Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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29
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 ...
27
votes
4answers
4k views

Can neural networks be used to prove conjectures?

Imagine I have a list (in a computer-readable form) of all problems (or statements) and proofs that math relies on. Could I train a neural network in such a way that, for example, I enter a problem ...
20
votes
1answer
6k 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 a function where the ...
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 ...
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....
14
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2answers
657 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 ...
13
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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?
13
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 ...
11
votes
2answers
1k 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-...
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?
10
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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 ...
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?
9
votes
1answer
228 views

How does the forget layer of an LSTM work?

Can someone explain the mathematical intuition behind the forget layer of an LSTM? So as far as I understand it, the cell state is essentially long term memory embedding (correct me if I'm wrong), ...
8
votes
3answers
2k 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 ...
8
votes
2answers
2k views

Which areas of applied math are relevant to AI? [duplicate]

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 ...
8
votes
3answers
940 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
1answer
86 views

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

As I know, a single layer neural network can only do linear operations, but multilayered ones can. Also, I recently learned that finite matrices/tensors, which are used in many neural networks, can ...
7
votes
3answers
918 views

Can we get the inverse of the function that a neural network represents?

I was wondering if it's possible to get the inverse of a neural network. If we view a NN as a function, can we obtain its inverse? I tried to build a simple MNIST architecture, with the input of (784,...
7
votes
2answers
92 views

Interpretation of inverse matrix in mean calculation in Gaussian Process

The formula for mean prediction using Gaussian Process is $k(x_*, x)k(x, x)^{-1}y$, where $k$ is the covariance function. See e.g. equation 2.23 (in chapter 2) from Gaussian Processes for Machine ...
6
votes
3answers
220 views

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

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 ...
6
votes
2answers
980 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
149 views

Formal definition of the Object Detection problem

For many problems in computer science, there is a formal, mathematical problem defition. Something like: Given ..., the problem is to ... How can the Object Detection problem (i.e. detecting objects ...
6
votes
1answer
388 views

What is the mathematical definition of an activation function? [duplicate]

What is the mathematical definition of an activation function to be used in a neural network? So far I did not find a precise one, summarizing which criterions (e.g. monotonicity, differentiability, ...
6
votes
1answer
464 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 ...
6
votes
1answer
163 views

Can deep learning be used to help mathematical research?

I am currently learning about deep learning and artificial intelligence and exploring his possibilities, and, as a mathematician at heart, I am inquisitive about how it can be used to solve problems ...
5
votes
3answers
202 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 ...
5
votes
1answer
444 views

What is “conditioning” on a feature?

On page 98 of Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning the author writes; Redacted phase space: Studying the distribution of inputs ...
5
votes
1answer
551 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
137 views

Why does a Lipschitz continuous discriminator in GANs assure statistical boundedness?

I have been reading the paper which introduced spectral normalization in GANs. At some point the paper mentions the following: The machine learning community has been pointing out recently that ...
5
votes
2answers
114 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
114 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
219 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
1answer
99 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 $$ \frac{\partial C}{\partial b_{j}^{l}}=\delta_{j}^{l} \tag{BP3}\label{BP3}, $$ ...
5
votes
0answers
140 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 ...
5
votes
1answer
222 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
2answers
528 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
4
votes
1answer
2k views

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

In the policy gradient method, there's a trick to reduce the variance of policy gradient. We use causality, and remove part of the sum over rewards so that only actions happened after the reward are ...
4
votes
2answers
870 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 ...
4
votes
2answers
164 views

Mathematical foundations of the ability to learn

I am an undergraduate student in applied mathematics with an interest in artificial intelligence. I am currently exploring topics where I could do research. Coming from a mathematical background I am ...
4
votes
1answer
61 views

What do the subscripts mean in $N_{t,n,\sigma,L}$?

A neural network can apparently be denoted as $N_{t,n,\sigma,L}$. What do these subscripts $t, n, \sigma$ and $L$ mean? Could you link me to a paper, article or webpage with an explanation for this?
4
votes
1answer
85 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
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?
4
votes
1answer
227 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
2answers
466 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
82 views

Can we use ML to do anything else other than predicting (in the case of mathematical problems)?

(The math problem here just serves as an example, my question is on this type of problems in general). Given two Schur polynomials, $s_\mu$, $s_\nu$, we know that we can decompose their product into a ...
4
votes
1answer
69 views

How can a single sample represent the expectation in gradient temporal difference learning?

I was reading the gradient temporal difference learning version 2(GTD2) from rich Sutton's book page-246. At some point, he expressed the whole expectation using a single sample from the environment. ...
4
votes
1answer
177 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
95 views

How is the Jacobian a generalisation of the gradient?

I came across these slides Natural Language Processing with Deep Learning CS224N/Ling284, in the context of natural language processing, which talk about the Jacobian as a generalization of the ...
4
votes
1answer
118 views

Why is my derivation of the back-propagation equations inconsistent with Andrew Ng's slides from Coursera?

I am using the cross-entropy cost function to calculate its derivatives using different variables $Z, W$ and $b$ at different instances. Please refer image below for calculation. As per my knowledge, ...
4
votes
1answer
175 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 ...