Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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80 views

What does the formula $1-\sum_i(e_i-a_i)^2$ mean in this NEAT Python API?

I have looked at the documentation for the NEAT Python API found here, but it shows calculus like this: The error for each genome is $1-\sum_i(e_i-a_i)^2$ I haven't learned calculus at the moment....
4
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3answers
164 views

Is it ok to struggle with mathematics while learning AI as a beginner?

I have a decent background in Mathematics and Computer Science .I started learning AI from Andrew Ng's course from one month back. I understand logic and intuition behind everything taught but if ...
2
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2answers
79 views

Why is MSE used over other quadratic loss functions?

So I was wondering, why I have only encountered square loss function also known as MSE. The only nice property of MSE I am so far aware of is its convex nature. But then all equations of the form $x^{...
0
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1answer
25 views

Backpropagation: Chain Rule to the Third Last Layer

I'm trying to solve dLoss/dW1. The network is as in picture below with identity activation at all neurons: Solving dLoss/dW7 is simple as there's only 1 way to output: $Delta = Out-Y$ $Loss = abs(...
3
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2answers
66 views

Detecting Sine Waves with a Neural Network?

I am recording the vibrations of an AC Motor (50Hz Europe) and I am trying to find out whether it is powered on or not. When I record these vibrations, I basically get the vibration values (-1 to +1) ...
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1answer
133 views

Which machine learning models are universal function approximators?

The universal approximation theorem states that a feed-forward neural network with a single hidden layer containing a finite number of neurons can approximate a wide variety of interesting (...
5
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1answer
123 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 ...
2
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2answers
93 views

How can I determine the mathematical relation between the input and output variables?

I would like to take in some input values for $n$ variables, say $R$, $B$, and $G$. Let $Y$ denote the response variable of these $n$ inputs (in this example, we have $3$ inputs). Other than these, I ...
2
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1answer
69 views

Choice of fuzzification function

I'm a relative newbie to fuzzie logic systems but I have some knowledge in mathematics. I have the following problem: I want to fuzzify certain values. Some are in the range [-$\inf$,$\inf$] and some ...
3
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1answer
38 views

What are the differences between stability and convergence in reinforcement learning?

The terms are mentioned in the paper: “An Emphatic Approach to the Problem of off-Policy Temporal-Difference Learning.” (Sutton, Mahmood, White; 2016) and more, of course. In which paper, they ...
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1answer
33 views

Given an axis-angle rotation vector, how can I find the unit rotation axis and angle?

I have a robotics assignment, which I am unable to solve. Given the axis-angle rotation vector $\Theta = (2, 2, 0)$, how can I calculate the unit vector of the rotation axis $k$ and the angle $\theta$?...
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0answers
30 views

Show that if $H$ is PAC learnable (in the standard one-oracle model), then $H$ is also learnable in the two-oracle model

Consider a variant of the PAC model in which there are two example oracles: one that generates positive examples and one that generates negative examples, both according to the underlying distribution ...
3
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2answers
54 views

Why is the max a non-expansive operator?

In certain reinforcement learning (RL) proofs, the operators involved are assumed to be non-expansive. For example, on page 6 of the paper Generalized Markov Decision Processes: Dynamic-programming ...
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2answers
22 views

Is it still called linear separation with a layer of more than 1 neuron

A single neuron will be able to do linear separation. For example, XOR simulator network: ...
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1answer
54 views

Is there a mathematical example for Conditional Random Fields?

I am learning about probabilistic graphical models and I was wondering if there is an example explaining the math behind conditional random fields. Looking solely on the formula, I have no idea what ...
4
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1answer
180 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, ...
8
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1answer
1k views

What is the Bellman operator in reinforcement learning?

In mathematics, the word operator can refer to several distinct but related concepts. An operator can be defined as a function between two vector spaces, it can be defined as function where the domain ...
9
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2answers
580 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 ...
6
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3answers
1k views

Why is the derivative of the activation functions in neural networks important?

I'm new to NN. I am trying to understand some of its foundations. One question that I have is: why the derivative of an activation function is important (not the function itself), and why it's the ...
4
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2answers
76 views

How would an AI work out this question?

I am trying to create an AI that makes reasonable guesses at truths of statements. However... Human: "Prove that no number exists which is one more than a billion." AI: "Is it true for the number 1? ...
1
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1answer
43 views

Is there a rigorous proof for finding Hopfield minima?

I am looking for a rigorous mathematical proof for finding the several local minima of the Hopfield networks. I am searching for something rigorous, a demonstration, not just let the network keep ...
2
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1answer
38 views

How can I derive the rotation matrix from the axis-angle rotation vector?

Given an axis-angle rotation vector $\Theta = (2,2,0)$, after finding the unit vector $k=(1/\sqrt{2}, 1/\sqrt{2}, 0)$ and angle $\theta = 2\sqrt{2}$ representing the same rotation, I need to derive ...
2
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1answer
51 views

How can I learn tensors for deep learning?

