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Questions tagged [math]

For questions about mathematics related to artificial intelligence.

3
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0answers
18 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 ...
2
votes
2answers
87 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
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1answer
30 views

Is the next state draw from the joint distribution of the previous state and action?

Suppose $G_t$, the discounted return at time $t$ is defined as: $$ G_t \triangleq R_t+\gamma R_{t+1}+\gamma^{2}R_{t+2} + \cdots = \sum_{j=1}^{\infty} \gamma^{k}R_{t+k}$$ where $R_t$ is the reward at ...
0
votes
1answer
47 views

How are vectors and matrices multiplied in supervised machine learning?

I've recently started reading a book about deep learning. The book is titled "Grokking Deep Learning" (by Andrew W Trask). In chapter 3 (pages 44 and 45), it talks about multiplying vectors using dot ...
-1
votes
0answers
15 views

Constant in Loss Function of Style Transfer

After I read paper by Gatys, Image Style Transfer Using Convolutional Neural Networks, I notice there aren't any explanations for the constant in Eq. (4): $$E_l = \frac{1}{4N_l^2M_l^2}\sum_{i,j}(G_{...
-1
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0answers
12 views

Logarithm of determinantal function in DPP is submodular

I am learning about Determinantal Point Processes, as described in the paper Determinantal point processes for machine learning In this setting, one of the key elements is the determinantal function $...
0
votes
0answers
27 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
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0answers
11 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
31 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
votes
1answer
46 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
1answer
86 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-...
-1
votes
1answer
35 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?
0
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1answer
52 views

Is the parent cost in A* added in every extended child?

How do we determine the cost of the parent path to its child in A* ("A star") search?
1
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0answers
150 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
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0answers
43 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
vote
1answer
66 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 ...
6
votes
3answers
186 views

Applied Math relevant to AI

My background is in electrical engineering (BS, MS EE/Signal Processing) and I have a good grasp of CS foundations (Data Structures, Algorithms, OS, Discrete Math) and software engineering. I have ...
3
votes
2answers
379 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 ...
1
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1answer
39 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 ...
5
votes
2answers
109 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
votes
2answers
435 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
votes
1answer
63 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
votes
2answers
76 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. ...
1
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0answers
28 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 ...
10
votes
4answers
1k 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 ...
7
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3answers
251 views

Mathematics for 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
101 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?
1
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0answers
22 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?
1
vote
0answers
68 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)?
11
votes
2answers
242 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 ...
4
votes
1answer
123 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, ...
5
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?
2
votes
0answers
361 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
3answers
99 views

Cost Function Question

I have completed week 1 of Andrew Ngs course and I understand that the cost function for linear regression is defined as J (theta0,theta1) = 1/2m*sum (h(x)-y)^2 and the h is defined as h(x) = theta0 + ...
1
vote
1answer
50 views

Please explain this “log probability function”? What does each part mean?

Can anyone explain what information the formula gives us. What does the notations mean? Where i can find more material about what does the log probability function do?
3
votes
1answer
99 views

K-Armed Bandit and Reinforcement Learning

In the book "Reinforcement learning" by Sutton there is a discussion of the k-armed bandit problem, where the expected reward from the bandits changes slightly over time (is non-stationary). Instead ...
3
votes
2answers
320 views

Viola Jones Algorithm

Can Viola Jones algorithm can 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 ...
3
votes
5answers
546 views

Artificial Intelligence and its mathematics

I would like to ask community members what kind of knowledge is required to jump into the field of AI. Currently I have just started programming and development. What should I pursue in order to get ...
2
votes
1answer
161 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: ...
7
votes
6answers
921 views

Getting started with Artificial intelligence

I'm currently pursuing Computer science engineering.So I would like to know where to start and what mathematics is needed to jump in.
9
votes
6answers
13k 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 but each article suggests a different way. I was wondering if some of you experts ...
2
votes
1answer
49 views

Why expression of cost function divides by 2? [closed]

Here is formula for calculating cost value of single neuron: C_x = (1/2) * || y - a ||^2 why there is 1/2?
7
votes
5answers
1k 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?
2
votes
1answer
725 views

Are FFNN (MLP) Lipschitz functions?

My question is regarding standard dense-connected feed forward neural networks with sigmoidal activation. I am studying Bayesian Optimization for hyper-parameter selection for neural networks. There ...
5
votes
1answer
258 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?
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votes
2answers
204 views

What are the approaches to predict sequence of π numbers? [closed]

Given list of fixed numbers from a mathematical constant such as Pi, is it is possible to train AI to attempt to predict the next numbers? Which AI or neural network would be more suitable for this ...
16
votes
5answers
10k 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 ...