# Questions tagged [backpropagation]

For questions about the back-propagation (aka "backprop", and often abbreviated as "BP") algorithm, which is used to compute the gradient of the objective function (e.g. the mean squared error) with respect to the parameters (or weights) of the neural network, when trained with gradient descent.

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### XOR problem with bipolar representation

I am taking a course in Machine Learning and the Professor introduced us to the XOR problem. I understand the XOR problem is not linearly separable and we need to employ Neural Network for this ...
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### How is the error calculated with multiple output neurons in the neural network?

Machine Learning books generally explains that the error calculated for a given sample $i$ is: $e_i = y_i - \hat{y_i}$ Where $\hat{y}$ is the target output and $y$ is the actual output given by the ...
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### How to properly build a neural net of a physics simulation [closed]

I have a rocket simulation that produces 4 inputs and 4 outputs. My plan is to run 5000 simulation runs and disperse the 4 inputs then write the 4 outputs to a CSV file. I will then use TensorFlow and ...
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### In LSTMs, how does the additive property enables better balancing of gradient values during backpropagation?

There are two sources that I'm using to to try and understand why LSTMs reduce the likelihood of the vanishing gradient problem associated with RNNs. Both of these sources mention the reason LSTMs are ...
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### Linear output layer back propagation

So I'm stack to something that it's probably very easy but I can't get my head around it. I'm building a Neural Network that will consist of many layers with non-linear activation functions (probably ...
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### Computation of initial adjoint for NODE

I'm reading the paper Neural Ordinary Differential Equations and I have a simple question about adjoint method. When we train NODE, it uses a blackbox ODESolver to compute gradients through model ...
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### How does back-propagation through time work for optimizing the weights of a bi-directional RNN?

I am aware that back-propagation through time is used for training the recurrent neural network. But I am not able to understand how this happens for the bi-directional versions of the recurrent ...
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### What is the time complexity for training a gated recurrent unit (GRU) neural network using back-propagation through time?

Let us assume we have a GRU network containing $H$ layers to process a training dataset with $K$ tuples, $I$ features, and $H_i$ nodes in each layer. I have a pretty basic idea how the complexity of ...
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### How are weight matrices in attention trained?

I have been looking into transformers lately and been reading tons of tutorials. All of them address the intuition behind attention, which I understand, but they treat training the weight matrices for ...
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I am trying to comprehend how the Gradient Descent works. I understand we have a cost function which is defined in terms of the following parameters, $J(𝑤_{1},𝑤_{2},.... , w_{n}, b)$ the derivative ...
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### Back propagation approach to logistic regression: why is cost diverging but accuracy increasing?

Background I have tried to fit a logistic regression model - written using a forward / back propagation approach (as part of Andrew Ng's deep learning course) - to a very non-linear data set (see ...
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### What are the rules behind vector product in gradient?

Let's suppose we have calculated the gradient and it came out to be $f(WX)(1-f(W X))X$, where $f()$ is the sigmoid function, $W$ of order $2\times2$ is the weight matrix, and $X$ is an input vector of ...
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### How to normalise image input to backpropogation algorithm?

I am implementing a simple backpropagation neural network for classifying images. One set of images are cars another set of images are buildings (houses). So far I have used Sobel Edge detector after ...
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### Can the normal equation be used to optimise the RNN's weights?

I have made an RNN from scratch in Tensorflow.js. In order to update my weights (without needing to calculate the derivatives), I thought of using the normal equation to find the optimal values for my ...
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### Doing backpropagation in an Tensorflow.js Neural Network

I have a neural network (which I am making from scratch). In order to make the neural network "learn" I need to conduct back-propagation. Using the code at the below how would I conduct back-...
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### Would a different learning rate for every neuron and layer mitigate or solve the vanishing gradient problem?

I'm interested in using the sigmoid (or tanh) activation function instead of RELU. I'm aware of RELU advantages on faster computation and no vanishing gradient problem. But about vanishing gradient, ...
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### How to find the derivative of a dynamic neuron model, which depends on previous states of the neuron?

This is the equation where n denotes the current state, (n-1) denotes the state in the previous step etc. And to do back-propagation I need to find partial derivatives over each of the variables. For ...
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### Finding the energy function given update rule of a single layer non-linear neural network

Consider the network with N neurons, each of which takes a $2 \times k$ input specified by the tuple $(\vec c_t, \vec \theta_t)$ to produce output $\vec{R}_t$ through an update rule on the pairwise ...
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### Why does a neuron in a multi-layer network need several input connections?

For example, if I have the following architecture: Each neuron in the hidden layer has a connection from each one in the input layer. 3 x 1 Input Matrix and a 4 x 3 weight matrix (for the ...
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### Backpropagation implementation with Java

I've been trying to implement a Multilayer Perceptron Network using java language with the ultimate goal of creating and teaching a neural network to recognize handwritten digits. Pretty simple and ...
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### What should I do with the flatten layer during back-propagation?

I'm creating a CNN network without other frameworks such as PyTorch, Keras, Tensorflow, and so on. During the forward pass, the Flatten layer reshapes the previous ...
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### Is my understanding of back-propogation correct?

I am trying to learn backpropagation and this is what I know so far. To update the weights of the neural network you have to figure out the partial derivative of each of the parameters on the loss ...
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### Why is it that having a duplicate in features set makes training to work bad

I'm defining a deep network to emulate a multitarget regression. When I costruct my training set, I take information from a graph; without going into too much detail, it could happen that I take 2 ...
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### I need help understanding general back propagation algorithm

In section 6.5.6 of the book Deep Learning by Ian et. al. general backpropagation algorithm is described as: The back-propagation algorithm is very simple. To compute the gradient of some scalar z ...
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### How does backpropagation work in LSTMs?

After reading a lot of articles (for instance, this one Understanding LSTM Networks), I know that the long short-term memory (LSTM) is an artificial recurrent neural network (RNN) architecture used in ...
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### How do I calculate the partial derivative with respect to $x$?

I am trying to implement CNN using python Numpy. I searched so much, but all I found was for one filter with one channel for Convolution. Suppose we have an X as Image with this shape: ...
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### Backward pass of CNN like Resnet: how to manually compute flops during backprop?

I've been trying to figure out how to compute the number of Flops in backward pass of ResNet. For forward pass, it seems straightforward: apply the conv filters to the input for each layer. But how ...
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### Backpropagation of neural nets with shared weight

I am trying to understand the mathematics behind the forward and backward propagation of neural nets. To make myself more comfortable, I am testing myself with an arbitrarily chosen neural network. ...
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### Why do code implementations average the loss over a batch instead of finding the expected sample of that batch (using sampling probabilities)

Usually, our training objective over a batch is written in terms of the expected value of a sample in that batch such as $objective = E_{x \sim data} * log(P(x))$ But in the code implementations, ...
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### Should I compute the gradients with respect to the flatten layer in a convolutional neural network?

I'm trying to create a convolutional neural network without frameworks (such as PyTorch, TensorFlow, Keras, and so on) with Python. Here's a description of CNN taken from the Wikipedia article In ...