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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22 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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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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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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backward-chaining problem

Can a forward-chaining expert system that works be run as a backward-chaining system? I believe that it can, but forward-chaining is easier, at least in the case below. But I'm looking to confirm/...
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18 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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100 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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20 views

Sugarscape Axis'

How are the axis' of Growing Artificial Societies 51x51 grid interpreted? What do they denote? The configuration is unfamiliar to me being 5 sequential lots of [0,1,2 ... 9] each. It seems related to ...
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1answer
54 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 ...
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2answers
34 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
81 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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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
48 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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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
23 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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29 views

What arithmetic can be used to reduce a ratio to its lowest form?

In designing a chess heuristic, I find myself with three coefficients to balance to define the AI behavior. The heuristic is like below: $$h = c_1v + c_2m + c_3p$$ Where $v$ is material value, $m$ ...
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31 views

hybrid action space in reinforcement learning

I would like to know what kind of method we should use when the action space is a compound of discrete and continuous space. For example, an auto-drive car could go three directions: forward, left, ...
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1answer
57 views

Can dummy True/False be in the consequent side of the implication and what it could mean?

It is known that False -> SomeFact is the use of the implication for the representation of the facts in the propositional and first order logic. The Sequent (of ...
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10 views

AI: search algorithms stop criteria

I hope this is the right place to ask this question (if not, please tell me where). I need help on Artificial Intelligence: in search algos, what is (if it exists) the stop criteria? I.E. if i have to ...
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Are there games with multiple (parallel, competing) gain/loss functions?

The conventional games contain one gain/loss function for each agent. This can formalize the monetary reward for the agent. But are there games with multiple gain/loss function for each agent? E.g. ...
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1answer
38 views

how to calculate number of states for this logistics problem?

Consider a logistics problem with 3 cities, 5 trucks and 3 packages. Each truck can be at any of the locations. A package can either be at one of the locations or in one of the trucks. What would the ...
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How to write SVR's constraint from into a single function with loss function in linear case?

The loss function is an e-insensitive loss meaning won't punish anything smaller than a setting e. The slide simply says if choosing the right $\lambda$, the SVR is equivalent to solve the right one. ...
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Is there a class of functions that have a cyclical or constant derivative?

I'm working on approximating functions in A.I., and I noticed that everyday functions seem to, at some point, have either a cyclical, or constant, derivative. For example, a straight line has a ...
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Consider the Car-Starting network in Figure 1.

Consider the Car-Starting network in Figure 1 and let B = Battery, F = Fuel, G = Gauge, T = Turn Over, and S = Start. The conditional probabilities are then given by: P(B = bad) = 0.02 P(F = empty) = ...
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135 views

How does a hinge loss function work?

I have been taking this course of Artificial Neural Network online and can't understand what the expression: means. What does max{0,1 - this part I understand } mean? I have searched online, but ...
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1answer
99 views

Probability and Statistics book for recent math graduate working in machine learning

I know similar request have been made numerous times, but I am looking for a very specific type of a probability/stat book. I just graduated with a Bachelor's in mathematics and am currently working ...
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What are the differences between a linear logic based planner and a first order logic based planner

Linear logic based planners and first order logic based planners must have different strengths and weaknesses. I would appreciate help in understanding what these strengths and weaknesses are and ...
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1answer
102 views

Softmax policy parametrization and binary state features

I have a fairly simple "mountain car"-ish problem, where the agent is in some position and must decide whether to go left or right. The state space is continuous and the action space is discrete. I'm ...
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2answers
91 views

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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1answer
34 views

(A ⇔ B) ∧ (¬A ∨ B) is it satisfyable ? Artificial intelligence a modern approach by norvig

Hi I am not able to solve this question, it's from book artificial intelligence a modern approach by Norvig and peter. Help would be appreciated.
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1answer
47 views

What kind of math should I learn before I tackle policy search PEGASUS research paper by Andrew Ng?

I provided the link below https://ai.stanford.edu/~ang/papers/uai00-pegasus.pdf the paper was referenced in the AI: Modern Approach book, and I would like to dive in depth into it. But my math is ...
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1answer
85 views

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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43 views

mathematical proof of fast convergence of an nature-inspired algorithm

I am using the Moth-flame optimization algorithm to solve a problem. The algorithm uses logarithmic spiral to update the position of the moths. I have been asked to provide a mathematical proof to ...
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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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1answer
78 views

how is local minima possible in gradient descent?

gradient descent works on the equation of mean squared error, which is an equation of a parabola y=x^2 we often say weight adjustment in a neural network by ...
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1answer
44 views

Markov Decision Process - Discounted return

I was reading this article about Discounted return (in the context of MDP): http://deeplizard.com/learn/video/a-SnJtmBtyA I got the section: ...
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1answer
2k views

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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1answer
29 views

Different order of insertion - different Bayesian network ? how to prove formally?

I have some Bayesian network which i constructed from some data, say it consists of nodes A, B, C and D and that was the initial order of insertion. If i ...
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2answers
289 views

First Order Logic to CNF for Knowledge Base

I am doing some Homework for an Artificial Intelligence Course, we are covering some First Order Logic and Conjuctive Normal Form. Here are the questions that I have to answer that I am having ...
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31 views

Variable transformation for training a machine learning model

Suppose you have a train set $\mathbf{T}$ and you want to train some Machine Learning models. Each row of $\mathbf{T}$ consists in a set(vector) of attributes or variables $\mathbf{x} = (x_1, x_2...)$ ...
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1answer
118 views

MGU - most general unifier for skolem functions?

I have trouble understanding MGU for functions, especially skolem functions. Is it correct that in order to find MGU for 2 functions, say f(x) and g(y) then they ...
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Derivation Contrastive Divergence

I am trying to follow the original paper of GE Hinton: Training Products of Experts by Minimizing Contrastive Divergence However I can't verify equation (5) where he says: $$ -\frac{\partial}{\...
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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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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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1answer
173 views

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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1answer
483 views

What is the output in a RNN?

I have recently been looking for some information about recurrent neural networks. Some people use a layer between the hidden state and the output and other ones use the hidden state as output. What ...
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What's going on in this sum?

This is part of a slope calculation example to update the new weight of a neural network from the slope. From a Deep Learning course on DataCamp My math is a bit dodgy and what I don't understand is ...
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1answer
89 views

reverse mapping of SVM kernel into original feature space

I am experimenting with support vector machines (SVM) following this book Without a kernel, it is very easy to "summarize" the SVM optimal solution, as you only need the separator hyperplane w, equal ...
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1answer
138 views

Turn into Proposition logic

I am new to logic. I am suffering to turn one of the following sentences from normal form into propositional logic. Paragraph as follows: ...
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What courses should I take in my Masters for PhD in mathematics - artificial intelligence? [closed]

I am currently enrolled in a masters programme in mathematics and I am taking mostly courses in mathematical statistics, but also dynamical systems and analysis. And I'm wondering if I want to go ...