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 ?

European Union:

1. Firouzja 2777
2. Giri 2760
3. Rapport 2752
4-5. Topalov 2727
4-5. Vachier-Lagrave 2727
6. Duda 2726
7. Keymer 2717
8. Van Foreest 2707
9. Sjugirov 2705
10. Deac 2701

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. Martirosyan 2696
10. Eljanov 2695

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 2738
9-10. Harikrishna 2716
9-10. Vidit 2716

Asia:

1. Ding 2780
2. Gukesh 2758
3. Anand 2754
4. Praggnanandhaa 2738
5. Le 2733
6. Wei 2726
7. Yu 2720
8-10. Harikrishna 2716
8-10. Abdusattorov 2716
8-10. Vidit 2716

Born later than the world champion:

1. Firouzja 2777
2. Giri 2760
3. Gukesh 2758
4. So 2753
5. Rapport 2752
6. Praggnanadhaa 2738
7-8. Duda 2726
7-8. Wei 2726
9. Yu 2720
10. Keymer 2717

Nuclear powers:

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

Old Guard:

2) a different question , If you please.

Israel - hamas war . I was reminded of your post from many , many years ago where you said (if i recall correctly ) something like "<I, <alexmagnus> , may be considered a Jew according to some criterion ...I have relatives in israel ...I have visited Israel...I find amusing the overcharged intense positions of online supporters of Israel and Palestinians both who have never met Palestinians or israelites in real life ...both Palestinians and israelites are nowhere that intense about these issues ">

Things changed over the last few years though when it comes to the Conflict.

What happened, in a long process that started probably some 5-6 years ago, is that both Israel and the Palestinians stopped thinking that there are <any> civilians on the other side. The massacre of October 7 and Israel's reaction to it were just the culmination of this "de-civilizaation" of the respective enemy.

Now, to an (average) Israeli, every Palestinian is a terrorist, be it a baby. And to an (average) Palestinian, every Israeli is an occupier, be it a baby.

This mindset, on both sides, is not born outof nowhere but is the consequence of the actions of each side. Even more, both sides are <interested> in maintaining the respective image in the enemy's eyes. Because both sides want to provoke the otehr side to a war. Especially with the current extreme government in Israel (the Hamas has always been extreme, so on the Palestinian side not much changed).

This "there are no civilians" approach explains both things like the October 7 massacre and the treatment of the Palestinians by Israel.

Both sides act logically if you consider this view. But both have a flaw even under this barbaric view: the enemy has nowhere to go.

Israel considers Palestinians terrorists, so they turned Palestine into a prison. But unlike an actual prison, there is no way out: no parole, no pardon, no release on good behavior, no end of the term. So there is no incentive for Palestinians to give up violence and terrorism, and such treatment only creates more violence and terrorism.

Palestine thinks every Israeli is an occupier, and so they deal the way colonized nations deal with occupiers: terrorism. But unlike actual occupiers driven out by terrorism, Israel has nowhere to go. There is no "colonial motherland" here. Israel <is> their home.

The Palestinians should adopt peaceful resistance. Apartheid South Africa models their situation mch better than Algeria. And note, by the way, the apartheid in South Africa ended because the whites were <convinced> to end it. Not by the violence in Soweto, but by international sanctions, pressure, and peaceful parts of the black resistance. Eventually it was a white president that intiated the reforms to end the apartheid and a white-only referendum that approved those reforms.

Palestinians should take up peaceful resistance and the international community should sanction Israel. In return, Palestinians should <give up> any claim to Israel within the 1967 borders. And be merciless on those who still raise such claims or sabotage peaceful resistance.

Israel, in turn, should reward non-violence. And offer a comprehensive deoccupation plan in case the Palestinians hold to non-violence. And stick to that plan, ignoring any internal protests of religious fanatics and "security" freaks, who in reality don't give a damn about security.

<alexmagnus> says average Israeli considers all Palestinians enemy, be it a baby and average Palestinian considers all Israeli occupier be it a baby . I tried to be a worthy student of <johnlspouge> and looked for substantiation by goggling like <how many Israeli consider all Palestinians as enemy >.

Did not get any relevant result.

So , search is not that simple/easy.