Questions tagged [artificial-intelligence]
For questions about artificial intelligence, the intelligence of machines and robots and the branch of computer science that aims to create it.
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Mathematical preparation for postgraduate studies in Linguistics
I am an undergraduate student in Mathematics and I would like to continue my postgraduate studies in the harder, more mathematical aspects of Linguistics. What exactly would that include is unknown ...
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What areas of math can be tackled by artificial intelligence?
Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able ...
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Applications of Differential Geometry in Artificial Intelligence
I am new to this wonderful site. I searched around a bit but I couldn't find any well-discussed posts on applications of differential geometry to artificial intelligence, or more generally to computer ...
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Mathematics base for data mining and artificial intelligence algorithms. [closed]
Could you give me some clarification about data mining and artificial intelligence algorithms? What mathematics base they used for? Could you give me starting point, in mathematics, to understand ...
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Category Theory & Artificial Intelligence (AI)
Category theory turns out to be useful in more and more areas.
(see e.g. MSE - Category Theory & Biology)
Question. Does anyeone know of some connection of category theory to (convolutional) ...
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Application of computers in higher mathematics
Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc.
It is at all possible to delegate the thinking of a ...
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What would be the shortest path between 2 points when there are objects obstructing the straight path?
How would an algorithm find the shortest distance between 2 points on a horizontal 2d plane , especially when a straight path is not possible? Could it be something on the lines of calculating least ...
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What Maths are the most important for Artificial Intelligence?
I am just curious about this. Please don't include anything about programming.
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What about Genetic Algorithms from a mathematical point of view?
Last year I've attended an Artificial Intelligence course (it was very simple, just a summary of the main ideas); we've seen what a genetic algorithm is and the idea seems very interesting to me.
Now ...
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Algebra & Artificial Intelligence (AI)
Artificial intelligence, especially deep learning & neural networks for image processing and classfication, are related to statistics and physics e.g. as decribed in below papers.
Statistics and ...
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Some doubts about the differences between logic implication and inference rule
I am studying for an Artificial Inteligence university exam that includes a section dedicated to mathematical logic. I am finding some difficulty in understanding the difference between logical ...
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Mathematics in cognitive sciences
Which areas of Maths can be formally studied in a cognitive sc major? Or: which areas of maths can support the study of brain. Some areas that seem relevant would be: mathematical logic, graph theory, ...
Zeph
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Policy gradient reinforcement learning for continuous state and action space
I am a novice in the field of machine learning, I have a moderate level understanding of linear/non-linear regression, support vector machines, neural networks, and q-learning (for discrete finite ...
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What is the sigmoid *squashing* function?
I've just read the following
The basic unit ("neuron" i) performs the following computation to update its state $y_i$: it computes a weighted sum $v_i$ of its inputs $x:j$ which is passed
through ...
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What aspects of convex optimization are used in artificial intelligence, if any?
I work on convex optimization with Stephen Boyd's book.
As an example, support vector machines are mentioned as an application of separating hyperplanes theorem. I am wondering if there is any other ...
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State space for 8-queen problem
While reading Artificial Intelligence a Modern Approach I came across the following formulation for the 8-queen problem:
Initial state: No queens on the board.
States: Arrangements of n queens (0 <...
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Convert a WFF to Clausal Form
I'm given the following question:
Convert the following WFF into clausal form:
\begin{equation*}
\forall(X)(q(X)\to(\exists(Y)(\neg(p(X,Y)\vee r(X,Y))\to h(X,Y))\wedge f(X)))
\end{equation*}
...
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AI strategies for losing positions [closed]
I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the ...
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Regarding Research in Artificial Intelligence [closed]
Which mathematical areas are important for research purposes in artificial intelligence? Specifically, If I have Masters in Statistics how much it will be beneficial for research in artificial ...
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Can I interpret $\models$ as $\implies$ while proving logical expressions using different techniques?
In the book by Artificial Intelligence by Norvig and Russel, I came across following problem:
Prove if correct: $(A ∧ B) \models (A ⇔ B).$
I quickly interpreted $\models$ as $\implies$ and tried to ...
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First order logic.
In Artificial intelligence, I saw the following question and answer in website.
Question:
Politicians can fool some people all of the time, and they can fool all
people some of the time, ...
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Markov Decision Process - Utility Function
Reward $R(S)$ in a Markov Decision Process is a mapping from a State $S \rightarrow$ Bounded number. I want to know how a Utility Function is defined for an MDP.
I think it has to be a mapping from a ...
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Gödel's Incompleness Theorems and the "Minds vs. Machines" conundrum
As a part of my self-learning about Gödel's Incompleness Theorems, I try to dive a little bit into their different interpretations and (possible) philosophical implications. One that immediately ...
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Are neural networks with bounded parameters a compact subset of the Banach space of continuous functions?
Let $d, n \in \mathbb{N}$. Moreover, let $D \subset \mathbb{R}^d$ be compact and denote with
$\mathcal{C}(D, \mathbb{R}^n) $
the set of continuous functions from $D$ to $\mathbb{R}^n$. Then $\mathcal{...
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Find sectors in a racing line.
Consider the following photo:
To magnify image, right click and select open-image in new tab or something similar
The photo above is a random race circuit data I've collected. What I'm trying to do ...
4
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2
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Are there some functions that cannot be optimized using calculus?
I've been working on a project to maximize a functions output using a genetic algorithm. However, from the limited calculus I know I thought there were methods to find the maximum of a mathematical ...
