European Union:

1. Firouzja 2785
2. Giri 2768
3. Rapport 2745
4. Vachier-Lagrave 2742
5. Topalov 2728
6. Duda 2724
7. Vallejo 2712
8-9. Deac 2700
8-9. Keymer 2700
10. Anton 2690

Former Soviet Union:

1. Nepomniachtchi 2794
2. Radjabov 2747
3. Grischuk 2745
4. Mamedyarov 2738
5. Abdusattorov 2731
6. Sjugirov 2712
7. Dubov 2708
8. Eljanov 2705
9. Artemiev 2701
10. Tomashevsky 2694

Former British Empire:

1. Nakamura 2775
2. Caruana 2764
3. So 2760
4. Anand 2754
5. Aronian 2745
6. Doninguez 2739
7. Gukesh 2732
8. Vidit 2731
9. Shankland 2711
10. Niemann 2708

Asia:

1. Ding 2789
2. Anand 2754
3. Maghsoodloo 2734
4. Gukesh 2732
5-6. Abdusattorov 2731
5-6. Vidit 2731
7. Yu 2729
8. Le 2728
9-10. Wang 2722
9-10. Wei 2722

Born later than the world champion:

1. Firouzja 2785
2. Giri 2768
3. So 2760
4. Rapport 2745
5. Maghsoodloo 2734
6. Gukesh 2732
7-8. Abdusattorov 2731
7-8. Vidit 2731
9. Yu 2729
10. Duda 2724

Nuclear powers:

1. Nepomniachtchi 2794
2. Ding 2789
3. Firouzja 2785
4. Nakamura 2775
5. Caruana 2764
6. So 2760
7. Anand 2754
8-9. Aronian 2745
8-9. Grischuk 2745
10. Vachier-Lagrave 2742

Old Guard:

Ding Liren was the highest rated blitz player in the world at 2875 in 2016. GM Ding's skill at speed chess served him well with a mere minute remaining in the dramatic fourth and final rapid tiebreaker when he eschewed a certain perpetual check draw to play for the win and did indeed win in dramatic fashion over Russia's Ian Nepomniachtchi. GM Ding had found himself in time trouble throughout the match.

European Union:

1. Firouzja 2786
2. Giri 2772
3. Rapport 2752
4. Vachier-Lagrave 2747
5. Duda 2732
6. Topalov 2728
7. Vallejo 2706
8. Van Foreest 2695
9. Shevchenko 2694
10. Deac 2693

Former Soviet Union:

1. Nepomniachtchi 2779
2. Karjakin 2750
3. Radjabov 2747
4. Mamedyarov 2740
5. Grischuk 2736
6. Abdusattorov 2732
7. Dubov 2716
8-9. Sjugirov 2699
8-9. Artemiev 2699
10-11. Eljanov 2694
10-11. Tomashevsky 2694

Former British Empire:

1. Nakamura 2775
2. Caruana 2773
3. So 2765
4. Anand 2754
5. Aronian 2742
6. Dominguez 2739
7. Gukesh 2736
8. Vidit 2712
9. Shankland 2711
10. Harikrishna 2704

Asia:

1. Ding 2780
2. Anand 2754
3. Gukesh 2736
4. Yu 2734
5. Abdusattorov 2732
6. Le 2728
7-8. Wang 2722
7-8. Wei 2722
9. Maghsoodloo 2716
10. Vidit 2712

Born later than the world champion:

1. Firouzja 2786
2. Giri 2772
3. So 2765
4. Rapport 2752
5. Gukesh 2736
6. Yu 2734
7-8. Duda 2732
7-8. Abdusattorov 2732
9. Wei 2722
10-11. Maghsoodloo 2716
10-11. Dubov 2716

Nuclear powers:

1. Firouzja 2786
2. Ding 2780
3. Nepomniachtchi 2779
4. Nakamura 2775
5. Caruana 2773
6. So 2765
7. Anand 2754
8. Karjakin 2750
9. Vachier-Lagrave 2747
10. Aronian 2742

Old Guard:

European Union:

1. Firouzja 2777
2. Giri 2775
3. Rapport 2752
4. Vachier-Lagrave 2739
5. Duda 2732
6. Topalov 2727
7. Vallejo 2706
8. Shevchenko 2694
9-10. Van Foreest 2693
9-10. Deac 2693

Former Soviet Union:

1. Nepomniachtchi 2779
2. Karjakin 2750
3. Radjabov 2747
4. Mamedyarov 2742
5. Grischuk 2736
6. Abdusattorov 2725
7. Dubov 2716
8. Sjugirov 2699
9. Artemiev 2698
10-11. Eljanov 2694
10-11. Tomashevsky 2694

