Questions tagged [gradient-descent]

For questions surrounding gradient descent, a method for finding the optimum state of a parameterized function based on another function often called the loss or error function. It iteratively descends the loss surface to the minimum loss by adjusting parameters based on the product of the partial derivatives comprising the gradient and a learning rate.

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38 views

What is relation between gradient descent and regularization in deep learning?

Gradient descent is used to reduce the loss and regularization is used to fight over-fitting. Is there any relation between gradient descent and regularization, or both are independent of each other?...
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40 views

Different methods of calculating gradients of cost function(loss function)

We require to find the gradient of loss function(cost function) w.r.t to the weights to use optimization methods such as SGD or gradient descent. So far, I have come across two ways to compute the ...
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16 views

How are the weights retained for filters for a particular class in a CNN?

I am new to CNN. What I have learned so far about the filters is that when we are giving a training example to our model, our model updates the weights by gradient descent to minimize the loss ...
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1answer
19 views

What is the difference between batch and mini-batch gradient decent?

I am learning deep learning from Andrew Ng's tutorial Mini-batch Gradient Descent. Can anyone explain the similarities and dissimilarities between batch GD and mini-batch GD?
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25 views

Which activation functions can lead to the vanishing gradient problem?

From this video tutorial Vanishing Gradient Tutorial, the sigmoid function and the hyperbolic tangent can produce the vanishing gradient problem. What other activation functions can lead to the ...
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3answers
79 views

How to prove that gradient descent doesn't necessarily find the global optimum?

How can I prove that gradient descent doesn't necessarily find the global optimum? For example, consider the following function $$f(x_1, x_2, x_3, x_4) = (x_1 + 10x_2)^2 + 5x_2^3 + (x_2 + 2x_3)^4 + ...
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1answer
37 views

What is the purpose of argmax in the PPO algorithm?

I'm kinda new to machine learning and still not too solid on math and particularly calculus. I'm currently trying to implement PPO algorithm as described in the spiningUp website : This line is ...
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1answer
27 views

How do you perform a gradient based adversarial attack on an SVM based model?

I have an SVM currently and want to perform a gradient based attack on it similar to FGSM discussed in Explaining And Harnessing Adversarial Examples. I am struggling to actually calculate the ...
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1answer
104 views

Understanding the derivation of the first-order model-agnostic meta-learning

According to the authors of this paper, to improve the performance, they decided to drop backward pass and using a first-order approximation I found a blog which discussed how to derive the math ...
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How to store the gradients as array in Python? [migrated]

I want to store the final gradient vector of a model as a bumpy array. Is there an easy and intuitive way to do that using Tensorflow?
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1answer
22 views

Oscillating around the saddle point in gradient descent?

I was reading a blog post that talked about the problem of the saddle point in training. In the post, it says if the loss function is flatter in the direction of x (local minima here) compared to ...
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53 views

Why gradients are so small in deep learning?

The learning rate in my model is 0.00001 and the gradients of the model is within the distribution of [-0.0001, 0.0001]. Is it ...
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7 views

How to perform PGD on a pretrained CNN?

I have a pretrained CNN model using the keras library. I now need to perform a Projected Gradient Descent (PGD) to develop some adversarial examples. To do this, I will need to perform a gradient ...
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1answer
51 views

Is there a reason to choose regular momentum over Nesterov momentum for neural networks?

I've been reading about Nesterov momentum from here and it seems like a nice improvement over regular momentum with no extra cost whatsoever. However, is this really the case? Are there instances ...
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29 views

Is Gradient Descent algorithm a part of Calculus of Variations?

As in https://en.wikipedia.org/wiki/Calculus_of_variations The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and ...
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25 views

How would I go about performing a single step of gradient descent on this model?

I have a classification model that consists of a CNN followed by an SVM. I used the Keras library for the CNN portion and sklearn for the SVM portion. I am assuming I will have to fiddle with the ...
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3answers
159 views

What's the function that SGD takes to calculate the gradient?

