The fact that there’s randomness here means that if we use the same prompt multiple times, we’re likely to get different essays each time. But if sometimes (at random) we pick lower-ranked words, we get a “more interesting” essay. Because for some reason-that maybe one day we’ll have a scientific-style understanding of-if we always pick the highest-ranked word, we’ll typically get a very “flat” essay, that never seems to “show any creativity” (and even sometimes repeats word for word). But this is where a bit of voodoo begins to creep in. the one to which the highest “probability” was assigned).
But which one should it actually pick to add to the essay (or whatever) that it’s writing? One might think it should be the “highest-ranked” word (i.e. (More precisely, as I’ll explain, it’s adding a “token”, which could be just a part of a word, which is why it can sometimes “make up new words”.)īut, OK, at each step it gets a list of words with probabilities. But the end result is that it produces a ranked list of words that might follow, together with “probabilities”:Īnd the remarkable thing is that when ChatGPT does something like write an essay what it’s essentially doing is just asking over and over again “given the text so far, what should the next word be?”-and each time adding a word. ChatGPT effectively does something like this, except that (as I’ll explain) it doesn’t look at literal text it looks for things that in a certain sense “match in meaning”. Imagine scanning billions of pages of human-written text (say on the web and in digitized books) and finding all instances of this text-then seeing what word comes next what fraction of the time. So let’s say we’ve got the text “ The best thing about AI is its ability to”. The first thing to explain is that what ChatGPT is always fundamentally trying to do is to produce a “reasonable continuation” of whatever text it’s got so far, where by “reasonable” we mean “what one might expect someone to write after seeing what people have written on billions of webpages, etc.” (And the essence of what I’ll say applies just as well to other current “large language models” as to ChatGPT.) I should say at the outset that I’m going to focus on the big picture of what’s going on-and while I’ll mention some engineering details, I won’t get deeply into them. But how does it do it? And why does it work? My purpose here is to give a rough outline of what’s going on inside ChatGPT-and then to explore why it is that it can do so well in producing what we might consider to be meaningful text. That ChatGPT can automatically generate something that reads even superficially like human-written text is remarkable, and unexpected. text - text formulas are displayed inline, that is, within the body of text where it is declared, for example, I can say that a + a = 2 a įor more integral symbols, including those not included by default in the Computer Modern font, try the esint package.“Wolfram|Alpha as the Way to Bring Computational Knowledge Superpowers to ChatGPT” » A discussion about the history of neural nets ».They can be distinguished into two categories depending on how they are presented:
Therefore, special environments have been declared for this purpose. This is because LaTeX typesets math notation differently from normal text. LaTeX needs to know when the text is mathematical. 17.3 Write an equation with the align environment.17 Advanced Mathematics: AMS Math package.1.1 Inserting "Displayed" maths inside blocks of text.The mathtools package fixes some amsmath quirks and adds some useful settings, symbols, and environments to amsmath. If you are writing a scientific document that contains numerous complex formulas, the amsmath package introduces several new commands that are more powerful and flexible than the ones provided by basic LaTeX. If your document requires only a few simple mathematical formulas, plain LaTeX has most of the tools that you will ever need. It is also a large topic due to the existence of so much mathematical notation. Typesetting mathematics is one of LaTeX's greatest strengths.
The fact that he succeeded was most probably why TeX (and later on, LaTeX) became so popular within the scientific community.
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One of the greatest motivating forces for Donald Knuth when he began developing the original TeX system was to create something that allowed simple construction of mathematical formulae, while looking professional when printed. Collaborative Writing of LaTeX Documents.Scientific Reports (Bachelor Report, Master Thesis, Dissertation).
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