Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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17
votes
3answers
1k views

What are the mathematical prerequisites for an AI researcher?

What are the mathematical prerequisites for understanding the core part of various algorithms involved in artificial intelligence and developing one's own algorithms? Please, refer some specific books....
3
votes
1answer
188 views

How does one even begin to mathematically model an AI algorithm?

How does one even begin to mathematically model an AI algorithm, like alpha-beta pruning or even its thousands of variations, to determine which variation is best?
2
votes
0answers
28 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?
1
vote
0answers
77 views

How does this sigma work?(Harris algorithm) [closed]

May someone explains some first iterations of this sigma? Also, how did it convert the above expression to below expression? What it the meaning of I(x) and I(y)?
5
votes
1answer
165 views

How could an AI be used to improve the teaching and learning of mathematics?

I have been working with AI methods. I am thinking about how my daughter (and also other kids) could learn mathematics with the help of AI. For example, how could an AI be used to show the mistakes ...
13
votes
2answers
645 views

Is there any scientific/mathematical argument that prevents deep learning from ever producing strong AI?

I read Judea Pearl's The Book of Why, in which he mentions that deep learning is just a glorified curve fitting technology, and will not be able to produce human-like intelligence. From his book ...
3
votes
4answers
2k views

AI applications of the Fibonacci series

I have been looking at Fibonacci series, the golden ratio and its uses in nature, like how flowers and animals grow based on the series. I was wondering whether we could use the Fibonacci series and ...
4
votes
1answer
209 views

Which functions can be activation functions?

What are the required characteristics of an activation function (in a neural network)? Which functions can be activation functions? For example, which of the functions below can be used as an ...
4
votes
1answer
213 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, ...
0
votes
1answer
120 views

What is Bayes' theorem?

What is Bayes' theorem? How does it relate to conditional probabilities?
9
votes
3answers
4k views

What are the mathematical prerequisites to be able to study artificial general intelligence?

What are the mathematical prerequisites to be able to study artificial general intelligence (AGI) or strong AI?
3
votes
0answers
697 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 ...
1
vote
2answers
4k views

What is the derivative of the Leaky ReLU activation function?

I am implementing a feed-forward neural network with leaky ReLU activation functions and back-propagation from scratch. Now, I need to compute the partial derivatives, but I don't know what the ...
3
votes
3answers
235 views

Understanding a few terms in Andrew Ng's definition of the cost function for linear regression

I have completed week 1 of Andrew Ng's course. I understand that the cost function for linear regression is defined as $J (\theta_0, \theta_1) = 1/2m*\sum (h(x)-y)^2$ and the $h$ is defined as $h(x) = ...
3
votes
2answers
640 views

What does the argmax of the expectation of the log likelihood mean?

What does the following equation mean? What does each part of the formula represent or mean? $$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$
5
votes
1answer
206 views

What is a weighted average in a non-stationary k-armed bandit problem?

In the book Reinforcement Learning: An Introduction (page 25), by Richard S. Sutton and Andrew G. Barto, there is a discussion of the k-armed bandit problem, where the expected reward from the bandits ...
4
votes
2answers
464 views

Viola Jones Algorithm

Can Viola Jones algorithm be used to detect the facial emotion. Actually it was used in creating harr-cascade file for object and facial detection, but what confused me is whether it can be used to ...
4
votes
2answers
861 views

How good is AI in math?

Currently, AI is advancing fast in deep learning: Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours. As a layman, I'm taking this as a quite powerful searching ...
6
votes
1answer
413 views

Why is the denominator ignored in the Bayes' rule?

The naïve Bayes' generative algorithm is often represented by the following formula: $$\text{argmax}_{y} p(y|x) = \text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$$ Why do we ...
1
vote
1answer
72 views

What does “probabilistically” mean?

I'm reading the A. E. Eiben and J. E. Smith book Introduction to Evolutionary Computing (Springer 2003). On section 3.5 Recombination, page 47, the second paragraph said: Recombination operators ...
1
vote
1answer
678 views

What is the intuition behind the entropy formula used in the ID3 algorithm?

What is the intuition behind the following entropy formula used in the ID3 algorithm? $$ \text{info}(D) = -\sum_{i=1}^m p_i \log_2(p_i) $$
2
votes
1answer
271 views

Problems getting ADADELTA to converge

I have followed the pseudocode in the ADADELTA paper (top right on page 3), and wrote the following Python code for solving the optimization problem L(x) = x^2: ...
10
votes
2answers
3k views

Is the mean-squared error always convex in the context of neural networks?

Multiple resources I referred to mention that MSE is great because it's convex. But I don't get how, especially in the context of neural networks. Let's say we have the following: $X$: training ...
13
votes
13answers
2k views

How should I get started with artificial intelligence? [duplicate]

What is the mathematical background required to start learning AI? What else should I also learn?
18
votes
6answers
16k views

How does one start learning artificial intelligence? [duplicate]

I am a software engineering student and I am complete beginner to AI. I have read a lot of articles on how to start learning AI, but each article suggests a different way. I was wondering if some of ...
8
votes
3answers
908 views

How can I start learning mathematics for machine learning?

I am an Android programmer. Now, I would like to learn machine learning. I know it requires a mathematical background, like statistics, probability, calculus and linear algebra. However, I am a bit ...
5
votes
1answer
97 views

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 $$ \frac{\partial C}{\partial b_{j}^{l}}=\delta_{j}^{l} \tag{BP3}\label{BP3}, $$ ...
4
votes
1answer
95 views

Why does the cost function contain a 2 at the denominator?

A cost function used in machine is often the following $$C = \frac{1}{2} \| y - \hat{y} \| ^2$$ Why is there $\frac{1}{2}$ in front of the squared distance?
10
votes
5answers
5k views

Why do activation functions need to be differentiable in the context of neural networks?

Why should an activation function of a neural network be differentiable? Is it strictly necessary or is it just advantageous?
2
votes
1answer
816 views

Are FFNN (MLP) Lipschitz functions?

My question is regarding standard dense-connected feed forward neural networks with sigmoidal activation. I am studying Bayesian Optimization for hyper-parameter selection for neural networks. There ...
5
votes
1answer
540 views

Is recursion used in practice to improve performance of AI systems?

Is there any methods by which artificial intelligence use recursion(s) to solve a certain issue or to keep up working and calculating?
-4
votes
2answers
629 views

What are the approaches to predict sequence of π numbers? [closed]

Given list of fixed numbers from a mathematical constant such as Pi, is it is possible to train AI to attempt to predict the next numbers? Which AI or neural network would be more suitable for this ...
28
votes
5answers
20k views

Is it possible to train the neural network to solve math equations?

I'm aware that neural networks are probably not designed to do that, however asking hypothetically, is it possible to train the deep neural network (or similar) to solve math equations? So given the ...

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