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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33 views

What is the correct formula for updating the weights in a 1-single hidden layer neural network?

I'm creating a neural network with 3 layers and no bias. On internet I saw that the expression for the derivative of the weights between the hidden layer and the output layer was: $$\Delta W_{j,k} = (...
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20 views

Backpropagation - what does rate of change calculated from the partial derivatives actually relate to?

I understand conceptually how backpropagation works according to the chain rule, and I understand that partial derivatives calculate the rate of change of a function containing multiple variables with ...
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Do $V_\theta$ and $V_s$ represent partial or total derivatives in the paper “Learning Continuous Control Policies by Stochastic Value Gradients”?

I was reading up on the Stochastic Value Gradients paper by Heess et al. In the paper, they describe a recursive process to calculate path-wise derivatives via equations (3) and (4), at the bottom of ...
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1answer
87 views

Is the bias also a “weight” in a neural network?

I'm learning about how neural networks are trained. I understand how a neuron works, backpropagation, and all that. In neurons, there is a clear distinction between a "weight" and a "...
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1answer
103 views

Why is the Backpropagation algorithm used to train the Multilayer Perceptron?

I've read on the book NND by Martin Hagan et al (chapter 11), that to train the feed-forward neural network: Multilayer Perceptron one uses the Backpropagation algorithm. Why this algorithm? Could ...
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27 views

Double DQN backpropagation of negative final rewards?

My problem is that in my Double DQN model, negative final rewards are not being backpropagated into action Q-values, and so some Q-values are positive, when they should be negative, and hence ...
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29 views

Backpropagation in REINFORCE algorithms with Categorical / Multinomial Distribution

From a paper by Williams, I know in general how to backpropagate log-probabilities of chosen actions when applying the REINFORCE weight update rule. However, I was wondering about a case not being ...
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1answer
42 views

How to improve a trained model over time (i.e. with more predictions)?

I built a model using the tutorial on the TensorFlow site. It was a simple image classification neural network. I trained it and saved the model and weights together on a ...
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In a convolutional neural network, how is the error delta propagated between convolutional layers?

I'm coding some stuff for CNNs, just relying on numpy (and scipy just for the convolution operation for pure performance reasons). I've coded a small network consisting of a convolutional layer with ...
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43 views

Are there relatively new research papers that describe how to make back-propagation more efficient?

I read Yann LeCun's paper Efficient BackProp, which was published in 2000. I looked for similar but more recent papers on Arxiv, but I have not yet found any. Are there relatively new research papers ...
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1answer
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Why is it a problem if the outputs of an activation function are not zero-centered?

In this lecture, the professor says that one problem with the sigmoid function is that its outputs aren't zero-centered. Are the explanation provided by the professor regarding why this is bad is that ...
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Is vectorizing backpropagation feasible?

Does it make sense to have the backpropagation of a neural network layer happen all at once if the learning rate is lowered? This would mean the new weights of that layer would be independent of each ...
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1answer
68 views

In gradient descent's update rule, why do we use $\sigma(z^{l-1})\frac{\delta C_0}{ \delta w^{l}}$ instead of $\frac{\delta C_0}{\delta w^{l}}$?

I am trying to code a two layered neural network simple NN as I have described here https://itisexplained.com/html/NN/ml/5_codingneuralnetwork/ I am getting stuck on the last step of updating the ...
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How can I model any structure for a neural network?

Hello I am currently doing research on the effect of altering a neural network's structure. Particularly I am investigating what affect would putting a random DAG (directed acyclic graph) in the ...
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How to update all the weights in case only one data out of n signals is observable

If we have cost function as $$E_i = (D_i -Y_i)^T Q (D_i -Y_i)$$, where $$Q=\begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}$$( in case only one data signal can ...
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Why is the error curve of a neural network trained with MSE to output $\frac{3 I_1 + 5 I_2}{2}$ given inputs $I_1$ and $I_2$ oscillating weirdly?

I just "finished" my first AI program. I programmed in Excel VBA, and I think it works well. I was checking every formula and the whole algorithm several times to make sure every formula is ...
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1answer
60 views

What are examples of good free books that cover the back-propagation algorithm?

What are examples of good free books that cover the back-propagation used to train multilayer perceptrons? I've just started to learn about artificial neural networks, so I'm looking for books that ...
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132 views

Why did the developement of neural networks stop between 50s and 80s?

In a video lecture on the development of neural networks and the history of deep learning (you can start from minute 13), the lecturer (Yann LeCunn) said that the development of neural networks ...
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Bias gradient of layer before batch normalization always zero

From the original paper and this post we have that batch normalization backpropagation can be formulated as I'm interested in the derivative of the previous layer outputs $x_i=\sigma(w X_i+b)$ with ...
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48 views

Why is Openai's PPO2 implementation differentiable?

I'm trying to understand the concept behind the implementation of the OpenAI PPO2 algorithm. The loss function that is minimized is as follows: ...
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2answers
70 views

Why is tf.abs non-differentiable in Tensorflow?

I understand why tf.abs is non-differentiable in principle (discontinuity at 0) but the same applies to tf.nn.relu yet, in case of this function gradient is simply set to 0 at 0. Why the same logic is ...
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Are all activation functions in a layer same? [duplicate]

I understand that for you can have multiple activation functions in different layers. CNN's usually have Relu followed by softmax for the classification. But what stops us in having multiple ...
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1answer
23 views

Why are the weights of the previous layers updated only considering the old values of the weights of the later layer, not the updated values?

Why are the weights of a neural net updated only considering the old values of the later layer, not the already updated values? I use this example to explain my problem. When applying the ...
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Why does sigmoid saturation prevent signal flow through the neuron?

As per these slides on page 35: Sigmoids saturate and kill gradients. when the neuron's activation saturates at either tail of 0 or 1, the gradient at these regions is almost zero. the gradient and ...
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1answer
68 views

How to compute the gradient of the cross-entropy loss function with respect to the parameters with softmax activation function?

I've seen plenty of examples of people doing Sigmoid + MSE backpropagation implementations, yet I do not seem to understand how to implement backpropagation as stated in the title in the case of multi-...
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Neural Network trains towards 1 despite target

So I'm trying to make my first neural network and have just finished my back propagation functions. I got the algebra from brilliant and thought I'd understood it, but my bug proves otherwise. The bug ...
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23 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 $L$ ...
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30 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 ...
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27 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, ...
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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. ...
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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 ...
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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 ...
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1answer
37 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)...
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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 ...
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1answer
98 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 ...
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24 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 ...
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1answer
108 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 ...
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64 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: ...
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1answer
53 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 ...
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42 views

How am I supposed to code equation 4.57 from the book “Machine Learning: An Algorithmic Perspective”?

Consider the equation 4.57 (p. 108) from section 4.6 of the Book Machine Learning: An Algorithmic Perspective, where the derivative of the softmax function is explained $$\delta_o(\kappa) = (y_\kappa -...
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29 views

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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2answers
78 views

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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28 views

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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31 views

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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1answer
68 views

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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1answer
130 views

How does back-propagation through time work for optimizing the weights of a bidirectional 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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83 views

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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58 views

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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1answer
54 views

How parameter adjustment works in Gradient Descent?

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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1answer
29 views

How much can an inclusion of the number of iterations have on the training of an MLP?

My doubt is like this : Suppose we have an MLP. In an MLP, as per the backprop algorithm (back-propagation algorithm), the correction applied to each weight is : $$ w_{ij} := -\eta\frac{\partial E}{\...

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