# 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 ...
16 views

### 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 ...
1k views

### 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 ...
31 views

### 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 ...
56 views

### 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 - ...
41 views

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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 $$\frac{\partial C}{\partial b_{j}^{l}}=\delta_{j}^{l} \tag{BP3}\label{BP3},$$ ...
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 ...
30 views

### 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=...