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.
216
questions
0
votes
1answer
41 views
PAC Learnability (Finite Hypothesis) The Realizability Assumption [closed]
I am currentyl reading "Understanding Machine Learning Theory and Algorithms " and can't understand one part.
For finite hypothesis classs to be PAC-learnable, the sample complextiy is $m_{\...
0
votes
0answers
26 views
Which standard deviation for model averaging?
I hope math stack exchange is the right place for this question, even though it comes from an AI point of view.
Say I have a machine learning model and for robustness of results, I initialize it with ...
0
votes
1answer
20 views
ReLU on a feature map
I have produced a feature map, that is 5x3, of a input layer which was 5x7. I have obtained "2:s" and "3:s" and also one "1". The aim is now to use the ReLU neuron on ...
0
votes
0answers
7 views
How to do clustering on a set of paraboloids and on a set of planes?
I am performing cluster analysis in two parts: in the first part (a), it is clustering on a set of paraboloides and in the second part (b), on a set of planes. The parts are separated, but in both I ...
1
vote
0answers
51 views
Help with Resolution Refutation Problem
I'm trying to convert Solve a Resolution Refutation problem. The problem states: Knowledge Base is ∀𝑥𝑦 𝐹(𝑥, 𝑦). Prove using resolution-refutation that ∀𝑥𝑦 𝐹(𝑦, 𝑥). Note: β = F(y, x) This ...
0
votes
1answer
48 views
water jug problem [closed]
The original version of water jug problem is that we have two empty jugs and an infinite source of water and the goal is to find a way to reach a state so that one of the jugs contains a specific ...
2
votes
1answer
71 views
Converting an English Sentence to WFF
I have been practicing conversion to WFF lately and am trapped in the following example:
...
4
votes
1answer
107 views
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 ...
0
votes
1answer
30 views
Removing Implication in the Conversion of WFF to Clausal Form
I understand the conversion algorithm, my concern is regarding the first step of 'Removing Implication'.
Example: In the following figure when one removes implication, the negation comes before ...
0
votes
0answers
14 views
saddle point of a min-max problem over convex compact polytopes
In my optimisation notes, I have come across how one may "compute a Nash equilibrium in a two-player zero sum game by finding a saddle point of a min-max problem over convex compact polytopes&...
-1
votes
1answer
39 views
Solve this by converting sentences to clausal form? [closed]
If:
$E\land R \implies B$
$E\implies R\lor P\lor L$
$K\implies B$
$\lnot(L\land B)$
$P\implies \lnot K$
Which of the following can't be deducted?
$E\land P$
$K \land E \implies R$
$L \land P \implies\...
3
votes
1answer
61 views
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 ...
0
votes
1answer
72 views
Does empty set entails everything?
I am new to propositional logic, and I am trying to figure out whether the below statement is correct:
[a |= c] or [ b |= c] → [a^b |= c]
First of all, it is ...
0
votes
1answer
48 views
Determining Independence in Bayesian Network
Consider the Bayesian Network Structure Below, decide whether the statements are true or false.
b) $G \perp \!\!\! \perp A$ (G is independent of A)
c) $E \perp \!\!\! \perp H | \{D,G\}$ (E and H are ...
0
votes
1answer
65 views
You know the probability that an object is dirty. An unreliable sensor tells you its true state. What is the new probability that the object is dirty?
I have encountered a statistics related problem for an AI project that I don't know how to solve, but I'm also nearly statistically illiterate so I'm not sure where to look. Hoping I can get a tip ...
0
votes
0answers
5 views
Decision tree root
I have a set of examples in the table : https://imgur.com/a/mBc2td4 , there are 3 properties with possible values "a","b","c". I am going to build a decision tree on this ...
1
vote
0answers
45 views
Why does k-means have more bias than spectral clustering and GMM?
I ran into a 2019-Entrance Exam question as follows:
Which of the following algorithm has the higher bias?
GMM
GMM (identity covariance matrix)
spectral clustering
k-means
The answer mentioned is (...
0
votes
0answers
111 views
Are Resnet Neural Networks non-affine transformations with linear activation functions
Given an Artificial Neural Network that allows "skip" connections or inter-layer connections such as found in Resnet, is it possible to get non-affine mappings of the input to the output ...