Former British Empire:

1. Nakamura 2787
2. Caruana 2782
3. So 2769
4. Anand 2754
5. Gukesh 2744
6. Aronian 2742
7. Dominguez 2739
8. Vidit 2719
9. Shankland 2711
10. Erigaisi 2710

Asia:

1. Ding 2780
2. Anand 2754
3. Gukesh 2744
4. Yu 2735
5. Le 2728
6. Wei 2726
7. Abdusattorov 2725
8-9. Maghsoodloo 2719
8-9. Vidit 2719
10. Erigaisi 2710

Born later than the world champion:

1. Firouzja 2777
2. Giri 2775
3. So 2769
4. Rapport 2752
5. Gukesh 2744
6. Yu 2735
7. Duda 2732
8. Wei 2726
9. Abdusattorov 2725
10-11. Maghsoodloo 2719
10-11. Vidit 2719

Nuclear powers:

1. Nakamura 2787
2. Caruana 2782
3. Ding 2780
4. Nepomnaichtchi 2779
5. Firouzja 2777
6. So 2769
7. Anand 2754
8. Karjakin 2750
9. Gukesh 2744
10. Aronian 2742

Old Guard:

European Union:

1. Firouzja 2777
2. Giri 2769
3. Rapport 2752
4. Vachier-Lagrave 2739
5. Duda 2732
6. Topalov 2727
7. Vallejo 2706
8. Keymer 2701
9. Deac 2698
10. Van Foreest 2697

Former Soviet Union:

1. Nepomniachtchi 2779
2. Karjakin 2750
3. Mamedyarov 2747
4. Grischuk 2736
5. Abdusattorov 2725
6. Dubov 2716
7. Sjugirov 2705
8. Artemiev 2698
9. Eljanov 2695
10. Tomashevsky 2694

Former British Empire:

1. Nakamura 2787
2. Caruana 2782
3. So 2769
4. Anand 2754
5. Gukesh 2751
6. Aronian 2742
7. Dominguez 2739
8. Vidit 2723
9. Harikrishna 2711
10. Shankland 2708

Asia:

1. Ding 2780
2. Anand 2754
3. Gukesh 2751
4. Le 2740
5. Wei 2726
6. Abdusattorov 2725
7. Vidit 2723
8. Yu 2721
9. Harikrishna 2711
10. Praggnanandhaa 2707

Born later than the world champion:

1. Firouzja 2777
2-3. Giri 2769
2-3. So 2769
4. Rapport 2752
5. Gukesh 2751
6. Duda 2732
7. Wei 2726
8. Abdusattorov 2725
9. Vidit 2723
10. Yu 2721

Nuclear powers:

1. Nakamura 2787
2. Caruana 2782
3. Ding 2780
4. Nepomniachtchi 2779
5. Firouzja 2777
6. So 2769
7. Anand 2754
8. Gukesh 2751
9. Karjakin 2750
10. Aronian 2742

Old Guard:

I recall that you had completed PhD in mathematics many years ago . Correct ?

Regards

2) can I ask you , if it is not intrusive , what career you chose after masters in maths ?

Thank you for sharing <alexmagnus>

I intend to start studying MSc maths soon . So , that is the context of my interest in this conversation

2) I have something more to say about it and intend to post soon here in this forum of yours that stuff , within next few days (if not today) , if you please.

European Union:

1. Firouzja 2777
2. Giri 2760
3. Rapport 2752
4-5. Vachier-Lagrave 2727
4-5. Topalov 2727
6. Duda 2726
7. Keymer 2717
8. Vallejo 2712
9. Sjugirov 2705
10. Deac 2702

Former Soviet Union:

1. Nepomniachtchi 2771
2. Karjakin 2750
3. Radjabov 2745
4. Mamedyarov 2734
5. Grischuk 2732
6. Abdusattorov 2716
7. Dubov 2710
8. Artemiev 2697
9. Eljanov 2695
10. Tomashevsky 2694

Former British Empire:

1. Caruana 2786
2. Nakamura 2780
3. Gukesh 2758
4. Anand 2754
5. So 2753
6. Dominguez 2745
7. Aronian 2742
8. Praggnanandhaa 2727
9. Vitiugov 2719
10. Vidit 2716

Asia:

1. Ding 2780
2. Gukesh 2758
3. Anand 2754
4. Le 2733
5. Praggnanandhaa 2727
6. Wei 2726
7. Yu 2720
8-9. Vidit 2716
8-9. Abdusattorov 2716
10. Erigaisi 2712

