the input shape $F$ is the filter ...
adityagabbar's user avatar
1 vote
1 answer
217 views

Is a convolutional layer capable of converting, for example, a binary image into an RGBA image?

I am asking this question for a better understanding of the concept of channels in images. I am aware that a convolutional layer generates feature maps from a given image. We can adjust the size of ...
hanugm's user avatar
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2 votes
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Is there any animation that illustrates the "fold" and "unfold" operations of convolutional layers?

There are fourteen convolution layers in PyTorch. Among them six are related to convolution, another six are related to transposed convolution. The remaining two are fold and unfold operations. The ...
hanugm's user avatar
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1 vote
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593 views

Is there any gain by lazy initialization of weights, biases and number of input channels for a convolution operation?

The basic layers for performing convolution operations 1,2,3 in PyTorch are ...
hanugm's user avatar
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2 votes
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What does 'input planes' mean in the phrase 'input signal/image composed of several input planes'?

PyTorch documentation provided the following descriptions to the Convolution layers ...
hanugm's user avatar
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What does 'channel' mean in the case of an 1D convolution?

While reading about 1D-convolutions in PyTorch, I encountered the concept of channels. ...
hanugm's user avatar
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2 votes
1 answer
81 views

How is the convolution operation connected to neural networks?

I've been reading up on the convolution operation and neural networks. I understand that the convolution operation is defined as: $$(f * g)(t)=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$ The ...
Dariyoush's user avatar
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6 votes
1 answer
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Are there any advantages of the local attention against convolutions?

Transformer architectures, based on the self-attention mechanism, have achieved outstanding performance in a variety of applications. The main advantage of this approach is that the given token can ...
spiridon_the_sun_rotator's user avatar
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0 answers
353 views

Has positional encoding been used in convolutional layers?

Positional encoding (PE) is an essential part of the self-attention layers in the transformer architectures since without adding it in some way (fixed of learnable) to the input embeddings model has ...
spiridon_the_sun_rotator's user avatar
2 votes
0 answers
43 views

How to implement a (3 + 2)-dimensional convolutional layer where the 2d space is "internal"?

I am trying to train a CNN to learn 5D (kind of) data. The data is structured as follows. It has three spatial dimensions [x, y, z], but it also has two "...
play's user avatar
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1 vote
1 answer
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Why the non-exploitation of edge labels in current graph convolutions "results in an overly homogeneous view of local graph neighborhoods"?

I am currently reading a paper called Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017, CPPR), and I cannot understand the following sentence: We identify that the ...
S.Rucinski's user avatar
1 vote
0 answers
721 views

Convolutional Layer Multichannel Backpropagation Implementation

I have been working on coding a CNN in python from scratch using numpy as a semester project and I think I have successfully implemented it up to backpropagation in the MaxPool Layers. However, my ...
Ahmed Mustafa's user avatar
1 vote
1 answer
7k views

What is the difference between same convolution and full convolution in terms of feature map size?

In valid convolution, the size of the output shrinks at each layer. So after some point of time additional layers cannot meaningfully performs convolution. For this reason, same convolution is ...
satya's user avatar
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3 votes
0 answers
49 views

Why might the convolution be inappropriate when the task involves incorporating information from very distant locations in the input?

When I am reading about convolutional neural networks, I have encountered the following sentence from the textbook(page 341) that says about the limitation of the usage of the convolution in CNNs. ...
satya's user avatar
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1 vote
1 answer
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What is meant by "real-valued argument" in this context of the convolution operation?

Consider the following statement from Deep Learning book (p. 327, chapter 9: Convolutional Networks) In its most general form, convolution is an operation on two functions of a real-valued argument. ...
hanugm's user avatar
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2 votes
1 answer
764 views

Is it a good idea to use different width and height of the kernel in a CNN?

I always see that the width and height of the kernel are the same. But is it a good idea to use different numbers? Recently I tried to use GoogLeNet (which expects images to be 224x224) on my images (...
user avatar
2 votes
1 answer
115 views

What do the variables in the cross-correlation formula mean?

I understand what cross-correlation does given a kernel and an input image, but the formula confuses me a little. Given here in Goodfellow's Deep Learning (page 329), I can't quite understand what $m$ ...
InvestingScientist's user avatar
3 votes
1 answer
220 views

What is the use of the regular convolutional layer in expansion path of U-Net?

I was going through the paper on U-Net. U-net consists of a contracting path followed by an expanding path. Both the paths use a regular convolutional layer. I understand the use of convolutional ...
Bhuwan Bhatt's user avatar
2 votes
0 answers
34 views

Do filters have as many layers as the depth of the input in CNNs? [duplicate]

Firstly as an example here is the architecture of YOLOv2 I am trying to understand the depth of an output of a convolutional layer. For example, the first convolutional layer has the shape 3x3x32. So ...
Reactionic's user avatar
4 votes
1 answer
584 views

Is there anything that ensures that convolutional filters don't end up the same?

I trained a simple model to recognize handwritten numbers from the mnist dataset. Here it is: ...
mark mark's user avatar
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1 vote
1 answer
585 views

Is average pooling equivalent to a strided convolution with a specific constant kernel?

It seems to me that average pooling can be replaced by a strided convolution with a constant kernel. For instance, a 3x3 pooling would be equivalent to a strided convolution (of stride $3$) with a $3 \...
1110101001's user avatar
0 votes
1 answer
375 views

In CNNs, why do we sum the filter derivatives w.r.t the loss function to get the final gradient?

In a Convolutional Neural Network, unlike the fully connected layers, the same filter is used multiple times on the input while convolving - so during backpropagation, we get multiple derivatives for ...
Manu Soman's user avatar
1 vote
0 answers
177 views

Is the 3d convolution associative given that it can be represented as matrix multiplication?

I'm trying to understand if a 3D convolution of the sort performed in a convolutional layer of a CNN is associative. Specifically, is the following true: $$ X \otimes(W \cdot Q)=(X \otimes W) \cdot Q, ...
HereItIs's user avatar
5 votes
1 answer
2k views

When should we use separable convolution?

I was reading the "Deep Learning with Python" by François Chollet. He mentioned separable convolution as following This is equivalent to separating the learning of spatial features and the ...
Enes's user avatar
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2 votes
1 answer
1k views

How to mathematically describe the convolution operation (with a Gaussian kernel)?

I have to build a model where I pre-process the data with a Gaussian kernel. The data are an $n\times n$ matrix (i.e one channel), but not an image, thus I can't refer to this matrix as an image and ...
Ruli's user avatar
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1 vote
0 answers
87 views

Is it possible to express attention as a Fourier convolution?

Convolutions can be expressed as a matrix-multiplication (see e.g. this post) and as an element-wise multiplication using the Fourier domain (https://en.wikipedia.org/wiki/Convolution_theorem). ...
ZeroMaxinumXZ's user avatar