0
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0answers
124 views
T-algebra and a matrix paradigm over the algebra
We established a novel semisimple commutative algebra called t-algebra, which is backward-compatible to the field of complex numbers. Many notions of complex numbers and matrices are generalized. The ...
0
votes
0answers
21 views
Does lattices (partially ordered sets) admit some kind of metrics / geometry - “distance” among elements?
I am reading article https://arxiv.org/abs/2101.05125 (at least partially completed at Google DeepMind and which features the gradual move of Artificial Intelligence community from subsymbolic big ...
1
vote
1answer
55 views
Is this textbook's combinatorial reasoning for $n \times n! / (b!(n - b)!)$ incorrect?
I recently asked this question on cs.stackexchange.
I am currently studying the textbook Artificial Intelligence: A Modern Approach, 4th Edition, by Russell and Norvig. Chapter 3 Solving Problems by ...
0
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0answers
14 views
Different type of XGBoost trees
I was going through StatQuest's video on XGBoost and came across the following note by the author:-
"There are many ways to build XGBoost trees. This video focuses on the most common way to build ...
0
votes
0answers
33 views
Updating probability distribution for decision making in game AI.
I'm programming an AI simulation where a car is randomly driving around a area. Within this area there are 5 repair shops. While driving, the car get's damaged (1% for every step). Once the damage of ...
2
votes
0answers
18 views
Using Bayesian Networks to solve this localization problem?
I'm reading this paper, which I'll summarize here:
Let a sensor network (in this case, a network of radio receivers)
consist of $N$ sensor nodes at locations $S = \{ S_1 \cdots S_N\}$.
Let $S_i^x$ ...
0
votes
0answers
26 views
Non continuous Fuzzy Set
I stuck in this question for a few hours now. Can anyone help me?
$ A ̃ $ is a non continuous fuzzy set and is defined by:
$ A ̃ = \{0.6/x_1 +0.5/x_2 + 1/x_3 + 0.75/x_4 + 0.7/x_5 + 0.8/x_6 + 1/...
0
votes
3answers
28 views
Mean of unormalized Gamma distribution
If $X$ follows a gamma distribution with parameters $\alpha$ and $\beta$ then:
$ p(x|\alpha,\beta) = \frac{\beta^{\alpha}x^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)}$
with $\Gamma(\alpha) = (\alpha - 1)!$...
0
votes
0answers
28 views
In CNNs, why do we sum the filter derivatives w.r.t the loss function to get the final gradient?
In a Convolutional Neural Network, unlike the fully connected layers, the same filter is used multiple times on the input while convolving - so during backpropagation, we get multiple derivatives for ...
0
votes
0answers
12 views
How to interpret this discriminator loss
It's from this paper: https://arxiv.org/pdf/2008.12205.pdf
I'm confused about the last part of the equation and how to interpret it. In the paper, it mentions x(hat) is sampled from the real and fake ...
0
votes
0answers
10 views
Reforming coordinate data from axis histograms?
So, I have a set of ~2 million datapoints from a microscopy image that I have plotted in R, and then used histogram analysis on the x- and y-axes in order to detect bands of datapoints (it's a very ...
0
votes
1answer
82 views
Introduction to AI
In the book Introduction to artificial intelligence the author ask this question:
Why is a deterministic agent with memory not a function from the set of all inputs to the set of all outputs, in the ...
-1
votes
1answer
40 views
Saying either or both in first-order predicate logic?
I have a statement along the gist of "Each member of A is either Y, Z, or both"
Would the appropriate way to write this using first-order logic be:
∀x (A(x) → (Y(x) ∨ Z(x)))
Would it suffice ...
0
votes
1answer
153 views
Ways to write CNF for an implication with disjunction?
I have the following statement before it's converted to CNF: p → (s ∨ q). When I initially convert this to a CNF, I get the following: ¬p ∨ (s ∨ q).
I'm wondering if I could use laws of associativity ...
0
votes
1answer
96 views
Biconditional elimination and implication elimination rules canceling statement out?
I'm learning about propositional logic and converting statements to conjunctive normal form. If I have a statement such as $t \leftrightarrow q$, a biconditional statement,
and I apply apply ...
0
votes
0answers
14 views
How to design a loss function that encourages the approximator approach the real funtion in a given direction?
Consider that we have an approximator (i.e. neural networks) $g(x; \theta)$ parameterized by $\theta$, the goal is to approximate the real function $f(x)$ from below as much as possible but not over ...
