Fundamental theorems - Revision history

Wiki: /* Theorems of Machine Learning */

2026-02-08T13:08:19Z

Theorems of Machine Learning

Wiki: /* Theorem types */

2026-02-08T13:07:42Z

Theorem types

Wiki: /* References */

2026-02-08T13:07:26Z

References

Wiki at 13:06, 8 February 2026

2026-02-08T13:06:36Z

Wiki at 13:02, 8 February 2026

2026-02-08T13:02:46Z

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Wiki: /* Theorems */

2026-02-08T12:18:06Z

Theorems

Wiki: /* Fundamental theorems of Machine Learning with proofs */

2026-02-08T12:17:25Z

Fundamental theorems of Machine Learning with proofs

Vs at 19:20, 11 February 2024

2024-02-11T19:20:02Z

Vs at 19:17, 11 February 2024

2024-02-11T19:17:31Z

Vs at 19:16, 11 February 2024

2024-02-11T19:16:39Z

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 # Bootstrap theorem (statistical estimations): Ergodic theorem
 # Miscellaneous [http://www.machinelearning.ru/wiki/images/3/33/BershteinFonMises.pdf BershteinFonMises-1], [http://www.machinelearning.ru/wiki/images/3/33/BershteinFonMises.pdf BershteinFonMises-2], PАС_learning (compression induces learning), [http://www.machinelearning.ru/wiki/images/b/ba/PAC_learning_compress.pdf PAC_learning_compress]
 ===Theorem types===

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-==Theorem types==
+===Theorem types===
 <!--* Должна быть показана связь между различными областями машинного обучения
 * Вероятность, обоснованность, порождение и выбор, корректность по Адамару, снижение размерности, сходимость алгоритмов -->

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 ==References==
 # Mathematical statistics by A.A. Borovkov, 1998
 # [https://www.di.ens.fr/~fbach/ltfp_book.pdf Learning Theory from First Principles] by Francis Bach, 2021 <!--https://www.di.ens.fr/~fbach/learning_theory_class/index.html-->

@@ Line 50: / Line 50: @@
 # Miscellaneous [http://www.machinelearning.ru/wiki/images/3/33/BershteinFonMises.pdf BershteinFonMises-1], [http://www.machinelearning.ru/wiki/images/3/33/BershteinFonMises.pdf BershteinFonMises-2], PАС_learning (compression induces learning), [http://www.machinelearning.ru/wiki/images/b/ba/PAC_learning_compress.pdf PAC_learning_compress]
 ==Theorem types==
@@ Line 71: / Line 56: @@
 * Uniqueness, existence
 * Universality
-* Convergence <!--[https://www.youtube.com/watch?v=Ajar_6MAOLw] -->
+* Convergence[https://www.youtube.com/watch?v=Ajar_6MAOLw YouTube]
 <!--Поточечно
 **Равномерно
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 * Properties of estimations
 * Bounds
 ==References==
@@ Line 126: / Line 123: @@
 # Theorems on flows by Johann Brehmera and Kyle Cranmera [https://arxiv.org/pdf/2003.13913v2.pdf arXiv:2003.13913v2]
 * GitHub project to upload your text [https://github.com/Intelligent-Systems-Phystech/FundamentalTheoremsML  Intelligent-Systems-Phystech/FundamentalTheoremsML]

@@ Line 21: / Line 21: @@
 In practice, we mimic the first part of the progression, then learn to discover patterns and formulate theorems.
-==Theorems==
+==Theorems of Machine Learning==
 # Fundamental theorem of linear algebra [https://www.engineering.iastate.edu/~julied/classes/CE570/Notes/strangpaper.pdf S]
 # Singular values decomposition and spectral theorem [https://en.wikipedia.org/wiki/Spectral_theorem W]

@@ Line 5: / Line 5: @@
   |description=The course Fundamental Theorems of Machine Learning studies techniques and practice of theorem formulations and proofs in machine learning.
   }}
-==Fundamental theorems of Machine Learning with proofs==
+To make the results of scientific research well-founded, introduce the techniques and practices of theorem formulations and proofs in machine learning.
-The goal of the course is to boost the quality of bachelor's and master's thesis works; to make the results of student scientific research well-founded. The course studies techniques and practice of theorem formulations and proofs in machine learning.
+Why does one need to convey an important message, a scientific result, as a theorem?
 # Theorems are the most important messages in the field of research.
 # Theorems present results in the language of mathematics by generality and rigor.
 # Theorems are at the heart of mathematics and play a central role in its aesthetics.
-Theorems present the message immediately and leave reasoning after. The direct narration puts reason first and the results after that.
+Theorems present the message immediately and leave reasoning for later. The direct narration puts reason first and the results later.
 * How does direct narration transform into fast narration?
 * How to find, state, and prove theorems in our work?
-This course shows both narration styles. It refers to our educational study and our work experience:
+Both narration styles refer to progressions
-# Educational mimic progression
+# Textbook: Definition <math>\to</math> (Axiom set)  <math>\to</math> Theorem  <math>\to</math> Proof  <math>\to</math> Corollaries <math>\to</math> Examples <math>\to</math> Impact to applications
-#* Definition <math>\to</math> (Axiom set)  <math>\to</math> Theorem  <math>\to</math> Proof  <math>\to</math> Corollaries <math>\to</math> Examples <math>\to</math> Impact to applications
+# Scientific discovery: Application problems <math>\to</math> Problem generalisations  <math>\to</math>  Useful algebraic platform <math>\to</math>  Definitions <math>\to</math> Axiom set
-# Scientific discovery progression
+In practice, we mimic the first part of the progression, then learn to discover patterns and formulate theorems.
 ==Theorems==

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 {{#seo:
   |title=Fundamental Theorems of Machine Learning
-  |titlemode= replace
+  |titlemode=replace
   |keywords=Fundamental theorems of Machine Learning
   |description=The course Fundamental Theorems of Machine Learning studies techniques and practice of theorem formulations and proofs in machine learning.

← Older revision		Revision as of 19:16, 11 February 2024
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		+	{{#seo:
		+	\|title=Fundamental Theorems of Machine Learning
		+	\|titlemode= replace
		+	\|keywords=Fundamental theorems of Machine Learning
		+	\|description=The course Fundamental Theorems of Machine Learning studies techniques and practice of theorem formulations and proofs in machine learning.
		+	}}
	=Fundamental theorems of Machine Learning with proofs=		=Fundamental theorems of Machine Learning with proofs=