# Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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### Is there a mathematical formula that describes the learning curve in neural networks?

In training a neural network, you often see the curve showing how fast the neural network is getting better. It usually grows very fast then slows down to almost horizontal. Is there a mathematical ...
70 views

### What are the main benefits of using Bayesian networks?

I have some trouble understanding the benefits of Bayesian networks. Am I correct that the key benefit of the network is that one does not need to use chain rule of probability in order to calculate ...
195 views

### Defining formula for fuzzy equation

I'm learning fuzzy logic and more or less understand the basic concept, but i'm having a hard time understanding how to apply it to a method. I tried browsing online for explanation on how to use it, ...
217 views

### What are the algebraic properties of intelligence?

Some have said, "Two heads are better than one." That's true if they are collaborating. If not, the two together may be worse than zero. Although that's a rhetorical opening paragraph, this is a ...
39 views

### How does the memory mechanism (reading and writing) work in a neural Turing machine?

In neural Turing machine (NTM), reading memory is represented as \begin{align} r_t \leftarrow \sum\limits_i^R w_t(i) \mathcal{M}_t(i) \tag{2} \end{align} and writing to memory is represented as ...
73 views

### What characteristics make it difficult for a Neural Network to approximate a function?

What are the characteristics which make a function difficult for the Neural Network to approximate? Intuitively, one might think uneven functions might be difficult to approximate, but uneven ...
531 views

### How to calculate gradient of filter in convolution network

I have similar architecture like in image:CNN. I don't understand how to calculate gradient of filter F. I found these equations(source): Gradient and delta, where first equation calculate gradient ...
37 views

### How does the update rule for the one-step actor-critic method work?

Can you please elucidate the math behind the update rule for the critic? I've seen in other places that just a squared distance of $R + \hat{v}(S', w) - \hat{v}(S,w)$ is used, but Sutton suggests an ...
49 views

### What is the meaning of the words 'bias' and 'variance' in RL?

In algorithms like MC/TD (tabular value approximation) two of the metrics used to measure their performance are the bias and the variance. What do these terms mean? And which characteristic of the ...
36 views

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### Optimization step in Apprenticeship Learning via Inverse Reinforcement Learning

Why the optimization step of the algorithm a quadratic program? [See: Apprenticeship Learning via Inverse Reinforcement Learning; page 3] Isn't the objective function linear? Why don't we treat ...
25 views

### Simple question about HS algorithm's formul(Optical flow)

In the below pic, I can not understand what U vector is? It says flow field but I can not imagie what really is the flow field?
37 views

### How is the convolution operation used in CNNs a special case of the convolution operator?

How is the convolution operation used in convolutional neural networks (CNNs) a special case of the mathematical convolution operator? Most of us, when we think of the "convolution operation", we ...
226 views

### What are the skills and disciplines I need to learn to get a job in Artificial Intelligence?

I'm in high school but hoping to have a career in artificial intelligence. What should I be pursuing educationally to get into this field?