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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31 views

Is my calculation of the partial derivative of the cost function with respect to a single weight in the first layer correct?

I'm trying to understand the chain rule of backpropagation. This is what I understood. Is it correct? $$ \frac{\partial E }{ \partial w} = \sum_{i} \frac{\partial E }{ \partial a_i^{(l)} } (\sum_{j} \...
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67 views

Why is the cross-entropy a cost function?

The question looks foolish, but I think cross-entropy is somewhat weird as a cost function. As a cost function for linear regression, the mean square error $ \sum_{i=1}^{n} (y_i - (ax_i+b)) ^2$ seems ...
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25 views

Deep Learning Architecture where outputs from two different inputs are used for error calculation

Is there a deep learning architecture where outputs of the same model with two different inputs are used for error calculation (backpropagation)? Workflow: Input1 -----> Model ------> Output1 ...
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54 views

How does backprop work through the random sampling layer in a variational autoencoder?

Implementations of variational autoencoders that I've looked at all include a sampling layer as the last layer of the encoder block. The encoder learns to generate a mean and standard deviation for ...
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61 views

Why "large set of training data" is needed in Neural Network AI training?

I often heard people saying, "large set of training data is needed for producing an accurate AI". But when I looked for articles explaining backpropagations online, it all seems like you ...
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How are partial derivatives calculated in a computational graph?

I am trying to understand how are partial derivatives calculated in a computational graph. I understand reasoning behind computational graphs and I am bold enough to say I understand how they work, at ...
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25 views

CNN: Difficulties understanding backward pass derivatives

I have really quite hard difficulties to understand what is actually going on in the backward pass of a CNN. I am currently focusing on these references: https://towardsdatascience.com/forward-and-...
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23 views

In mini-batch gradient descent, are the weights updated after each batch or after all the batches have gone through an epoch?

Say I have a mini-batch of size 32, and I have 10 such batches. Assuming I only run it for one epoch (just for the sake of understanding it), Will the weights be updated using the gradients of one ...
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40 views

How does backpropagation know which weights to change?

I'm currently working on constructing a neural network from scratch (in JavaScript). I'm in the middle of working on the backpropagation, but there's something I don't understand: how does the ...
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1answer
37 views

Does the ANN's training data include the proper output for every neuron?

I was designing an Artificial Neural Network a while back, but hit a bump when I got to the backpropagation. I was having trouble making the script choose whether to add or subtract from the weights, ...
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How Long Can BPTT Truncated?

I wanted to ask what is, in general, the maximum value (the order of magnitude) of the number of time steps I can back-propagate in the past using TBTT (Truncated Backpropagation Through Time) in an ...
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18 views

Discrepancy of backpropagation formula between Andrew Ngs ML Course and those derived by neuralnetworksanddeeplearning.com

I'm currently working through Week 5 of Andrew Ngs Machine Learning course on Coursera, which goes through the backprop algorithm for basic neural networks. Whilst trying to derive the formulae he ...
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20 views

RNN - Backpropagation through time - Gradient Calculation

I think I got it right after reading multiple resources but im still not 100%. Seems like everyone is calculating it different. Or they just shortcut explaining the calculation. (or my math skills ...
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1answer
69 views

Different ways to calculate backpropagation derivatives, any difference?

I'm studying error backpropagation in neural networks. I am interested in why we use only one path on the computational graph to get the value of the derivative for a weight? I ask the question ...
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1answer
25 views

Parallelize Backpropagation - How to synchronize the weights of each thread?

I implemented a parallel backpropagation algorithm that uses $n$ threads. Now every thread gets $\dfrac{1}{n}$ examples of the training data and updates its instance of the net with it. After every ...
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50 views

How does back propagation adjust the hidden layers' weights and biases?

I'm new to neural networks and trying to figure out its fundamentals but I cannot fully understand the back propagation algorithm. In back propagation, I understand we want to go backwards from the ...
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24 views

ReLU function converging to local optimum in one case and diverging in the other one

I implemented a simple neural network with 1 hidden layer. I used ReLU as activation function for the hidden layer and the output layer just uses the linear function. To check my implementation I ...
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1answer
78 views

How to create a neural network from a set of equations?

Say I have these equations: $$x_1 = x_2 + 2y_1 + b$$ $$x_2 = y_2 + c$$ $$y_1 = z + a$$ $$y_2 = y_3 + d$$ $$z = z_1 + e$$ $x_1$ depends on $x_2$ (depends on $y_2$ (depends on $y_3$)) and $y_1$ (depends ...
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48 views

Why doesn't anyone use reinforcement learning to find the best possible alternative to backpropagation?

To be clear, I'm very uninformed on the topic of alternative learning algorithms to backprop, all my knowledge comes from articles like these: lets-not-stop-at-backprop backprop-alternatives we-need-a-...
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76 views

What are the input and output gradients in PyTorch?

Suppose I want to train a neural network with $m-$length inputs of form $x = [x_1, x_2, x_3, \cdots, x_m]$ and $n-$length outputs of form $y = [y_1, y_2, y_3, \cdots, y_n]$. Let the number of ...
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18 views

when updating the bias matrix, do we get the total sum of dZ or the sum of the axis of dZ?

I'm currently studying how to implement a neural network from scratch to know how it works, I came across this article: https://www.samsonzhang.com/2020/11/24/understanding-the-math-behind-neural-...
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1answer
50 views

What does "differentiable architecture" mean?

I'm currently reading a paper that uses CNN's as a base approach to solving some image classification issues and I've found that they kept mentioning the term "Differentiable Architecture", ...
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1answer
69 views

Can some of the weights be fixed during the training of a neural network?

Is it possible to exclude specific layers from the optimization? For example, let's say I have an input layer, 2 hidden layers, and the output layer. I know there is a perfect solution for my problem ...
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47 views

Backpropagation not working as expected

I'm new to neural networks and I try to make a model that is guessing if a point is below or above relative to a function output. The idea is inspired from this video https://youtu.be/DGxIcDjPzac . ...
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20 views

Gradient of Scalar objective cannot be efficiently calculated?

Suppose we generate the vector output $y$ from model $h(x, \theta)$, with input $x$ and parameters $\theta$. Reverse mode differentiation says that we can calculate the gradient \begin{align*} \...
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21 views

Are there any good references that describe the equations of the forward pass of Graph Neural Networks?

I am trying to program Graph Neural Network from scratch. Can the community please suggest a good reference/s to read about the equations of the forward pass in Graph Neural Networks, especially in ...
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156 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 ...
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1answer
55 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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25 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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24 views

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
143 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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144 views

Why is the backpropagation algorithm used to train the multilayer perceptron?

I've read in the book Neural Network Design, by Martin Hagan et al. (chapter 11), that, to train the feed-forward neural network (aka multilayer perceptron), one uses the backpropagation algorithm. ...
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47 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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57 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
48 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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20 views

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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1answer
45 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
163 views

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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33 views

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
71 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 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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49 views

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
94 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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1answer
153 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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97 views

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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54 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
265 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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1answer
28 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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54 views

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
183 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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