Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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0answers
17 views

Since there are different types of neurons in adjacent positions in the brain's arrays, should heterogeneous layers be developed?

Below is a taxonomy of neurons. Some of these types occur in different locations in the brain, but there are adjacent neurons of varying types with clearly functional type diversity in many parts of ...
2
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1answer
75 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
298 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 ...
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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 ...
6
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1answer
566 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-...
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1answer
41 views

When will we have computer programs that can compose mathematical proofs?

When will it be possible to give a computer program a bunch of assumptions and ask it if a certain statement is true or false, giving a proof or a counterexample respectively?
3
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3answers
240 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 ...
1
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0answers
221 views

Solving equations using reinforcement learning

I was lately curious about a reinforcement learning approach that would solve maths equations. For example, if I have the following equation: $$ f(g(h(w))) = 0 , with \ w = \begin{matrix} a_{11} &...
5
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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 ...
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2answers
219 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?
2
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1answer
74 views

Reward-related formulation in reinforcement learning

I am referring to eq. 3.6 (p/g 49) based on Sutton's online book and can be found in an image below. I could not make sense of the final derivation of the equation $r(s, a, s')$. My question is ...
7
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3answers
805 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 ...
3
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2answers
578 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 ...
2
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1answer
65 views

Weight Normalization paper

I am trying to dissect paper about weight normalization: https://papers.nips.cc/paper/6114-weight-normalization-a-simple-reparameterization-to-accelerate-training-of-deep-neural-networks.pdf ...
4
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3answers
192 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 ...
3
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2answers
482 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
5
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2answers
514 views

Why is the log probability replaced with the importance sampling in the loss function?

In the Trust-Region Policy Optimisation (TRPO) algorithm (and subsequently in PPO also), I do not understand the motivation behind replacing the log probability term from standard policy gradients $$...
5
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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 ...
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. ...
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0answers
41 views

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 ...
21
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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 ...
10
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3answers
454 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.
3
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1answer
153 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?
11
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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 ...
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0answers
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?
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0answers
71 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)?
2
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2answers
232 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 ...
11
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2answers
400 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
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4answers
805 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
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 ...
4
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1answer
182 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, ...
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1answer
82 views

What is Bayes' theorem and error?

What is Bayes' theorem and Bayes' error?
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5answers
4k 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?
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0answers
498 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 ...
2
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4answers
145 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) = ...
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2answers
88 views

When is a measurable function a Bayesian decision function?

When is a measurable function a Bayesian decision function? How do I prove this? Can you give an example with standard or weighted binary classification?
3
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2answers
99 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
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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 ...
4
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2answers
394 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 ...
5
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5answers
734 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 ...
4
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1answer
129 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 ...
1
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1answer
68 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
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1answer
506 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
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1answer
199 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: ...
9
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2answers
674 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
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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?
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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 ...
7
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2answers
577 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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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?
8
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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?