Questions tagged [math]
For questions about mathematics related to artificial intelligence.
30
questions with no upvoted or accepted answers
5
votes
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 ...
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
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, ...
4
votes
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 ...
3
votes
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
votes
0answers
70 views
What characteristics make it difficult for a Neural Network to approximate a function?
What are the characteristics which make a function difficult for the Neural Network to approximate?
Intuitively, one might think uneven functions might be difficult to approximate, but uneven ...
3
votes
0answers
486 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
votes
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
votes
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 ...
2
votes
0answers
31 views
Should I use the hyperbolic distance loss in the case of Poincarè Disk Model?
I trained a neural network which makes a regression to a Poincarè Disk Model with radius $r = 1$.
I want to optimize using the hyperbolic distance
$$
\operatorname{arcosh} \left( 1 + \frac{2|pq|^2|...
2
votes
0answers
39 views
How can the convolution operation be implemented as a matrix-vector multiplication?
How can the convolution operation used by CNNs be implemented as a matrix-vector multiplication? We often think of the convolution operation in CNNs as a kernel that slides across the input. However, ...
2
votes
0answers
24 views
Calculating tangent vector of curve s(P,$\alpha$) at given point $\alpha$ = 0
I am reading the paper "Transformation Invariance in Pattern Recognition – Tangent Distance and Tangent Propagation", where the tangent vector is calculated for the given curve $s(P,\alpha)$ at $\...
2
votes
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 ...
2
votes
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....
2
votes
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^{...
2
votes
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 ...
1
vote
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$?...
1
vote
1answer
134 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 (...
1
vote
0answers
41 views
Why do we use the word “kernel” in the expression “Gaussian kernel”?
I've heard the expression "Gaussian kernel" in several contexts (e.g. in the kernel trick used in SVM). A Gaussian kernel usually refers to a Gaussian function (that is, a function similar to the ...
1
vote
3answers
83 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....
1
vote
0answers
15 views
Does a mechanical system repeats itself?
The inverted pendulum problem is a famous control task. It can be solved with a technique called system identification. System identification means to formalize the state-action space of a system in a ...
1
vote
0answers
28 views
Where does the expectation term in the derivative of the soft-max policy come from?
At slide 17 of the David Silver's series, the soft-max policy is defined as follows
$$
\pi_\theta(s, a) \propto e^{\phi(s, a)^T \theta}
$$
that is, the probability of an action $a$ (in state $s$) is ...
1
vote
0answers
17 views
Since there are different types of neurons in adjacent positions in the brain's arrays, should heterogeneous layers be developed?
Below is a taxonomy of neurons. Some of these types occur in different locations in the brain, but there are adjacent neurons of varying types with clearly functional type diversity in many parts of ...
1
vote
0answers
214 views
Solving equations using reinforcement learning
I was lately curious about a reinforcement learning approach that would solve maths equations.
For example, if I have the following equation:
$$ f(g(h(w))) = 0 , with \ w = \begin{matrix}
a_{11} &...
1
vote
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 ...
1
vote
0answers
24 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?
0
votes
0answers
31 views
How is the convolution operation used in CNNs a special case of the convolution operator?
How is the convolution operation used in convolutional neural networks (CNNs) a special case of the mathematical convolution operator? Most of us, when we think of the "convolution operation", we ...
-1
votes
2answers
218 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?
-1
votes
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?
-2
votes
1answer
81 views
