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From experience in reading machine learning and computer vision papers (shared by many of my peers), it's often way more enlightening to see the code correspond

From experience in reading machine learning and computer vision papers (shared by many of my peers), it's often way more enlightening to see the code corresponding to a paragraph of equations. Some non-programming math people are angry at this view, but really a lot of mathy presentation is there to impress and obfuscate. Many times the code is straightforward and clear but it has to be artificially dressed up in fancy Greek letters and symbols to make it look like "proper science". Also a lot of math notation is very sloppy, the opposite of unambiguous. Math people will say it's necessary for brevity, context is important, you must take the relevant courses beforehand etc, be properly initiated etc. then you will understand. But for me it's still annoying even after a CS master's with many math courses. In code, I can jump to the definition of anything and see precisely what is meant. But a math person would say ambiguity is a feature because, say, the integral sign may stand for different definitions, but in this context we don't care which one it is. They'd often say, well, here you could substitute anything, you could use anything here, it doesn't matter what we use for this and that. But really anything? Can I use a pound of dog fur? No. In working code there is at least one working example to suggest what you mean. I will have a much easier time to understand your abstraction and though process. I think people often think in concrete terms but intentionally keep this secret because abstract ideals are more prestigious, so it becomes the reader's job to figure out what the actual motivation and reasoning of the author was. Thankfully AI papers now mostly release their code so it's possible to see what they actually do behind the smokes and mirrors on the ground level. I'm all for abstraction and general patterns and proofs but there is such a thing as too much.

a-nikolaev 6y ago
I think, in some areas math language is more appropriate, in the others programs and algorithms are more appropriate. There is not wonder that a machine learning or a computer vision idea might be more accessible as an algorithm program, but this is not universally true for any kind of math. A well written paper would describe things in clear terms, choosing the most comprehensible means to convey their idea. So, they might provide all three: 1) concise math formulas, 2) corresponding algorithms, and 3) an explanation in English. Not always all three presentation forms are achievable, but all of them can be useful and enlightening for the reader. Unfortunately, in reality, there might be problems with presenting things in clear way: 1) A scientist might think that it is too verbose to repeat themselves, so they present the idea in only one form, at a single place in their paper, and think it's enough ("for the intelligent reader"). You want to find certain balance between conciseness and clarity, imo. 2) A scientist might be so immersed into the specific area of study they are writing about, so they don't see the reason for explanations for the more general audience. Here, it depends what audience the scientist is trying to reach. Also, not all papers present a good exposition of the field of study anyway. So try finding good papers that explain things in clear terms at your level of comprehension. Read those, then move on to find new sources.

a-nikolaev 6y ago

I think, in some areas math language is more appropriate, in the others programs and algorithms are more appropriate. There is not wonder that a machine learning or a computer vision idea might be more accessible as an algorithm program, but this is not universally true for any kind of math. A well written paper would describe things in clear terms, choosing the most comprehensible means to convey their idea. So, they might provide all three: 1) concise math formulas, 2) corresponding algorithms, and 3) an explanation in English. Not always all three presentation forms are achievable, but all of them can be useful and enlightening for the reader. Unfortunately, in reality, there might be problems with presenting things in clear way: 1) A scientist might think that it is too verbose to repeat themselves, so they present the idea in only one form, at a single place in their paper, and think it's enough ("for the intelligent reader"). You want to find certain balance between conciseness and clarity, imo. 2) A scientist might be so immersed into the specific area of study they are writing about, so they don't see the reason for explanations for the more general audience. Here, it depends what audience the scientist is trying to reach. Also, not all papers present a good exposition of the field of study anyway. So try finding good papers that explain things in clear terms at your level of comprehension. Read those, then move on to find new sources.