What is convergence in mathematics

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The game captivates with its atmosphere and unusual mechanics. For example, among other things, the player can climb into buckets, turn over paint cans, scratch objects and poke his nose into non-player characters.Convergence: What is convergence and non-convergence of an algorithm

And why “it all fits” is the best compliment for a data scientist

Analysis
December 19, 2024

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Convergence: What is convergence and non-convergence of an algorithm
Content

1.
What is convergence in mathematics
2.
Convergence in Machine Learning
3.
Types of Convergence in Machine Learning
4.
How to understand that convergence has been achieved
5.
Can a model "not converge"
6.
What does slow convergence mean?
7.
How to increase the speed of convergence
8.
Brief conclusions
Anna Mavrina
Anna Mavrina
Skillfactory author with engineering education

Machine learning algorithms and models are evaluated by various parameters: they determine how quickly and accurately the model works. One of these parameters is convergence of the algorithm. Convergence shows how quickly the model reaches its “optimum” — the point beyond which it makes fewer mistakes and makes more accurate predictions.

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Let's take a closer look. We'll explain in simple terms jamaica telegram data what convergence is, together with Alexander Nemaltsev, head of the machine learning group at VK.

By definition, convergence is a property that means that something has a finite limit. For example:

finite sum of the members of an infinite series of numbers;
final value of the integral;
a finite number in an infinite multiplication of numbers.
For example, a function may have a limit that tends to some specific value (lim 1/x tends to 0 as x-> ∞).

Accordingly, non-convergence is the absence of such a finite value. In mathematics, the terms are applied to a wide variety of entities: series, sequences, sums, and products of numbers.

There are also several types of convergence. For example, absolute convergence means that the sequence converges in all cases, and conditional convergence means that the series itself converges, but the series of its absolute values ​​does not.