When my first son was only two, he already loved cars, knew all brands and models (even more than I, thanks to my friends), could recognize them by a small part of the image. Everyone said: genius. Although they noted the complete uselessness of this knowledge. And the son, meanwhile, slept with them, rolled them, placed them exactly in a row or in a square.
When he was 4, he learned to count, and at 5 he could already multiply and add within 1000. We even played Math Workout (this game is on Android - I liked to calculate in the subway after work), and at some point he became me only do so. And in his free time, he counted up to a million, which froze those around him. Genius! - they said, but we suspected that not quite.
By the way, in the market he helped his mother quite well - he calculated the total amount faster than the sellers on the calculator.
At the same time, he never played on the court, did not communicate with peers, did not get along very well with children and teachers in the kindergarten. In general, he was a little reserved child.
The next step was geography - we tried to channel the love of numbers somewhere, and gave our son an old Soviet atlas. He plunged into it for a month, and after that he began to ask us tricky questions in the style:
- Dad, which country do you think has a large area: Pakistan or Mozambique?
“Probably Mozambique,” I replied.
- But no! The area of Pakistan is as much as 2,350 km2 more, - the son happily answered.
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At the same time, he was absolutely not interested in either the peoples inhabiting these countries, or their languages, or clothes, or folk music. Only bare numbers: area, population, volume of mineral reserves, etc.
Everyone admired again. “Clever beyond his years,” they said around, but I again got worried, because I understood that this is completely useless knowledge, not tied to life experience, and which is difficult to continue to develop. The best application of all that I have found was a proposal to calculate how many cars will fit in a parking lot if a particular country is rolled up with asphalt (without taking into account mountainous terrain), but I quickly stopped, because it smacks of genocide.
Interestingly, by this time the topic of cars was completely gone, the son did not even remember the names of his favorite cars from his huge collection, which we began to distribute with a loss of interest. And then he began to count more slowly in his mind and soon forgot the squares of countries. At the same time, he began to communicate more with his peers, became more contact. The genius passed, the friends stopped admiring, the son became just a good student with a penchant for mathematics and exact sciences.
Repetition is the mother of learning
It would seem what all this is for. This is seen in many children. Their parents declare to everyone that their children are genius, grandmothers admire and praise children for their "knowledge". And then they grow into ordinary, simply smart children, no more genius than the son of my mother's friend.
While studying neural networks, I encountered a similar phenomenon, and it seems to me that certain conclusions can be drawn from this analogy. I'm not a biologist or neuroscientist. All further - my guesses without a claim to be particularly scientific. I would be glad to receive comments from professionals.
When I tried to understand how my son learned to count faster than me so cool (he completed the level in Math Workout in 20.4 seconds, while my record was 21.9), I realized that he does not count at all. He memorized that when 55 + 17 appears, you need to click on 72. On 45 + 38, you need to click on 83, and so on. At first, of course, he counted, but the jump in speed occurred at the moment when he was able to remember all the combinations. And quite quickly he began to memorize not specific inscriptions, but combinations of symbols. This is exactly what they teach in school, studying the multiplication table - remember the correspondence table MxN -> P.
It turned out that he perceived most of the information precisely as a connection between the input data and the output, and that very general algorithm that we are used to scrolling through to get an answer was not just reduced to a very well-honed highly specialized algorithm for counting two-digit numbers. He did some excellent tasks, but much slower. Those. what everyone thought was super cool was actually just simulated by a well-trained neural network for a specific task.
Extra knowledge
Why do some children have the ability to memorize this way, while others do not?
Imagine the child's field of interest (here we approach the question qualitatively, without any measurements). On the left is the field of interests of an ordinary child, and on the right is the field of interests of a "gifted" child. As expected, the main interest is concentrated in areas for which special aptitudes. But for everyday things and communication with peers, the focus is no longer enough. He considers this knowledge superfluous.
The interests of an ordinary child 5 years old.
The interests of a "brilliant" child of 5 years old.
In such children, the brain analyzes and conducts training only on selected topics. Through training, the neural network in the brain must learn to successfully classify the incoming data. But the brain has many, many neurons at its disposal. Much more than is necessary for normal work with such simple tasks. Usually, children solve many different problems in life, but here all the same resources are thrown into a narrower range of tasks. And training in this mode easily leads to what ML professionals call overfitting. The network, using an abundance of coefficients (neurons), has trained in such a way that it always gives exactly the necessary answers (but it can give out complete nonsense on intermediate input data, but no one sees it). Thus, the training led not to the fact that the brain selected the main characteristics and remembered them, but to the fact that it adjusted many coefficients,to give an accurate result on already known data (as in the picture on the right). Moreover, the brain has learned so-so on other topics, having poorly trained (as in the picture on the left).
What is underfitting and overfitting?
For those who are not in the subject, I will tell you very briefly. When training a neural network, the task is to select a certain number of parameters (weights of communication between neurons) so that the network responds to the training data (training sample) as closely and accurately as possible.
If there are too few such parameters, then the network will not be able to take into account the details of the sample, which will lead to a very rough and averaged answer that does not work well even on the training sample. Similar to the picture on the left above. It's underfitting.
With an adequate number of parameters, the network will give a good result, "swallowing" strong deviations in the training data. Such a network will respond well not only to the training sample, but also to other intermediate values. Like the middle picture above.
But if the network is given too many configurable parameters, then it will train itself to reproduce even strong deviations and fluctuations (including those caused by errors), which can lead to complete nonsense when trying to get a response to input data not from the training sample. Something like the picture on the right above. It's overfitting.
A simple illustrative example.
Let's say you have multiple points (blue circles). You need to draw a smooth curve to predict the position of other points. If we take, for example, a polynomial, then at small degrees (up to 3 or 4), our smooth curve will be quite accurate (blue curve). In this case, the blue curve may not pass through the original points (blue points).
However, if the number of coefficients (and therefore the degree of the polynomial) is increased, then the accuracy of passing the blue points will increase (or even there will be a 100% hit), but the behavior between these points will become unpredictable (see how the red curve fluctuates).
It seems to me that it is the child's tendency towards a specific topic (obsession) and complete ignorance of the rest of the topics that leads to the fact that when teaching too many "coefficients" are given to these very topics.
Considering that the network is configured for specific input data and did not highlight the "features", but stupidly "remembered" the input data, it cannot be used with slightly different input data. The applicability of such a network is very narrow. With age, the horizons broadens, the focus becomes blurred, and there is no longer an opportunity to assign the same number of neurons to the same task - they begin to be used in new tasks more necessary for the child. The "settings" of that overfitted network collapse, the child becomes "normal", the genius disappears.
Of course, if a child has a skill that is useful in itself and can be developed (for example, music or sports), then his “genius” can be maintained for a long time, and even brought these skills to a professional level. But in most cases this does not work, and there will be no trace of old skills by 8-10 years.
conclusions
- do you have a genius child? it will pass;)
- outlook and "genius" are related things, and they are connected precisely through the learning mechanism
- this apparent "genius" is most likely not genius at all, but the effect of too strong training of the brain on a specific task without understanding it - just all resources were devoted to this task
- when correcting the narrow interests of the child, his genius disappears
- if your child is "genius" and a little more reserved than peers, then you need to develop these same skills further carefully, actively developing your horizons in parallel, and not focus on these "cool", but usually useless skills
Author: Sergey Poltorak