1
vote
4answers
107 views
Why $A \rightarrow B \Leftrightarrow \textrm{( A is False or B is True )} $
I am reading a book about Artificial intelligence and Knowledge representation and there is a logic formula that I cannot explain
Why $A \rightarrow B \Leftrightarrow \textrm{( A is False or B is True ...
1
vote
1answer
143 views
Calculate a formula using back-propagation algorithm
English isn't my first language, so I'm sorry if I am unable to clearly describe the problem. Recently I have encountered a question in my artificial intelligence course that I am unable to wrap my ...
0
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0answers
20 views
SAT-Solver for default extensions
Assume I have written an algorithm to get a default extension of a normal default theory by employing a SAT solver that often terminates fast when the formula is satisfiable.
My algorithm has the ...
1
vote
0answers
32 views
What is the parameter update rule for neural networks
I am currently taking a machine learning course and had a question about the update rule for $\theta$ in neural networks. In the discussion of previous learning algorithms, the professor defined:
$$\...
1
vote
0answers
110 views
Associative property in discrete 2D convolution
In CNN is tipically put on in cascade differents types of convolution layers, for example a 2D Convolution along with 2D Average Pooling. The convolution has the associative property:
$$(A*B)*C=A*(B*C)...
1
vote
1answer
21 views
What's the fundamental difference between Tabular Q-learning and Q-learning (with off policy TD-control)
I have two equations.
Q-learning with off policy TD-control :
$$Q(S_t, A_t) \leftarrow Q(S_t, A_t) + \alpha[R_{t+1} + \gamma_{max}Q(S_t, A_t)]$$
Tabular Q-learning:
$$Q(s,a) \leftarrow (1-\alpha)...
1
vote
1answer
22 views
Can L1 Distance Give Underestimates In a 2-D Rectangular Lattice?
I am working on this program that plays PacMan and involves calculating the Manhattan distance between the player and some enemies.
Here's my problem, if we have an enemy straight ahead of the ...
0
votes
1answer
21 views
More concise way of saying this?
I have written this:
For the one highlighted in red, is there a more compact way of writing it?
-4
votes
1answer
114 views
Why hasn't artificial intelligence tackled axiom-heavy math such as abstract algebra yet?
(the question is contained in the title)
Abstract algebra is my first axiom-and-proof based mathematics course. Granted there are a limited number of axioms for the thing you're studying, it seems ...
0
votes
1answer
59 views
Whats meant by the identity function in this question?
It is generally desirable in the context of perceptron learning to have a trainable
threshold s. Prove that a one-input neuron with a fixed threshold s =−1 could ...
0
votes
2answers
42 views
Representing a sentence using propositional logic
I am confused regarding a propositional logic representation of a sentence.
Please note that this sentence is not realistic:
"A person who is male (M) is smart (S) if he is tall (T), but otherwise ...
0
votes
2answers
127 views
Can someone please explain this chain rule based derivation to me?
$$
\text{Loss}(y, \hat{y}) = \sum_{i=1}^n \left( y- \hat{y} \right)^2
$$
$$
\begin{split}
\frac{\partial \text{Loss}(y, \hat{y})}{\partial W} &= \frac{\partial \text{Loss}(y, \hat{y})}{\...
0
votes
0answers
26 views
Artificial intelligence - Search algorithm from coordinates
Assume that we have have this grid with coordinates.
We start at 0.0 (it's actully 0,0 but my Libre Office cannot handle 0,0 due to my settings) and we want to go to -3.10
Is there any search ...
1
vote
1answer
49 views
Can I compute the trajectory in a maze if I know the walls? [closed]
Let's assume that I have a mouse in a maze and the mouse need to find the exit.
I know where the exit is and where my position is. I also know the position of the walls.
How can I compute the ...
1
vote
0answers
8 views
Implementing Actor-Critic with Experience Replay for Continuous Action Spaces
I have been trying to implement the ACER algorithm for continuous action spaces in reinforcement learning. The paper for the algorithm can be found here:
Sample Efficient Actor-Critic with Experience ...
0
votes
1answer
32 views
Proving two different universal machine types give equivalent results in original Solomonoff induction paper
Solomonoff's original paper about Solomonoff induction contains the following (p. 18):
Suppose $M$ to be a universal machine with binary input alphabet, and an output alphabet that is the same as ...
