Chaos, fractal and artificial intelligence

Chaotic

Chaos here is not the meaning of chaos, but a property of all things in the world. People try to find a certain law of the development of natural things, and then use the mathematical formula to abstract out, hoping to predict the future of things development trajectory, most of the time can be effective, but very rarely, there will be problems, unpredictable conditions, such as climate change, the stock market suddenly plunged. All these embody the chaotic properties of things. Chaos means that in a system that can be accurately described by mathematical equations, unpredictable phenomena can be generated spontaneously and without any external intervention. One misconception is that chaos is all things are very complex and confusing. The facts are simpler and more complex than this. By using a very simple law or equation, and without any randomness in it, all elements of the system are deterministic, and we fully grasp the rules of the system, and even such systems produce completely unpredictable phenomena. Due to the internal structure of the system, in some cases, even at the initial time there is a little error, even if the error is too small to measure, this error will continue to be magnified with each calculation, as the system, the state of the system will deviate from the state you expect 1.1 points, resulting in the butterfly effect. Chaos is a basic law of physics. Simple mathematical equations can breed complex behaviors that are more complex than we imagined. So a simple and mechanical system can show complex and rich behavior. Nature has inherent unpredictability, and this unpredictable internal driving force can also make the system show a specific structure.

Fractal

Order and chaos are closely related, the common denominator of all shapes in nature is self-similarity, constantly repeating themselves at a smaller scale. The white clouds floating in the sky, if viewed from a smaller scale, you will find very similar to the whole; When you zoom in locally, you will also find that this part is made up of a number of small peaks, and you will find that each part is made up of smaller parts similar to itself, from the trunk to the channel of the Leaf; Flying flock of birds. This repetition of one's own characteristics on a smaller scale creates the complexity of a system that is made up of simple structures. For example, the Mandebro set is represented by a formula as follows:
z = z   2   +C The resulting Mandebro set image is as follows:

From the picture as a whole, will think this is a very complex image, but when you zoom in, you will find that each of its small scale is the same as the larger scale, and to achieve this effect behind, is just a simple mathematical formula, The result of the previous step (the dependent variable) is again assigned to the argument (in fact both the variable and the argument are the same variable), which is much like the iteration in the program. Is this system (Mandebro set pattern) made up of simple constructs (the simple formula above) look complicated?

Artificial intelligence

Fractals are repeating themselves on a much smaller scale, and I can interpret this repetition as a self-feedback, and for a neural network with feedback, this feedback is reflected in the output structure of one processing once again returning to the previous level to calculate again. This is a system with self-feedback. Frequent use of this feedback method makes it possible to learn and evolve the network, and this extremely simple law breeds complex phenomena. While this complex phenomenon is unpredictable, you can judge a bird's movement by taking a bird, but the movement of a flock of birds is difficult to judge, either to the left or to the right, or up or down, and one of the reasons may be that one of the birds suddenly changes direction, but you can't predict it to happen. This results in the chaotic properties of the group. In the case of artificial intelligence, the individual believes there is such a situation. In training the network to learn, we do not know how it is learned, it is how to abstract a variety of concepts (can refer to the article Deep Neural network gray area: interpretative problems). Chaotic properties are likely to cause some unknown unpredictable behavior in AI. As Finch has said in the tracking of suspects, "We don t know AI".
(Purely personal point of view ... ）

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Chaos, fractal and artificial intelligence