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23

Yes, it has been done! However, the applications aren't to replace calculators or anything like that. The lab I'm associated with develops neural network models of equational reasoning to better understand how humans might solve these problems. This is a part of the field known as Mathematical Cognition. Unfortunately, our website isn't terribly informative,...


23

The notation I'll be using is from two different lectures by David Silver and is also informed by these slides. The expected Bellman equation is $$v_\pi(s) = \sum_{a\in \cal{A}} \pi(a|s) \left(\cal{R}_s^a + \gamma\sum_{s' \in \cal{S}} \cal{P}_{ss'}^a v_\pi(s')\right) \tag 1$$ If we let $$\cal{P}_{ss'}^\pi = \sum\limits_{a \in \cal{A}} \pi(a|s)\cal{P}_{ss'}^a ...


16

What is artificial intelligence? Artificial Intelligence is a very broad field and it covers many and very deep areas of computer science, mathematics, hardware design, and even biology and psychology. What math do you need? As for math, I think calculus, statistics, and optimization are the most important topics, but learning as much math as you can won'...


15

Good Mathematics Foundation Begin by ensuring full competency with intermediate algebra and some other foundations of calculus and discrete math, including the terminology and basic concepts within these topics. Infinite series Logical proofs Linear algebra and matrices Analytic geometry, especially the distinction between local and global extremes (minima ...


13

In artificial intelligence (sometimes called machine intelligence or computational intelligence), there are several problems that are based on mathematical topics, especially optimization, statistics, probability theory, calculus and linear algebra. Marcus Hutter has worked on a mathematical theory for artificial general intelligence, called AIXI, which is ...


12

First, a small clarification; they do not say that "the gradient of a deterministic policy is 0" (I'm not sure what, if anything, "the gradient of a policy") would mean. They are talking about how "this gradient" (referring to the gradient on the slide visible in the video) is 0 in the case where the policy ($\pi$) is deterministic. Now, here is the ...


10

To excel in in AI you need a mathematical intuition or point of view. In order to become a full stack AI engineer, it is important that you have a firm understanding of the mathematical foundations of machine learning. My advice to anyone preparing to jump into the field is that learning mathematics is about doing. Remember the 20/80 rule. You need to ...


10

Start with Andrew Ng's introduction to Machine Learning course on Coursera. There are not many prerequisites for that course, but you will learn how to make some useful things. And, more importantly, it will clearly show you which subjects you need to learn next.


9

Not really. Neural networks are good for determining non-linear relationships between inputs when there are hidden variables. In the examples above the relationships are linear, and there are no hidden variables. But even if they were non-linear, a traditional ANN design would not be well suited to accomplish this. By carefully constructing the layers and ...


9

I work as a professor, and recently designed the mathematics requirements for a new AI major, in consultation with many of my colleagues at other institutions. The other answers, particularly this one do a good job of cataloging all the specific topics that might be useful somewhere in AI, but not all of them are equally useful for understanding core topics. ...


9

EE Math Refresh AI is an interdisciplinary field. You can begin by ensuring you are fresh in the mathematics you've already taken. You may already have all the books from your BS and MS. Infinite series Logical proofs Linear algebra and matrices Analytic geometry, especially the distinction between local and global extremes (minima and maxima), saddle ...


9

Let's start by looking at: $$\max_s \Bigl\lvert \mathbb{E}_{\pi} \left[ G_{t:t+n} \mid S_t = s \right] - v_{\pi}(s) \Bigr\rvert.$$ We can rewrite this by plugging in the definition of $G_{t:t+n}$: \begin{aligned} & \max_s \Bigl\lvert \mathbb{E}_{\pi} \left[ G_{t:t+n} \mid S_t = s \right] - v_{\pi}(s) \Bigr\rvert \\ % =& \max_s \Bigl\lvert \mathbb{...


9

An important thing we're going to need is what is called the "Expected Grad-Log-Prob Lemma here" (proof included on that page), which says that (for any $t$): $$\mathbb{E}_{\tau \sim \pi_{\theta}(\tau)} \left[ \nabla_{\theta} \log \pi_{\theta}(a_t \mid s_t) \right] = 0.$$ Taking the analytical expression of the gradient (from, for example, slide 9) ...


7

The derivative of $\mathcal{L_1}(y, x) = (\hat{y} - y)^2 = (f(x) - y)^2$ with respect to $\hat{y}$, where $f$ is the model and $\hat{y} = f(x)$ is the output of the model, is \begin{align} \frac{d}{d \hat{y}} \mathcal{L_1} &= \frac{d}{d \hat{y}} (\hat{y} - y)^2 \\ &= 2(\hat{y} - y) \frac{d}{d \hat{y}} (\hat{y} - y) \\ &= 2(\hat{y} - y) (1) \\ &...


