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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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_{\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
71 views

Converting an English Sentence to WFF

I have been practicing conversion to WFF lately and am trapped in the following example: ...
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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 ...
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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 ...
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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&...
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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\...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $S_i^x$ ...
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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/...
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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 $\Gamma(\alpha) = (\alpha - 1)!$...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: $$\...
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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)...
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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)...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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})}{\...
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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 ...
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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 ...
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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 ...
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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 ...

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