Geoffrey E. Hinton's advice for students (from Coursera)

This part is taken from an Interview of Prof. Geoffrey E. Hinton by Prof. Andrew (in Coursera course)

What is your advice to students to want to pursue a career in Deep Learning?

(I thin that the answer given by Prof. Geoffrey E. Hinton is useful to any researcher irrespective of the field of research)

Here is the answer.

"Read the literature, but don't read too much of it. So this is advice I got from my advisor, which is very unlike what most people say. Most people say you should spend several years reading the literature and then you should start working on your own ideas. And that may be true for some researchers, but for creative researchers I think what you want to do is read a little bit of the literature. And notice something that you think everybody is doing wrong, I'm contrary in that sense. You look at it and it just doesn't feel right. And then figure out how to do it right. And then when people tell you, that's no good, just keep at it. And I have a very good principle for helping people keep at it, which is either your intuitions are good or they're not. If your intuitions are good, you should follow them and you'll eventually be successful. If your intuitions are not good, it doesn't matter what you do."

[Prof. Andrew Ng: I usually advise people to not just read, but replicate published papers. And maybe that puts a natural limiter on how many you could do, because replicating results is pretty time consuming.]

"Yes, it's true that when you're trying to replicate a published you discover all over little tricks necessary to make it work. The other advice I have is, never stop programming. Because if you give a student something to do, if they're botching, they'll come back and say, it didn't work. And the reason it didn't work would be some little decision they made, that they didn't realize is crucial. And if you give it to a good student, like for example. You can give him anything and he'll come back and say, it worked. I remember doing this once, and I said, but wait a minute. Since we last talked, I realized it couldn't possibly work for the following reason. And said, yeah, I realized that right away, so I assumed you didn't mean that. "

[Prof. Andrew Ng: ny other advice for people that want to break into AI and deep learning?]

"Basically, read enough so you start developing intuitions. And then, trust your intuitions and go for it, don't be too worried if everybody else says it's nonsense."

"If you think it's a really good idea, and other people tell you it's complete nonsense, then you know you're really on to something."

I think that this advice is applicable to any technical field. Some researchers spend too much time on reading and this lead to too much bias in the published results. If researchers read just enough so that they can think and work on a problem, they can contribute something new in that field. Otherwise, they will be doing just what others have done (mostly incremental work).

Another thing I understand is that students and researchers should try to replicate seminar research papers from the scratch. This help the researchers understand the process the top researchers have undertone. This often provide the skills needed to find out something new in that field and contribute novel works in that field.

Reference:

Weblink: https://www.coursera.org/learn/neural-networks-deep-learning/lecture/dcm5r/geoffrey-hinton-interview

List of problems in Physics, Chemistry, Maths and interdisplinary

Platonic Solids and magic clusters: symmetry and molecular properties
Problems in describing dimer (simple molecules)

Problems in dimers

There are a number of interesting and challenging problems that are unsolved yet. At the first instance, these problems may seem simple, but, these problems are floating around for long time. The problem is to describe simple molecules made of the light-weight elements, eg. dimers of H, He, Li, Be, B, C, N, O, F, Ne (not just these: transition-metal dimers also)

Here, I will brief the challenges on each dimer.

• H dimer (H$_{2}$ molecule) : the description of the H$_{2}$ bond breaking (or even more astonishingly H$^{+}$ ion's at various bond lengths) is a difficulty problem to describe by theoretical methods. 
• He dimer This has many interesting features. The van der Waals force exists between helium atoms which is the reason for the existence of liquid helium. This is because, at a certain range of distances between atoms the attraction exceeds the repulsion. To understand vdW forces fundamentally, this molecule should be studied. This molecule has other interesting features: 1) He2 is the largest known molecule of two atoms when in its ground state, due to its extremely long bond length. 2) The He2 molecule has a large separation distance between the atoms of about 5200 pm (= 52 ångström). 3) This is the largest for a diatomic molecule without ro-vibronic excitation. 4) The binding energy is only about 1.3 mK, 10−7eV or 1.1×10−5 kcal/mol, or 150 nanoelectron Volts. 5) The bond is 5000 times weaker than the covalent bond in the hydrogen molecule (more on this see this on Wikipedia
• Li dimer This is the lightest metal dimer. (will be updated)
• Be dimer (Be$_{2}$ and Be$_{2+} dimer: It has been difficult to explain the bonding of Be dimer (see this recent Science paper on this topic and this paper using Quantum Monte-Carlo method). Molecular orbital theory, valance band theory, SCF (HF theory), configuration interaction, etc are not able to capture the properties of this elusive molecule. Multi-reference methods also have lead to controversy by predicting different strengths between Be atoms with different bond lengths.
• C dimer (C$_{2}$ molecule) is a difficult problem because of the associated strong static correlation and the difficulty in finding the ground state electron density (see this paper by Ayers and discussion in this paper)
• N dimer (Nitrogen molecule) : The splitting of N$_{2}$ is a difficult problem because of increasing strong static correlation effects as bond is stretched. See this view point by Prof. Burke: "[....its [nitrogen molecule's] triple bond exhibits a high level of static correlation (loosely, electron correlations that arise from the the symmetry of the molecule), which increases as the molecule is stretched. If a computational tool can handle N$_{2}$ well, it can tackle most main-group chemistry correctly."
• O dimer (oxygen molecule): The room temperature O$_{2}$ is largely triplet in ground state and a small portion of the O$_{2}$ are in singlet state. See this JACS article Dioxygen: What Makes This Triplet Diradical Kinetically Persistent?. Also, the dissociation of O$_{2}$ is well studied?
• Transition metal dimers?

Morse potential has been important in understanding molecular spectroscopy of dimers (as well as poly atomic molecules). Here is a Wikipedia text.

"An important extension of the Morse potential that made the Morse form very useful for modern spectroscopy is the MLR (Morse/Long-range) potential.^[4] The MLR potential is used as a standard for representing spectroscopic and/or virial data of diatomic molecules by a potential energy curve. It has been used on N₂,^[5] Ca₂,^[6] KLi,^[7] MgH,^[8][9][10] several electronic states of Li₂,^{[4][11][12][13][9][12]} Cs₂,^[14][15] Sr₂,^[16] ArXe,^[9][17] LiCa,^[18] LiNa,^[19] Br₂,^[20] Mg₂,^[21] HF,^[22][23] HCl,^[22][23] HBr,^[22][23] HI,^[22][23] MgD,^[8] Be₂,^[24] BeH,^[25] and NaH.^[26] More sophisticated versions are used for polyatomic molecules.

"

While these problems are of interest on the fundamental level, the dimers of transition metal atoms provide applications such as memory storage. Monomer, dimer, trimer on different 2D materials (graphene, phosphorene, etc) are widely studied for their MAE, etc.

(Is there any other dimer which gives challenge to theory or experiment? comment here.

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