7

The MSE can be defined as $(\hat{y} - y)^2$, which should be equivalent to $(y - \hat{y})^2$ They are not just "equivalent". It is actually the exact same function, with two different ways to write it. $$(\hat{y} - y)^2 = (\hat{y} - y)(\hat{y} - y) = \hat{y}^2 -2\hat{y}y + y^2$$ $$(y - \hat{y})^2 = (y -\hat{y})(y - \hat{y}) = y^2 -2y\hat{y} + \hat{y}^2$$ ...


6

You'll find that both Calculus and Linear Algebra have some application in AI/ML techniques. In many senses, you can argue that most of ML reduces to Linear Algebra, and Calculus is used in, eg. the backpropagation algorithm for training neural networks. You'd be well served to take a class or two in probability and statistics as well. Programming ...


6

1) It is possible! In fact, it's an example of the popular deep learning framework Keras. Check out this link to see the source code. 2) This particular example uses a recurrent neural network (RNN) to process the problem as a sequence of characters, producing a sequence of characters which form the answer. Note that this approach is obviously different ...


6

I think the key part of your question is "as a beginner". For all intents and purposes you can create a state of the art (SoTA) model in various fields with no knowledge of the mathematics what so ever. This means you do not need to understand back-propagation, gradient descent, or even mathematically how each layer works. Respectively you could just ...


6

If what you are asking is what is the intuition for using the derivative in backpropagation learning, instead of an in-depth mathematical explanation: Recall that the derivative tells you a function's sensitivity to change with respect to a change in its input. A high (absolute) value for the derivative at a certain point means that the function is very ...


6

Consider a dataset $\mathcal{D}=\{x^{(i)},y^{(i)}:i=1,2,\ldots,N\}$ where $x^{(i)}\in\mathbb{R}^3$ and $y^{(i)}\in\mathbb{R}$ $\forall i$ The goal is to fit a function that best explains our dataset.We can fit a simple function, as we do in linear regression. But that's different about neural networks, where we fit a complex function, say: $\begin{align}h(...


6

A stochastic process has the Markov property if the probability distribution of future states conditioned on both the present and past states depends only on the present state or, more formally, the following equality holds. $$ p(s_{t+1} \mid s_{t}, s_{t-1:1}) = p(s_{t+1} \mid s_{t}), \forall t $$ The hidden Markov model (HMM) is an example of a model ...


5

You should begin from Dr Andrew Ng machine learning course on Coursera. It's probably the most popular course for newcomers in machine learning. It's a free course. You should also grab "Elements of Statistical Learning" ebook PDF. It's a free book. You may want to focus on: Regression Cross validation Bias-variance tradeoff Decision surface Gradient ...


5

When I got interested in AI, I started with the most basic things. My very first book was Russell&Norvig's Artificial Intelligence- A modern Approach. I think that's a good place to start, even if you're mostly interested in Deep Nets. It treats not just the basic AI concepts and algorithms (expert systems, depth-first and breadth-first search,knowledge ...


5

AI is quite large in scope and it sits at the intersection of several areas. However, there are a few essential fields or topics that you need to know Set theory Logic Linear algebra Calculus Probability and statistics I would recommend you to first explore the AI algorithms that you might be interested in. I advise you to start with machine learning and ...


5

To my knowledge, recursion does not play a strong role in the definition of modern AI techniques, although it does feature used in Lovasz's definition of 'Local Search' and Kurzweil is certainly an advocate. Recursion can be seen as an elegant 'architectural factorization' - building complexity by combining the results of smaller, similar patterns ...


5

In a genetic algorithm, crossover (recombination) is the analogy to mating in the real world. For example, you have some genetic information from each parent. In the case of an optimization where you have vectors of features (design variables), you could represent it as vector 1 and 2. Imagine each vector has 10 values. You grab the first 5 from vector 1, ...


5

Nim was actually one of the first games ever played by an electronic machine. It was called the Nimatron and was displayed at the 1940 New York World's Fair. It is also well known that neural networks can model the Xor-function, if they have enough layers. Despite that, Marvin Minsky is supposed to have killed neural networks in the sixties, by asserting ...


5

Your idea may be feasible in general, but a neural network is probably the wrong high level tool to use to explore this problem. A neural network's strength is in finding internal representations that allow for a highly nonlinear solution when mapping inputs to outputs. When we train a neural network, those mappings are learned statistically through ...


5

Not in such straight forward way as described, but neural networks are successfully applied to guide the search of proof. There are automated theorem provers. What they do look roughly like this: Get the mathematical statement Apply one of the known mathematical equivalence transformations (theorems, axioms, etc) Check, if the resulting statement is ...


5

Nonlinear relations between input and output can be achieved by using a nonlinear activation function on the value of each neuron, before it's passed on to the neurons in the next layer.


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