Abstract
Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI.
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Notes
- 1.
A typical usage of the big O notation is asymptotical and refers to the largest input value since its contribution grows the fastest and makes other inputs irrelevant.
- 2.
Caveat: it only performs faster than other algorithms for numbers with over \(2^{4096}\) digits, i.e. bits, which is seldom practical even for big-data purposes.
- 3.
Presuppose we have a computable function (that solves the halting problem). That function runs a subroutine which detects whether our function will halt, and if that subroutine returns true, it should loop forever. If the function fulfils the condition of halting and returns true, then it will loop forever and never halt. However, if it returns false and does not halt, it will not loop forever, so it will immediately halt. These two contradictions then bring down the presupposition that it was a computable function.
- 4.
That is, material things like brains, and hence computers, cannot have mental states.
- 5.
The subjective experiences are usually known in philosophy as qualia.
- 6.
Suppose that we were able to succeed in constructing a computer that seems to understand Chinese. The computer takes Chinese characters as input, follows the programmed instructions and produces other Chinese symbols as an output. Suppose that it does it so competently that it passes the Turing test and convinces a human who speaks Chinese that the program is a human Chinese speaker. Searle then asks the question does the machine really understand Chinese, or it is merely simulating that ability.
- 7.
That is, the decision version tests whether the given route is the shortest route or not.
- 8.
Feature extraction consists of finding the most informative and yet compact set of properties or characteristics for a given problem.
- 9.
Classification is giving a discrete class/category label. Our mapping function needs to be as accurate as possible so that whenever there is a new input data x, we can predict the output variable y, for example, for a picture of a cat, we can put it in a category cat and not dog. In supervised machine learning, where we are training on one (usually larger) dataset and then checking our performance on another dataset, there is also regression, where the output variable is numerical or continuous, for example, “the price of this bike is $1500”.
- 10.
Multilayer networks. For example, in computer vision, in face detection, the first layer in a neural network may find regions or edges, the second may find eyes, nose and mouth, the third will make a face contour, etc.
- 11.
Overfitting is when a model corresponds too closely to a particular dataset, which usually means it will fail on more general examples since it contains too many specific parameters. For example, if we were to train a model that can recognize animal and human faces, using pictures of cats, which we described thoroughly to form our relevant attributes, our model could look for pointy ears as a relevant property, and work on cats but not on other animals nor humans (maybe it would work on Vulcans and Elves).
- 12.
Gradient descent is an optimization algorithm for finding the minimum of a function.
- 13.
These are two-layer neural networks that are trained to reconstruct the context. If you remove a word, it can predict what the words next to it could be, and finally, as a result, words that share common contexts are close together in the vector space.
- 14.
Two diagrams, where one has a common attribute that is lacking in the other, see [8].
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Šekrst, K. (2020). AI-Completeness: Using Deep Learning to Eliminate the Human Factor. In: Skansi, S. (eds) Guide to Deep Learning Basics. Springer, Cham. https://doi.org/10.1007/978-3-030-37591-1_11
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