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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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2
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1answer
142 views

How long should the state-dependent baseline for policy gradient methods be trained at each iteration?

How long should the state-dependent baseline be trained at each iteration? Or what baseline loss should we target at each iteration for use with policy gradient methods? I'm using this equation to ...
3
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2answers
826 views

Why use semi-gradient instead of full gradient in RL problems, when using function approximation?

Semi-gradient methods work well in reinforcement learning, but what is there a reason of not using the true gradient if it can be computed? I tried it on the cart pole problem with a deep Q-network ...
0
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1answer
46 views

RMSprop equation - dividing by a matrix?

I've been trying to understand RMSprop for a long time, but there's something that keeps eluding me. $dW$ and $db$ are matrices (that's what I understand from the element-wise comment), so that must ...
5
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1answer
232 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. ...
6
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1answer
108 views

During neural network training, can gradients leak sensitive information in case training data fed is encrypted (homomorphic)?

Some algorithms in the literature allow recovering the input data used to train a neural network. This is done using the gradients (updates) of weights, such as in Deep Leakage from Gradients (2019) ...
3
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2answers
2k views

How to perform gradient checking in a neural network with batch normalization?

I have implemented a neural network (NN) using python and numpy only for learning purposes. I have already coded learning rate, momentum, and L1/L2 regularization and checked the implementation with ...
0
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1answer
65 views

Why is loss displayed as a parabola in mean squared error with gradient descent?

I'm looking at the loss function: mean squared error with gradient descent in machine learning. I'm building a single-neuron network (perceptron) that outputs a linear number. For example: Input * ...
3
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2answers
141 views

How to obtain a formula for loss, when given an iterative update rule in gradient descent?

From the reinforcement learning book section 13.3: Using pytorch, I need to calculate a loss, and then the gradient is calculated internally. How to obtain the loss from equations which are stated ...
-1
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1answer
30 views

How can the gradient of the weight be calculated in the viewpoint of matrix calculus?

Let $\sigma(x)$ be sigmoid function. Consider the case where $\text{out}=\sigma(\vec{x} \times W + \vec{b})$, and we want to compute $\frac{\partial{\text{out}}}{\partial{w} }.$ Set the dimension as ...
1
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0answers
31 views

Could the inputs of the mean squared-error loss function be transformed to allow larger learning rates?

In the context of a neural network $\hat{y} = f_\theta(\mathbf{x})$ with parameters $\theta$ that is trained to perform regression such that the prediction $\hat{\mathbf{y}} = [\hat{y}_1,\hat{y}_2,...,...
5
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3answers
205 views

Does gradient descent in deep learning assume a smooth fitness landscape?

I've come across the concept of fitness landscape before and, in my understanding, a smooth fitness landscape is one where the algorithm can converge on the global optimum through incremental ...
0
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1answer
125 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 ...
3
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1answer
133 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 ...
1
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0answers
34 views

Optimizer that prevents parameters from oscillating

When we perform gradient descent, especially in an online setting where the training data is presented in a non-random order, a particular 1-dimensional parameter (such as an edge weight) may first ...
2
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1answer
258 views

What is the impact of scaling the KL divergence and reconstruction loss in the VAE objective function?

Variational autoencoders have two components in their loss function. The first component is the reconstruction loss, which for image data, is the pixel-wise difference between the input image and ...
1
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2answers
157 views

Why the cost/loss starts to increase for some iterations during the training phase?

I am trying to build a recurrent neural network from scratch. It's a very simple model. I am trying to train it to predict two words (dogs and gods). While training, the value of cost function starts ...
0
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0answers
17 views

What is the effect and behavior of using mixed weight instead of normal weight matrix?

Suppose I try to find appropriate matrix A in differential equation $\dot{X}=A X$ using RNN. Current state is $X=\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$, and desired trajectory state is $X_d=\...
0
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0answers
24 views

Do Gradient Descent and Natural Gradient solve the same problem?

I am troubled by natural gradient methods. If we have a function f(x) we wish to minimize, gradient descent minimizes f(x) of course, but what does the natural gradient do? I found on https://...
1
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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 ...
1
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0answers
24 views

How to deal with losses on different scales in multi-task learning?

Say I'm training a model for multiple tasks by trying to minimize sum of losses $L_1 + L_2$ via gradient descent. If these losses are on a different scale, the one whose range is greater will dominate ...
2
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0answers
26 views

What is the name of this algorithm that estimates the gradient with an average by sampling from a distribution?

Consider maximizing the function $R(w)$ with parameter $w$ using gradient ascent. However, we don't know the gradient $\nabla_wR(w)$ formula. Now suppose $w$ is sampled from a probability distribution ...
4
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2answers
450 views

What is the advantage of using cross entropy loss & softmax?

I am trying to do the standard MNIST dataset image recognition test with a standard feed forward NN, but my network failed pretty badly. Now I have debugged it quite a lot and found & fixed some ...
2
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1answer
66 views

Is batch learning with gradient descent equivalent to “rehearsal” in incremental learning?

I am learning about incremental learning and read that rehearsal learning is retraining with old data. In essence, isn't this the exact same thing as batch learning (with stochastic gradient descent)? ...
2
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0answers
74 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 ...
7
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2answers
325 views

Is there an ideal range of learning rate which always gives a good result almost in all problems?

