I realized that derivatives are linear
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I realized that derivatives are linear
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Re: I realized that derivatives are linear
#2This is why you take linear algebra and calculus before doing machine learning.
Re: I realized that derivatives are linear
#3This is why you take linear algebra and calculus before doing machine learning.
I think it's great that machine learning is exciting enough that people want to learn the math behind it.
Re: I realized that derivatives are linear
#4[deleted]
Re: I realized that derivatives are linear
#5The derivative is a linear operator, but it's not a bounded operator. That is, for example, the vector norm of f(x) = k·sin(x/k) → 0 when k→0, but the norm of d/dx f(x) does not. This also means that it's not continuous.
Of the mappings between vector spaces, the most well behaving are the bounded linear operators, and the derivative doesn't belong to these. But yes, it's linear.
Edit: Originally wrote f(x) = k·sin(k·x), but meant f(x) = k·sin(x/k).
Re: I realized that derivatives are linear
#6Integrals and Fourier Transforms are also linear...
Re: I realized that derivatives are linear
#7This is why you take linear algebra and calculus before doing machine learning.
"Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something."
Re: I realized that derivatives are linear
#8This is why you take linear algebra and calculus before doing machine learning.
On the contrary - ML is a great motivator to finally grapple the "prerequisites".
During school I never understood what the math was for, so my unconscious brain never saw the necessity to actually learn it. Now I want to learn - with hugely better results.
This mechanism should be utilized much more often instead of shoving seemingly unrelated knowledge into peoples ears without letting them feel the need for it first.
Re: I realized that derivatives are linear
#9Well this is the whole point of derivatives (i.e. tangent maps): to be linear approximations of functions.
So yes, a linear approximation of a linear function is the function itself.
Re: I realized that derivatives are linear
#10Well this is the whole point of derivatives (i.e. tangent maps): to be linear approximations of functions. So yes, a linear approximation of a linear function is the function itself.
You are right, but what you are saying has nothing to do with the author's point: what he is saying is that the differentiation operator itself is linear, which is a meaningful and true fact even in spaces where you have no idea of what a linear function is.