Questions tagged [gradient]
For questions related to the gradient, a way of packing together all the partial derivative information of a function
22
questions
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1answer
51 views
PyTorch `torch.no_grad` vs `torch.inference_mode` [closed]
PyTorch has new functionality torch.inference_mode as of v1.9 which is "analogous to torch.no_grad... Code run under this ...
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29 views
Mathematically speaking, Is it only the product operation used in the chain rule causing the vanishing or exploding gradient?
I am asking this question from the mathematical perspective of the vanishing and exploding gradient problems that we face generally during training deep neural networks.
The chain rule of ...
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1answer
26 views
Isssue in understanding the derivation regarding mean squared error
The following derivation is taken from Chapter 5: Machine Learning Basics from the book titled Deep Learning (by Aaron Courville et al.)
I am facing difficulty in understanding the zero derivative ...
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1answer
45 views
How many directions of gradients exist for a function in higher dimensional space?
Gradient is used in optimization algorithms. Based on the values of gradient, we generally update weights of a neural network.
It is known that gradient have a direction and the direction opposite to ...
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25 views
What all does the gradient tells us?
Gradients are used in optimization algorithms.
I know that a gradient gives us information about the direction in which one needs to update the weights of a neural network. We need to travel in the ...
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1answer
28 views
What is the high-level algorithm followed by contemporary packages for the calculation of gradient?
Most of the neural network models in contemporary deep learning packages are trained based on gradients.
Let $f: \mathbb{R}^m \rightarrow \mathbb{R}^n$ be a function for which we want to find a ...
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25 views
Is there any significance for higher order gradients in artificial intelligence?
Although I don't know in detail, I am aware of the following facts regarding the usefulness of gradients in some domains of artificial intelligence, especially in optimization.
First order gradient: ...
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1answer
45 views
What does it mean by strong or sufficient gradient for training in this context?
It has been mentioned in the research paper titled Generative Adversarial Nets that generator need to maximize the function $\log D(G(z))$ instead of minimizing $\log(1 −D(G(z)))$ since the former ...
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18 views
How to handle critical points during generator training?
Using an MLP as generator introduces multiple critical points in parameter space. You can read this excerpt from research paper titled Generative Adversarial Nets
In practice, adversarial nets ...
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1answer
31 views
What is meant by "well-behaved gradient" in this context?
Consider the following statement about the success of discriminative models
So far, the most striking successes in deep learning have involved discriminative models,
usually those that map a high-...
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1answer
32 views
How to calculate the gradient penalty proposed in "Improved Training of Wasserstein GANs"?
The research paper titled Improved Training of Wasserstein GANs proposed a gradient penalty in order to avoid undesired behavior due to weight clipping of the discriminator.
We now propose an ...
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35 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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1answer
41 views
What does it mean by "zeros the networks parameters gradients" in the context of training a neural network?
Consider the following PyTorch code
...
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19 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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15 views
Terminology for the weight of likelihood ratio/score function?
If we estimate the gradient of $f(x)$ using the likelihood ratio/score function, i.e.
$$\nabla f = f^*\dfrac{\partial \log p(x)}{\partial \theta}$$
is there any agreed upon terminology to call "$...
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1answer
57 views
Why don't integrated gradients explain samples correctly?
I have a linear tabular dataset made of floats. The dataset follows a simple rule like:
...
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1answer
149 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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2answers
183 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
63 views
What is $ \nabla_{\theta_{k-1}} \theta_{k}$ in the context of MAML?
I am attempting to fully understand the explicit derivation and computation of the Hessian and how it is used in MAML. I came across this blog: https://lilianweng.github.io/lil-log/2018/11/30/meta-...
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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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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
$$
L_{i}(\theta_{i}) = \mathbb{E}_{(s,a,r,s') \sim U(D)} [(r+\gamma \max_{a'} Q(s',a',\theta_{i}^{-}) - Q(s,a;\theta_{i}))^2]
$$
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148 views
How can the sum of squared errors have negative gradient if it's defined as the squared of the error?
The formula for the sum of squared errors (SSE) is:
$$
\frac{1}{2} \sum_{i=1}^n (t^i - o^i)^2
$$
I have a few related questions.
If $t^i - o^i$ is negative, doesn't the power of 2 eliminate any ...
