Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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24
votes
5answers
14k 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 ...
21
votes
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 ...
14
votes
6answers
15k views

How does one start learning artificial intelligence?

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 ...
13
votes
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?
11
votes
2answers
4k 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 ...
11
votes
2answers
391 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 ...
10
votes
3answers
446 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.
9
votes
2answers
657 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 ...
8
votes
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 ...
8
votes
5answers
2k 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?
8
votes
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 ...
7
votes
2answers
574 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 ...
7
votes
3answers
781 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 ...
6
votes
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 ...
6
votes
5answers
3k views

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

What are the mathematical prerequisites to be able to study general artificial intelligence (AI) or strong AI?
6
votes
3answers
240 views

How is local minima possible in gradient descent?

Gradient descent works on the equation of mean squared error, which is an equation of a parabola $y=x^2$. We often say that weight adjustment in a neural network by gradient descent algorithm can hit ...
6
votes
1answer
458 views

How do we prove the n-step return error reduction property?

In section 7.1 (about the n-step bootstrapping) of the book Reinforcement Learning: An Introduction (2nd edition), by Andrew Barto and Richard S. Sutton, the authors write about what they call the "n-...
5
votes
5answers
730 views

What kind of knowledge is required to jump into the field of AI?

What kind of knowledge is required to jump into the field of AI? What mathematics is required? How good I should be in mathematics? Currently, I have just started programming. I would be grateful if ...
5
votes
2answers
541 views

Why exactly do neural networks require i.i.d. data?

In reinforcement learning, in general, successive states (actions and rewards) are highly correlated. An "experience replay" buffer was used, in the DQN architecture, to avoid training the neural ...
5
votes
1answer
389 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?
5
votes
1answer
67 views

What makes multi-layer neural networks be able to perform nonlinear operations?

As I know, a single layer neural network can only do linear operations, but multilayered ones can. Alao I recently learned that finite matrices/tensors, which are used in many neural networks can ...
5
votes
2answers
103 views

Are on-line backpropagation iterations perpendicular to the constraint?

Raul Rojas' Neural Networks A Systematic Introduction, section 8.1.2 relates off-line backpropagation and on-line backpropagation with Gauss-Jacobi and Gauss-Seidel methods for finding the ...
5
votes
1answer
58 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 ...
5
votes
1answer
124 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 ...
5
votes
3answers
183 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 ...
4
votes
3answers
193 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
votes
3answers
167 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 ...
4
votes
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? ...
4
votes
1answer
120 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 ...
4
votes
1answer
87 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?
4
votes
2answers
393 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
1answer
118 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 ...
4
votes
1answer
127 views

Why is the denominator ignored in the Bayes' rule?

The naive Bayes' generative algorithm is often represented by the following formula $$\text{argmax}_{y} p(y \mid x) = \text{argmax}_y \frac{p(x|y)p(y)}{p(x)} \approx \text{argmax}_y p(x|y)p(y)$$ Why ...
4
votes
0answers
63 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 ...
4
votes
1answer
181 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, ...
4
votes
3answers
109 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 ...
3
votes
2answers
481 views

Why is the derivative 0 if the policy is deterministic?

In the Berkeley RL class they mention the gradient would be 0 if the policy is deterministic. Why is that? https://www.youtube.com/watch?v=XGmd3wcyDg8&feature=youtu.be&t=1071
3
votes
2answers
55 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 ...
3
votes
1answer
282 views

Why does the “reward to go” trick in policy gradient methods work?

In policy gradient method, there's a trick to reduce a variance of policy gradient. We use causality, and remove part of the sum over rewards so that only actions happened after the reward are taken ...
3
votes
2answers
47 views

Which linear algebra book should I read to understand vectorized operations?

I am reading the 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 ...
3
votes
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 ...
3
votes
3answers
233 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 ...
3
votes
2answers
575 views

Is known math really enough for AI

As an Electronics & Communication Engineering student I've heard some stories and theories about "The math we have is not enough to complete a thinker-learner AI." What is the truth? Is humankind ...
3
votes
1answer
152 views

Mathematical modelling of A.I algorithms

How does one even begin to mathematically model an A.I algorithm like alpha-beta pruning or even its thousands of variations, to determine which variation is best?
3
votes
1answer
86 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 ...
3
votes
1answer
73 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 ...
3
votes
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
votes
4answers
788 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
votes
1answer
129 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 ...
3
votes
2answers
95 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? $$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$