Questions tagged [math]
For questions about mathematics related to artificial intelligence.
5
votes
2answers
52 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 that weight adjustment in a neural network by gradient descent algorithm can hit ...
1
vote
2answers
45 views
What does the formula $1-\sum_i(e_i-a_i)^2$ mean in this NEAT Python API?
I have looked at the documentation for the NEAT Python API found here, but it shows calculus like this:
The error for each genome is $1-\sum_i(e_i-a_i)^2$
I haven't learned calculus at the moment....
-1
votes
0answers
58 views
Can differential equations be replaced by a neural networks?
Introduction Artificial Intelligence can be realized in many ways. A common criteria is to distinct between Narrow AI and Strong AI. Strong AI is often described as a cognitive architecture which will ...
5
votes
2answers
93 views
Are on-line backpropagation iterations perpendicular to the constraint?
Raul Rojas' Neural Networks A Systematic Introduction, section 8.1.2 relates off-line backpropagation and on-line backpropagation with Gauss-Jacobi and Gauss-Seidel methods for finding the ...
2
votes
1answer
55 views
Which matrix represents the similarity between words when using SVD?
Two words can be similar if they co-occur "a lot" together. They can also be similar if they have similar vectors. This similarity can be captured using cosine similarity. Let $A$ be a $n \times n$ ...
5
votes
3answers
74 views
How can a collaboration game be defined mathematically?
One of the common conceptions in AI is the idea of game theory. We see that in the predominance of chess and other games in the literature as metrics of AI success. We see it in the names of machine ...
2
votes
0answers
31 views
How can the convolution operation be implemented as a matrix-vector multiplication?
How can the convolution operation used by CNNs be implemented as a matrix-vector multiplication? We often think of the convolution operation in CNNs as a kernel that slides across the input. However, ...
0
votes
0answers
19 views
How is the convolution operation used in CNNs a special case of the convolution operator?
How is the convolution operation used in convolutional neural networks (CNNs) a special case of the mathematical convolution operator? Most of us, when we think of the "convolution operation", we ...
8
votes
1answer
164 views
What is the Bellman operator in reinforcement learning?
In mathematics, the word "operator" can refer to several distinct but related concepts. An operator can be defined as a function between two vector spaces, it can be defined as function where the ...
1
vote
0answers
12 views
Does a mechanical system repeats itself?
The inverted pendulum problem is a famous control task. It can be solved with a technique called system identification. System identification means to formalize the state-action space of a system in a ...
0
votes
2answers
90 views
What are examples of applications of the Fourier transform to AI?
The (discrete and continuous) Fourier transform (FT) is used in signal processing in order to convert a signal (or function) in a certain domain (e.g. the time domain) to another domain (e.g., ...
1
vote
1answer
44 views
Why is MSE used over other quadratic loss functions?
So I was wondering, why I have only encountered square loss function also known as MSE. The only nice property of MSE I am so far aware of is its convex nature. But then all equations of the form $x^{...
1
vote
3answers
86 views
Is it possible to compute $P( F \mid S )$ given $P(F \mid S,A)$, $P(F \mid S, \lnot A)$?
I have a bayesian network, which has the following data:
$P(S) = 0.07$
$P(A) = 0.01$
$P(F \mid S,A) = 1.0$
$P(F \mid S, \lnot A) = 0.7$
$P(F \mid \lnot S, A) = 0.9$
$P(F \mid \lnot S, \lnot A) =...
1
vote
0answers
20 views
Calculating tangent vector of curve s(P,$\alpha$) at given point $\alpha$ = 0
I am reading the paper "Transformation Invariance in Pattern Recognition – Tangent Distance and Tangent Propagation", where the tangent vector is calculated for the given curve $s(P,\alpha)$ at $\...
5
votes
2answers
146 views
Why exactly do neural networks require i.i.d. data?
In reinforcement learning, in general, successive states (actions and rewards) are highly correlated. An "experience replay" buffer was used, in the DQN architecture, to avoid training the neural ...
4
votes
0answers
41 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
117 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
vote
1answer
48 views
Is the next state drawn 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
50 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 ...
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
vote
0answers
15 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
votes
1answer
39 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 ...
4
votes
1answer
79 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
136 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
votes
1answer
54 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
vote
0answers
169 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
vote
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
67 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
327 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
449 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
vote
1answer
48 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
...
6
votes
3answers
139 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
454 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
64 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
77 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
vote
0answers
29 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 ...
13
votes
4answers
2k 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
votes
3answers
272 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
votes
1answer
109 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
vote
0answers
24 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
69 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
259 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 ...
3
votes
3answers
495 views
AI applications of the Fibonacci series
I have been looking at Fibonacci series, the golden ratio and its uses in nature, like how flowers and animals grow based on the series.
I was wondering whether we could use the Fibonacci series and ...
4
votes
1answer
138 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
421 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
4answers
128 views
Understanding a few terms in Andrew Ng's definition of the cost function for linear regression
I have completed week 1 of Andrew Ng's course. I understand that the cost function for linear regression is defined as $J (\theta_0, \theta_1) = 1/2m*\sum (h(x)-y)^2$ and the $h$ is defined as $h(x) = ...
1
vote
1answer
52 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
102 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 ...