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Recursively Solving a Bellman Equation
Problem Overview
I am to figure out $v_\pi$ of a certain Markov state.
Given Information
A set of actions, $a$ containing ${up, down, left, right}$
$v_\pi(12), v_\pi(13), v_\pi(14)$ (I am given ...
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0
answers
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Advanced Math for Reinfrocement Learning - state space and state sequences (policies)
Reinforcement learning has two important notions and I am interested in advanced math that can investigate those notions:
State space - set of states. Apparently, deep structures should exist in this ...
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Modern Mathematical Theory for Neural Networks, Cellular Automata, Neuroscience
Is it possible for someone to do research on subjects like neural networks, cellular automata, or neuroscience as an applied mathematician?
I have in mind the theoretical development of these fields,...
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$i,j,k$ Values of the $\Theta$ Matrix in Neural Networks
SO I'm looking at these two neural networks and walking through how the $ijk$ values of $\Theta$ correspond to the layer, the node number.
Either there are redundant values or I'm missing how the ...
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Neural network cost function - why squared error?
Question: Why is the squared error most often used for training neural networks?
Context:
Neural networks are trained by adjusting the link weights.
The key factor that informs these adjustments is ...
3
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2
answers
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Negative introspection axiom and Euclidean property of accessibility relation
Revising the modal logic principles, I have encountered an negative introspection axiom:
$$ \vDash \neg \square \alpha \longrightarrow \square \neg \square \alpha $$
with additional information, that ...
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1
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Complexity analysis of alpha beta pruning of a full tree
I am trying to understand the derivation of a time complexity for an alpha-beta pruning algorithm but up till now have not found any reasonable recourse.
Many recourses claim that if you take a full ...
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Optimizing a function through reinforcement learning.
I want to know if reinforcement learning can be used for such optimization problems:
\begin{align}
& \max_{p_1^t, p_2^t}\quad\log_2(1+ p_1^t h_1^t)+\log_2(1+ p_2^t h_2^t) \\[6pt]
\text{s.t. } &...
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Books on AI, programming, optimization
I'm studying math (just started) and I like programming as well (just started this too), is there a career or a branch of research including deep aspect of this two aspects? Is there someone among you ...
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Why is the Error surface for a 2 input neural network with 2 weights a parabolic bowl
I am new to machine learning and AI in general and had a quick question regarding the error function surface regarding a simple neural net:
2 input neural net
After reading the following wiki: https:/...
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How to Calculate Values from Incoming Messages? - Evidence Propagation in Bayesian Network
I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process.
As an example, let's take ...
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3
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Games with human edge [closed]
Which are some two- or one-player games, where humans far outperforms the best computer programs? And how does the relative edge scale with time allowed to think? (In time frame 1 sec to 8 hours per ...
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Risk seeking utility
I am stuck on a question in an archived course on BerkeleyX's CS188x Artificial Intelligence.
Which of the following would be a utility function for a risk-seeking preference? That is, for which ...
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1
answer
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What does the following function mean?
The following is the mathematical definition of a Artificial Neuron,
$$\textbf{Activation function } f: \qquad y = f(w^t x) = f\left( \sum_{i=1}^n w_i x_i \right)$$
Given that $W$ is a vector, what ...
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Is there any mathematical work on formalizing problems and their solutions as mathematical objects?
Problems (tasks?) are an important part of life, science, math, basically everything. Do people study them as mathematical objects? Theorem proving seems close, however, I'm interested more in the ...
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binary resolution rule proof
I want to proof the binary resolution rule that is, if we For any two clauses $C_1$ and $C_2$, if there is a literal $L_1$ in $C_1$
that is complementary to a literal $L_2$ in $C_2$, then delete $L_1$ ...
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Memory of a neural network: is it forever?
As far as I remember a neural network cannot forget anything. Does this mean that no matters how evolved the network is, it's always going to throw me back the right output if I feed it an input?
And ...
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Definition of a neural network
I need a definition of neural networks in terms of mathematical mapping syntax. Since neural networks come in all different shapes I find it a little hard to come up with a definition that comprises ...
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What is the set of models of the empty set?
We have that :
$Mod (\emptyset) = \{ I \in Int_{At} / I \vDash \emptyset \}.$
My question is, what is the set of interpretations that satisfty the empty set?
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Why was the resolution method so important to AI/theorem proving?
I have read that the resolution method was literally a "miracle" for AI. So far, from what I understand, there are 2 things differentiating from other systems of inference rules:
Only a single ...
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How to solve $Ax = b$ using Simulated Annealing?
I have an idea how the Simulated-Annealing algorithm works w/ TSP, but I have no idea how to solve $Ax = b$, given an $n \times n$ matrix $A$ and a vector $b$. I know that it might sound stupid, but I ...
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Using implication with the Universal quantifier
While reviewing my AI textbook, I came across a paragraph that baffled me. It attempts to explain why the truth table for implication turns out to be perfect, as ...
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Gradient descent/ nonlinear optimization intuition needed
all. I'm taking an introductory AI class, and we're using the gradient descent algorithm to find the optimized/ lowest cost of a set of thetas (variable coefficients) to best fit a regression line. In ...
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Boolean Algebra Question
my problem is ,Please give the algorithm: how can rewrite an arbitrary propositional formula alfa(α) into a proposional formula beta(β) so that beta does not contain disjunction(∧) and alfa ...
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