I've seen in most deep learning papers use tensors. I understood what tensors are, but I want to dive into them, because I think that might be beneficial for further studies in Artificial Intelligence....
4
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3answers
108 views

How can a collaboration game be defined mathematically?

One of the common conceptions in AI is the idea of game theory. We see that in the predominance of chess and other games in the literature as metrics of AI success. We see it in the names of machine ...
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2answers
3k views

How to choose an activation function?

I choose the activation function for the output layer depending on the output that I need and the properties of the activation function that I know. For example, I choose the sigmoid function when I'm ...
5
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3answers
182 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 ...
2
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0answers
47 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 ...
1
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1answer
28 views

Why is the expectation calculated over finite number of points drawn from a probability distribution?

This is from the book Pattern Recognition by Bishop. Why is expectation here a simple average? Why is $f(x)$ not being multiplied by $p(x)$?
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2answers
156 views

Can we define the AI singularity mathematically?

The "AI Singularity" or "Technological Singularity" is a vague term that roughly seems to refer to the idea of: Humans can design algorithms Humans can improve algorithms Eventually algorithms we ...
4
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1answer
113 views

Where can I find the proof of the universal approximation theorem?

The Wikipedia article for the universal approximation theorem cites a version of the universal approximation theorem for Lebesgue-measurable functions from this conference paper. However, the paper ...
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2answers
217 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?
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4answers
757 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 ...
3
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1answer
78 views

How is G(z) related to x in GAN proof?

In the proofs for the original GAN paper, it is written: $$∫_x p_{data}(x) \log D(x)dx+∫_zp(z)\log(1−D(G(z)))dz =∫_xp_{data}(x)\log D(x)+p_G(x) \log(1−D(x))dx$$ I've seen some explanations asserting ...
5
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1answer
57 views

Is there a limit of minimum error for a particular training dataset in artificial Neural Network?

In error-based learning using gradient descent, if I give you a training dataset, then can you find the minimum error after training? And the minimum error should be true for all architectures of a ...
1
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1answer
59 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 ...
2
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2answers
227 views

What skills are needed to succeed in the artificial intelligence field?

I am currently studying information systems engineering (BA) and I'm thinking of getting a master degree in Artificial Intelligence. What are the main important skills do I need to succeed in this ...
8
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3answers
2k views

What sort of mathematical problems are there in AI that people are working on?

I recently got a 18-month postdoc position in a math department. It's a position with relative light teaching duty and a lot of freedom about what type of research that I want to do. Previously I was ...
10
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3answers
422 views

What are the mathematical prerequisites for an AI researcher?

What are the mathematical prerequisites for understanding the core part of the algorithms in artificial intelligence and developing own algorithm? Please, refer me the specific books.
7
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3answers
702 views

Which areas of applied math are relevant to AI?

My background is in electrical engineering. I have a good grasp of CS foundations (e.g. data structures, algorithms, operating systems, discrete math and software engineering). I have option of ...
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7answers
1k views

How should I get started with artificial intelligence?

What is the mathematical background required to start learning AI? What else should I also learn?
2
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1answer
43 views

Is the Markov property assumed in the forward algorithm?

I'm majoring in pure linguistics (not computational), and I don't have any basic knowledge regarding computational science or mathematics. But I happen to take "Automatic Speech Recognition" course in ...
3
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2answers
89 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? $$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$
3
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2answers
82 views

Are there any discount-factors based on branching factors?

I recently came across this function: $$\sum_{t = 0}^{\infty} \gamma^t R_t.$$ It's elegant and looks to be useful in the type of deterministic, perfect-information, finite models I'm working with. ...
3
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3answers
221 views

Which neural network should I use to approximate a specific function?

We have convolutional neural networks and recurrent neural networks for analysing respectively images and sequential data. How do I determine which neural network architecture is more appropriate to ...
7
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2answers
555 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 ...
4
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3answers
192 views

Which function $(\hat{y} - y)^2$ or $(y - \hat{y})^2$ should I use to compute the gradient?

The MSE can be defined as $(\hat{y} - y)^2$, which should be equal to $(y - \hat{y})^2$, but I think their derivative is different, so I am confused of what derivative will I use for computing my ...
4
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1answer
117 views

How are filters weights updated for a CNN?

I've been trying to learn backpropagation for CNNs. I read several articles like this one and this one. They all say that to compute the gradients for the filters, you just do a convolution with the ...
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4answers
3k views

Can deep networks be trained to prove theorems?

Assume we have a large number of proofs in first order predicate calculus. Assume we also have the axioms, corollaries, and theorems in that area of mathematics in that form too. Consider the each ...
3
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1answer
72 views

Standard deviation of the total input to a neuron

Raul Rojas' Neural Networks A Systematic Introduction, section 8.2.1 calculates the standard deviation of the output of a hidden neuron. From: $$ \sigma^2 = \sum^n_{i=0}E[w_i^2]E[x_i^2] $$ When I ...
4
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2answers
388 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 ...