I'm struggling to fully understand the stochastic gradient descent algorithm. I know that gradient descent allows you to find the local minimum of a function. What I don't know is what exactly that ...
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1answer
513 views

What is the formula for the momentum and Adam optimisers?

In the gradient descent algorithm, the formula to update the weight $w$, which has $g$ as the partial gradient of the loss function with respect to it, is: $$w\ -= r \times g$$ where $r$ is the ...
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50 views

How is the loss value calculated in order to compute the gradient?

The gradient descent step is the following \begin{align} \mathbf{W}_i = \mathbf{W}_{i-1} - \alpha * \nabla L(\mathbf{W}_{i-1}) \end{align} were $L(\mathbf{W}_{i-1})$ is the loss value, $\alpha$ the ...
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58 views

Is running more epochs really a direct cause of overfitting?

I've seen some comments in online articles/tutorials or Stack Overflow questions which suggest that increasing number of epochs can result in overfitting. But my intuition tells me that there should ...
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1answer
74 views

How many parameters are being optimised over in a simple CNN?

Okay so here's my CNN (simple example from a tutorial) along with some arithmetic to get the total number of free parameters. We've got a dataset of 28*28 grayscale image (MNIST). First layer is a ...
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23 views

How can I train a neural network to find the hyper-parameters with which the data was generated?

I have 10000 tuples of numbers (x1, x2, y) generated from the equation: y = np.cos(0.583 * x1) + np.exp(0.112 * x2). I want to ...
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1answer
84 views

Eligibility vector for softmax policy with policy gradients

There is this nice result for policy gradients that the gradient of some performance measure, $\nabla v_{\pi_{\theta}}(s_0)$ (here, in the episodic case for the starting state $s_0$ and policy $\pi$, ...
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1answer
36 views

How to reduce variance of the model loss during training?

I know that stochastic gradient descent always gives different results. What are the best practices to reduce this variance today? I tried to predict simple function with two different approaches and ...
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Can Grad CAM feature maps be used for Training?

I am trying to recreate the architecture of the following paper: https://arxiv.org/pdf/1807.03058.pdf Can someone help me in explaining how are the feature maps coming out of the output of GradCam ...
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Understanding the partial derivative with respect to the weight matrix and bias

Say we have the layer $X W + b = Y$. I want to get $\frac{dL}{dW}$ and we assume I have $\frac{dL}{dY}$. So all I need is to find $\frac{dY}{dW}$. I know that it should be $X^T\frac{dL}{dY}$ but don'...
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1answer
37 views

How to plot Loss Landscape with more than 2 weights in the network

For a single neuron with 2 weights, I can plot the loss landscape and it looks like this (OR data, sigmoid activation, MAE loss): But, when the neuron accepts more inputs, which means more than 2 ...
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2answers
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Is the gradient at a layer independent of the activations of the previous layers?

Is the gradient at a layer (of a feed-forward neural network) independent of the activations of the previous layers? I read this in a paper titled Mean Field Residual Networks: On the Edge of Chaos (...
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1answer
29 views

Backpropagation: Chain Rule to the Third Last Layer

I'm trying to solve dLoss/dW1. The network is as in picture below with identity activation at all neurons: Solving dLoss/dW7 is simple as there's only 1 way to output: $Delta = Out-Y$ $Loss = abs(...
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25 views

How to calculate multiobjective optimization cost for ordinary problems?

What I did: Created a population of 2D legged robots in a simulated environment. Found the best motor rotation values to make the robots move rightward, using an objective function with Differential ...
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1answer
44 views

Why is batch gradient descent performing worse than stochastic and minibatch gradient descent?

I have implemented a neural network from scratch (only using numpy) and I am having problems understanding why the results are so different between stochastic/minibatch gradient descent and batch ...
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1answer
60 views

Network doesn't converge with ReLU or Leaky ReLU, but works well with sigmoid/tanh

I have these training data to separate, the classes are rather randomly scattered: My first attempt was using tf.nn.relu activation function, but output was stuck ...
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1answer
155 views

Online Learning for Neural Networks

There seems to be a lot of literature and research on the problems of stochastic gradient descent and catastrophic forgetting, but I can't find much on solutions to perform online learning with neural ...
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1answer
117 views

An intuitive explanation of Adagrad, its purpose and its formula

It (Adagrad) adapts the learning rate to the parameters, performing smaller updates (i.e. low learning rates) for parameters associated with frequently occurring features, and larger updates (i.e. ...
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0answers
55 views

Does Retina-net's focal loss accomplish its goal?

