Questions tagged [calculus]

For questions related to calculus (developed, among others, by Newton and Leibniz), in the context of AI (and, in particular, machine learning).

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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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How did authors ensure that critical points do exist in GAN?

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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Are calculus and differential geometry required for building neural networks?

I've been studying geometry and linear algebra for months with the goal to build neural networks. But now I'm reading that perceptrons require fitting curves, and curves are not expressed as linear ...
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What are the Calculus books recommended for begineer to advanced researchers in artificial intelligence?

Calculus is a branch of mathematics that deals with the rate of change of outputs of a function w.r.t the inputs. It contains several concepts including limits, first-order derivatives, higher-order ...
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Why the partial derivative is $0$ when $F_{ij}^l < 0$?. Math behind style transfer

I am currently in the process of reading and understanding the process of style transfer. I came across this equation in the research paper which went like - For context, here is the paragraph - ...
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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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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 ...
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BlackOut - ICLR 2016: need help understanding the cost function derivative

In the ICLR 2016 paper BlackOut: Speeding up Recurrent Neural Network Language Models with very Large Vocabularies, on page 3, for eq. 4: $$ J_{ml}^s(\theta) = log \ p_{\theta}(w_i | s) $$ They have ...
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Which linear algebra book should I read to understand vectorized operations?

I am reading Goodfellow's book about neural networks, but I am stuck in the mathematical calculus of the back-propagation algorithm. I understood the principle, and some Youtube videos explaining this ...
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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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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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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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Why is the change in cost wrt bias in neural network equal to error in the neuron?

While reading the book on neural networks by Michael Nielson, I had a problem understanding equation (BP3), which is $$ \frac{\partial C}{\partial b_{j}^{l}}=\delta_{j}^{l} \tag{BP3}\label{BP3}, $$ ...
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116 views

How is the log-derivative trick of a trajectory derived?

I am looking at this formula which breaks down the gradient of $P(\tau |\theta)$ the first part is clear as is the derivative of $\log(x)$, but I do not see how the first formula is rearranged into ...
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Is there any wrong in my focal loss derivation?

Assume $\mathbf{X} \in R^{N, C}$ is the input of the softmax $\mathbf{P} \in R^{N, C}$, where $N$ is number of examples and $C$ is number of classes: $$\mathbf{p}_i = \left[ \frac{e^{x_{ik}}}{\sum_{j=...
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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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What is a bad local minimum in machine learning?

What is "bad local minima"? The following papers all mention this expression. Eliminating all bad Local Minima from Loss Landscapes without even adding an Extra Unit limination of All Bad Local ...