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In my Natural Language Processing class, we just talked about the Generalization of a Jacobian Matrix. So far I’ve been understanding the material, okay, but now I’m very confused.

I came across these slides Natural Language Processing with Deep Learning CS224N/Ling284, in the context of natural language processing, which talks about the Jacobian as a generalization of the gradient.

I'm not clear on when and why to perform a Generalization?

I know there is a lot of topic regarding this on the internet, and trust me, I've googled it. I got answers to generalizing the matrices and distributions but no proper explanation on "Generalization" and why it is so important?

Pluviophile
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  • What is the definition of the generalization that you were given? One way of defining a matrix is as an indexing function with indexing set $[m]\times [n]$ where $[n]={1,2,\ldots, n}$ is a section of the positive integers. You can generalize this to an arbitrary finite Cartesian product of sections of the positive integers. There are certainly applications of such a structure since you might want to iterate through some object of that many dimensions. – Favst Jun 12 '20 at 14:52
  • "Generalization" is an extremely broad term. You should give more details about exactly what kind of generalization you are asking about, otherwise it's impossible to answer your question. – Lee Mosher Jun 12 '20 at 15:00
  • Is this question somehow relevant? @Pluviophile – Alexey Burdin Jun 12 '20 at 15:13
  • @AlexeyBurdin Not completely – Pluviophile Jun 12 '20 at 15:18
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    @LeeMosher the reference that is linked by the author narrows the notion of generalization. I think it pertains to how Jacobian is generalization of gradient in multi-dimension. Please do care to check the reference and provide your input as this is quite interesting point. – GENIVI-LEARNER Sep 04 '20 at 15:24

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