Questions tagged [math]

For questions about mathematics related to artificial intelligence.

29 questions with no upvoted or accepted answers
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Is there a mathematical formula that describes the learning curve in neural networks?

In training a neural network, you often see the curve showing how fast the neural network is getting better. It usually grows very fast then slows down to almost horizontal. Is there a mathematical ...
4
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0answers
70 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
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1answer
195 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
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3answers
217 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 ...
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0answers
39 views

How does the memory mechanism (reading and writing) work in a neural Turing machine?

In neural Turing machine (NTM), reading memory is represented as \begin{align} r_t \leftarrow \sum\limits_i^R w_t(i) \mathcal{M}_t(i) \tag{2} \end{align} and writing to memory is represented as ...
3
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0answers
73 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
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0answers
531 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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0answers
37 views

How does the update rule for the one-step actor-critic method work?

Can you please elucidate the math behind the update rule for the critic? I've seen in other places that just a squared distance of $R + \hat{v}(S', w) - \hat{v}(S,w)$ is used, but Sutton suggests an ...
2
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0answers
49 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
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0answers
36 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
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0answers
45 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
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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
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1answer
205 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 ...
2
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1answer
105 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
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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....
2
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2answers
116 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^{...
1
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1answer
40 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
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1answer
262 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 (...
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0answers
43 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 ...
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0answers
16 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 ...
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0answers
32 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 ...
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0answers
21 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 ...
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0answers
244 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} &...
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0answers
42 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 ...
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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
37 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 ...
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2answers
226 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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2answers
90 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?
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1answer
83 views

What is Bayes' theorem and error?

What is Bayes' theorem and Bayes' error?