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In the podcast, Vladimir Vapnik discusses the role of mathematics in predicting outcomes and its usefulness for understanding the world. He argues that machine learning should focus on the two mechanisms of learning, strong and big convergence, and that predicate representation is a key part of this.

**00:00:00**Vladnik discusses the role of math in the natural sciences and its usefulness for predicting outcomes. He believes that math has limits, but is still a valuable tool for understanding the world.**00:05:00**Vladimir Vapnik discusses how mathematical structures can reveal principles of reality, and how human intuition is not too rich and primitive. He also discusses the role of imagination in the moment of discovery, and how it is not necessary to use imagination to derive principles of machine learning.**00:10:00**Vladimir Vapnik discusses the idea that learning is a process of interpretation, and that great teachers can introduce invariants and reduce the number of observations needed for learning. He argues that machine learning should focus on the two mechanisms of learning, strong and big convergence, and that predicate representation is a key part of this.**00:15:00**VC stands for "vacuum cleaner." It is a theory about how to create a small set of functions that are good for machine learning. The goal is to create a set of functions that is small in dimension and contains good functions.**00:20:00**In this podcast, Vladimir Vapnik discusses the goal of learning, which is to find a small VC dimension and then to pick up good functions. He says that this is done by creating an admissible set of functions that is invariant to the training data. He also says that deep learning is not effective in accomplishing this goal, and that the strengths of deep learning are its interpretations by computer scientists rather than its ability to discover new knowledge.**00:25:00**Vladimir Vapnik discusses the history of the discovery of the "piecewise linear function", which led to the development of deep learning, and argues that even though this method is effective, it is not the only way to learn and is not the most effective way to solve certain mathematical problems.**00:30:00**Vladimir Vapnik discusses the importance of using the law of large numbers in training algorithms, as well as the complexity of classification problems. He also discusses the importance of complexity in relation to worst-case scenario.**00:35:00**The video discusses the difference between edge cases and the average case, and how the average case can be derived from the edge cases. Vladimir Vapnik discusses how formal statistics requires large numbers of data points in order to be accurate, and how this limits the usefulness of edge cases for understanding the essence of a function.**00:40:00**Vladimir Vapnik discusses the limits of deep learning and how the use of invariants can improve the accuracy of machine learning models.**00:45:00**Vladimir Vapnik discusses the idea that there are ground truths that can be seen in all areas of life, including in music and poetry. He argues that these truths can be found by escaping into the work and that the best way to find them is to intuitively understand it rather than trying to analyze it mathematically.**00:50:00**Vladimir Vapnik discusses his work on statistical learning theory and how it has impacted his life and career. He explains that when he first discovered the theory, he had a sense of its profundity and that it would last forever. He discusses the invariant story that he has proven and how it separates statistical learning from intelligence.

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