Taking out the weighting factor we can define focal loss as $$FL(p) = -(1-p)^\gamma log(p) $$ Where $p$ is the target probability. The idea being that single stage object detectors have a huge ...
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1answer
41 views

Is it possible with stochastic gradient descent for the error to increase?

As simple as that. Is there any scenario where the error might increase, if only by a tiny amount, when using SGD (no momentum)?
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2answers
253 views

Can neuroevolution be combined with gradient descent?

Is there any precedent for using a neuroevolution algorithm, like NEAT, as a way of getting to an initialization of weights for a network that can then be fine-tuned with gradient descent and back-...
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1answer
42 views

In NN, as iterations of Gradient descent increases, the accuracy of Test/CV set decreases. how can i resolve this?

As mentioned in the title I'm using 300 Dataset example with 500 feature as an input. As I'm training the dataset, I found something peculiar. Please look at the data shown below. Iteration 5000 |...
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1answer
125 views

Sensitivity of neural network to inputs

I am trying to build intution regarding neural networks and their working and this is a question, I am interested in: I understand that we normalise inputs. The reason this is done is to capture the ...
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0answers
53 views

Neural networks when gradient descent is not possible

I am looking for an example in which it is simply impossible to use some sort of gradient descent to train a neural network. Is this available? I have read quite some papers about gradient-free ...
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1answer
79 views

How does NEAT find the most successful generation without gradients?

I'm new to NEAT, so, please, don't be too harsh. How does NEAT find the most successful generation without gradient descent or gradients?
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3answers
194 views

Which function $(\hat{y} - y)^2$ or $(y - \hat{y})^2$ should I use to compute the gradient?

The MSE can be defined as $(\hat{y} - y)^2$, which should be equal to $(y - \hat{y})^2$, but I think their derivative is different, so I am confused of what derivative will I use for computing my ...
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0answers
69 views

What is the right formula for weight update rule in Logistic Regression using stochastic gradient descent

Apologies for the lengthy title. My question is about the weight update rule for logistic regression using stochastic gradient descent. I have just started experimenting on Logistic Regression. I ...
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2answers
396 views

How is local minima possible in gradient descent?

Gradient descent works on the equation of mean squared error, which is an equation of a parabola $y=x^2$. We often say that weight adjustment in a neural network by gradient descent algorithm can hit ...
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1answer
57 views

How can we reach global optimum?

Gradient descent can get stuck into local optimum. Which techniques are there to reach global optimum?
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1answer
126 views

When is bias values updated in back propagation?

I am new to deep learning. I have doubts on modifying bias values during back propagation. My doubts are Does the back propagation algorithm modifies the weigh values and bias values in the same pass?...
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1answer
289 views

Is back propagation applied for each data point or for a batch of data points?

I am new to deep learning and trying to understand the concept of back propagation. I have a doubt on when the back propagation is applied. Assume that I have a training data set of 1000 images for ...
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2answers
107 views

Are on-line backpropagation iterations perpendicular to the constraint?

Raul Rojas' Neural Networks A Systematic Introduction, section 8.1.2 relates off-line backpropagation and on-line backpropagation with Gauss-Jacobi and Gauss-Seidel methods for finding the ...
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1answer
42 views

Which local minima to choose according to the shape of the error surface?

The following plot shows error function output based on system weights. Two equal local minima are shown in green pointers. Note that the red dots are not related to the question. Considering the ...
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2answers
61 views

Could error surface shape be useful to detect which local minima is better for generalization?

The following plot shows error function output based on system weights. Two equal local minima are shown in green pointers. Note that the red dots are not related to the question. Does the right one ...