I once read somewhere that there is a range of learning rate within which learning is optimal in almost all the cases, but I can't find any literature about it. All I could get is the following graph ...
2
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0answers
33 views

Should I use batch gradient descent when I have a small sample size?

I have a dataset with an input size of 155x155, with the output being 155 x 1 with a 3-4 layer neural net being used for regression. With such a small sample size, should I use full batch gradient ...
8
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2answers
169 views

Why is the perceptron criterion function differentiable?

I'm reading chapter one of the book called Neural Networks and Deep Learning from Aggarwal. In section 1.2.1.1 of the book, I'm learning about the perceptron. One thing that book says is, if we use ...
4
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0answers
57 views

Why are most commonly used activation functions continuous?

I have come to notice that the most commonly used activation functions are continuous. Is there any specific reason behind this? Results such as this paper have worked on training networks with ...
2
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0answers
23 views

Is it possible to ensure the convergence when training a RNN weight on its SVD decomposition?

I'm reading the following paper in which the author seems to do 2 things interesting: The hidden-to-hidden weight matrix of the RNN is SVD decomposed and train separately. Each orthogonal part of the ...
5
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1answer
137 views

Why evolutionary training of neural networks is not popular?

Evolutionary algorithms are mentioned in some sources as a method to train a neural network (finding weights, not hyperparameters). However, I have not heard about one practical application of such an ...
4
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1answer
1k views

How is the gradient of the loss function in DQN derived?

In the original DQN paper, page 1, the loss function of the DQN is $$ L_{i}(\theta_{i}) = \mathbb{E}_{(s,a,r,s') \sim U(D)} [(r+\gamma \max_{a'} Q(s',a',\theta_{i}^{-}) - Q(s,a;\theta_{i}))^2] $$ ...
1
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1answer
292 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 ...
0
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0answers
32 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 ...
0
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1answer
43 views

What is the derivative of a specific output with respect to a specific weight?

If I have a neural network, and say the 6th output node of the neural network is: $$x_6 = w_{16}y_1 + w_{26}y_2 + w_{36}y_3$$ What does that make the derivative of: $$\frac{\partial x_6}{\partial w_{...
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0answers
27 views

How to derive compact convex set K and its diameter D to program Accelegrad algorithm in practice?

Given the original paper (https://arxiv.org/pdf/1809.02864.pdf), I would like to implement the Accelegrad algorithm for which I report the pseudocode of the paper: In the pseudocode, the authors ...
0
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1answer
75 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 ...
2
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2answers
80 views

Is there anything that ensures that convolutional filters end up different from one another?

I found this question very interesting, and this is a follow up on it. Presumably, we'd want all the filters to converge towards some complementary set, where each filter fills as large a niche as ...
0
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1answer
39 views

Loss randomly changing, incorrect output (even for low loss) when trying to overfit on a single set of input and output

I am trying to make a neural network framework from scratch in C++ just for fun, and to test my backpropagation, I thought it would be an easy way to test the functionality if I give it one input - a ...
1
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0answers
64 views

Why do momentum techniques not work well for RNNs?

AFAIK, momentum is quite useful when training CNNs, and can speed-up the training substantially without any drop in validation accuracy. I've recently learned that it is not as helpful for RNNs, where ...
3
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2answers
120 views

Are filters fixed or learned?

No matter what I google or what paper I read, I can't find an answer to my question. In a deep convolutional neural network, let's say AlexNet (Krizhevsky, 2012), filters' weights are learned by means ...
1
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0answers
135 views

What is the gradient of an attention unit?

The paper Attention Is All You Need describes the Transformer architecture, which describes attention as a function of the queries $Q = x W^Q$, keys $K = x W^K$, and values $V = x W^V$: $\text{...
4
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1answer
395 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 $\pi$, ...
10
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2answers
901 views

Is neural networks training done one-by-one? [duplicate]

I'm trying to learn neural networks by watching this series of videos and implementing a simple neural network in Python. Here's one of the things I'm wondering about: I'm training the neural network ...
4
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1answer
1k 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 about when the back-propagation is applied. Assume that I have a training data set of 1000 images ...
4
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2answers
492 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-...
3
votes
1answer
72 views

Why is the learning rate generally beneath 1?

In all examples I've ever seen, the learning rate of an optimisation method is always less than $1$. However, I've never found an explanation as to why this is. In addition to that, there are some ...
2
votes
2answers
216 views

What is the gradient of the objective function in the Soft Actor-Critic paper?

In the paper Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor, they define the loss function for the policy network as $$ J_\pi(\phi)=\mathbb E_{s_t\...
1
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0answers
35 views

How to use unmodified input in neural network?

My question may be a bit hard to explain... My neural network learns a categorical distribution, which serves as an index. This index will look up the value (= action_mean) in Input 2. From this ...
2
votes
1answer
1k views

Does backpropagation update weights one layer at a time?

I am new to Deep Learning. Suppose that we have a neural network with one input layer, one output layer, and one hidden layer. Let's refer to the weights from input to hidden as $W$ and the weights ...
2
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0answers
65 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: ...