Born later than the world champion:

1. Firouzja 2777
2. Giri 2760
3. Gukesh 2758
4. So 2753
5. Rapport 2752
6. Praggnanandhaa 2727
7-8. Duda 2726
7-8. Wei 2726
9. Yu 2720
10. Keymer 2717

Nuclear powers:

1. Caruana 2786
2-3. Nakamura 2780
2-3. Ding 2780
4. Firouzja 2777
5. Nepomniachtchi 2771
6. Gukesh 2758
7. Anand 2754
8. So 2753
9. Karjakin 2750
10. Dominguez 2745

Old guard:

Carlsen somehow manages to escape all of my lists. He could have ended up on the "born later" list if Nepo had won either of his world championship matches.

<It’s safe to say that if you intend to be a creator of ML research rather than a consumer, you better get used to devoting a large part of your life to understanding advanced math. I speak from experience: I’m close to inaugurating my 40th year of my career as an ML researcher and it has only gotten harder to master the necessary math. I don’t mean the kid stuff, like basic linear algebra, multivariate calculus, optimization, probability and statistics. This level of math is simply the price of admission into the field. This gets you into the cheap seats in the ML research stadium. You’ll still struggle to understand the recent advances in the field. You want to really push the frontier in the field? Start getting used to reading graduate level math textbooks.

Here’s a short sampling of more advanced math that is increasingly proving essential to many sub fields in modern ML. I’ll briefly explain why each of these subfields is useful, so you’ll get to understand why.

<How important is a strong mathematical background in machine learning? Mathematics is the language that modern machine learning is built on, so trying to do machine learning without knowledge of math is like trying to play classical music without being able to read scores, i.e. not very well.

In essence, machine learning is about extracting structure from data: finding the patterns amongst a great deal of noise. Nothing prepares you better for a lifetime of doing machine learning as a deep knowledge of math.

In fact, one can turn this question on its head: often students who took my graduate ML class at UMass came to me and marveled at how they finally understood what their linear algebra or calculus or statistics class they took eons ago was trying to teach them!

The deeper one gets into a problem, the more math seems necessary to formulate and solve a machine learning task. Let’s consider an example, to make this more concrete.

A fundamental challenge for machine learning is how to transfer the results of learning from one setting to another. Humans seem to be able to do this fairly effortlessly, often to a level that befuddles any machine learning approach. I just returned from a trip to Norway and Sweden. I’d never been to either country before my trip. In essence, I had no training data of actually having been in either country. Did that pose a problem. Not an iota. I just applied the basic knowledge of how to get around cities or airports from past experience. We do this as humans as easily as we breathe.

Most machine learning approaches, from au courant deep learning to good old fashioned classical Gaussian least squares regression, will choke if the test data (e.g., taking a train from the airport in Stockholm or Oslo to city center) differs from the training data (e.g., prior experience of taking trains from San Francisco airport to the city center). The reason being that the statistics are entirely different. The distribution of features in Sweden or Norway is very different from San Francisco.

So, how does one solve the problem of transfer learning? Let’s imagine a very basic idea of computing some aggregate statistics of the source dataset (e.g., for every feature, compute its correlation against all other features) and doing the same for the target dataset. It might be helpful to recall that the source dataset is labeled but the target dataset is not (that is, from our prior experience, we know what the signs mean in San Francisco since we speak English, but we can't interpret the signs in Stockholm or Oslo since we don't speak Swedish or Norwegian).

So, we are in essence computing the covariance matrix of the source dataset and the covariance matrix of the target dataset. This matrix summarizes the second order statistics of the data. Under the simplifying assumption that the second order statistics are all that matter, in other words the distribution of features are Gaussian, we can now proceed to find a solution.

The source and covariance matrices are going to be different in transfer learning since the data are coming from two different multivariate Gaussian distributions. So, any approach like using Bayesian ML to find a classifier that labels source data will fail in the target domain since the covariances have changed. Even a method like support vector machines, which finds the best hyperplane that separates positive from negative examples in the source domain cannot be applied in the target domain since the data have shifted unpredictably in the space of instances.

OK, here’s a simple trick developed in a popular algorithm called CORAL (for correlational alignment). Find the matrix A such that the source covariance Σs can be transformed into something that matches the target covariance Σt. In the language of linear algebra, this amounts to solving the optimization problem (pardon the Latex):

minA∥ATΣsA−Σt∥2

Any inputs , if you please ?