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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24 views

During Backpropagation in LSTM, why is the previous output $h_{t-1}$ considered constant w.r.t any $W$ while computing derivative?

I've just started learning LSTM, and some points in the process of calculating the gradients are getting me confused. Say, for example, we want to compute $\frac{\partial}{\partial W_i}L$, where $L$ ...
34 views

Backpropagation implementation not applicable for other cases

I saw this implementation of backpropagation in MATLAB, where the loss function used is MSE, and the last layer's activation function was sigmoid. I denoted the portions of the formula for what I ...
30 views

How do gradients are flown back into the Siamese network when branching is done?

I am curious about the working of a Siamese network. So, let us suppose I am using a triplet loss for my network and I have instantiated single CNN 3 times and there are 3 inputs to the network. So, ...
14 views

Explanation of the partial derivatives in back-propogation algorithm

I understand that this is the method for conducting back-propogation: With a three layer network (input layer, one hidden layer, one output layer); start with input $I_i$ as an exemplar input. ...
20 views

For the generalised delta rule in back-propogation, do you subtract the target from the obtained output, or vice versa?

When I look up the generalised delta rule equation for back-propogation, I am seeing two conflicting equations. For example, here (slide 20), given $o$ (the output, defined in slide 18), $z$ (the ...
86 views

Why is the derivative of the softmax layer shaped differently than the derivative of other neurons?

If the derivative is supposed to give the rate of change of a function at that point, then why is the derivative of the softmax layer (a vector) the Jacobian matrix, which has a different shape than ...
39 views

Backpropogation rule for the output layer of a multi-layer network - What does the rule do in ambiguous cases?

This is the back-propogation rule for the output layer of a multi-layer network: $$W_{jk} := W_{jk} - C \dfrac{\delta E}{\delta W_{jk}}$$ What does this rule do in the more ambiguous cases such as: (1)...
13 views

How to update the error on hidden nodes using back-propogation, given the error on the output nodes and weights

I'm trying to solve question 30 of this paper. The short version of the question is if someone could show me how to do this, I would appreciate it (the answer should be A; -0.0660). The long version ...
117 views

What is asymmetric relaxation backpropagation?

In Chapter 8, section 8.5.2, Raul Rojas describes how the weights for a layer of a neural network can be calculated using a pseudoinverse of the sigmoid function in the nodes, he explains this is an ...
32 views

How do I infer exploding or vanishing gradients in Keras?

It may already be obvious that I am just a practitioner and just a beginner to Deep Learning. I am still figuring out lots of "WHY"s and "HOW"s of DL. So, for example, if I train a ...
207 views

Why is second-order backpropagation useful?

Raul Rojas's book on Neural Networks dedicates section 8.4.3 to explaining how to do second-order backpropagation, that is, computing the Hessian of the error function with respect to two weights at a ...
71 views

Why should the weight updates be proportional to input?

I'm reading the book Grokking Deep Learning. Regarding weight updates during training, it has the following code and explanation: ...
74 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 ...
44 views

260 views

What, exactly, does the REINFORCE update equation mean?

I understand that this is the update for the parameters of a policy in REINFORCE: $$\Delta \theta_{t}=\alpha \nabla_{\theta} \log \pi_{\theta}\left(a_{t} \mid s_{t}\right) v_{t}$$ Where 𝑣𝑡 is ...
65 views

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 ...
50 views

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 ...
41 views

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 ...
33 views

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 ...
99 views

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-...
44 views

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, ...
137 views

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 ...
543 views

What should I do with the flatten layer during back-propagation? [duplicate]

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 ...
69 views

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 ...
61 views

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 ...
46 views

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 ...
166 views

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: ...
240 views

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 ...
225 views

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. ...
92 views

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 ...
27 views

Class of functional equations that backpropagation can solve

There is a theorem that states that basically a neural network can approximate any function whatsoever. However, this does not mean that it can solve any equation. I have some notes where it states ...
55 views

Does net with ReLU not learn when output < 0?

The derivative of ReLU is 0 if its output is lower than 0 - $d ReLU(x)/dReLU$ is $0$ if $x < 0$. Let's denote some net's output by $Out$, so if this net's last layer is ReLU then we get that \$dOut/...
47 views

Why are all weights of a neural net updated and not just the weights of the first layer

Why are all weights of a neural net updated and not only the weights of the first hidden layer? The error-influence of the prediction by the weights of a neural net is calculated using the chain rule....
867 views

What exactly is averaged when doing batch gradient descent?

I have a question about how the averaging works when doing mini-batch gradient descent. I think I now understood the general gradient descent algorithm, but only for online learning. When doing mini-...
282 views

Why do we update all layers simultaneously while training a neural network?

Very deep models involve the composition of several functions or layers. The gradient tells how to update each parameter, under the assumption that the other layers do not change. In practice, we ...
180 views

What is symbol-to-number differentiation?

I recently came across symbol-to-symbol and symbol-to-number differentiation, out of which symbol to symbol seemed fairly straightforward - the computational graph is extended to include gradient ...
150 views

How to perform back propagation with different sized layers?

I'm developing my first neural network, using the well known MNIST database of handwritten digit. I want the NN to be able to classify a number from 0 to 9 given an image. My neural network consists ...
289 views

Why is it called back-propagation?

While looking at the mathematics of the back-propagation algorithm for a multi-layer perceptron, I noticed that in order to find the partial derivative of the cost function with respect to a weight (...