And multiplication is a fancy addition
Convolution Is Fancy Multiplication
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Re: Convolution Is Fancy Multiplication
#82And multiplication is a fancy addition
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Re: Convolution Is Fancy Multiplication
#83Earlier quoted context omitted.
The parents point is that when you do the primary school multiplication algorithm, you are actually performing a discrete convolution.
You really aren't. That assertion is like commenting that elementary arithmetics is discrete signal analysis because 1+1=2, which happens to match the amplitude of a resonance of a normalized vibration mode. It isn't. It's a cherry picked example. A broken clock which coincides with the current time.
> It isn't. It's a cherry picked example. A broken clock which coincides with the current time.
No. It really is. Look at the example.
Nobody can convince you if you are already set up against that idea, but look at what happens when you multiply two polyomials P(z)Q(z). You obtain a polynomial whose coefficients are the convolution of those of P and Q. Now, a decimal number is "just" a polynomial evaluated on z=10. And a vibrating string is "just" a polynomial evaluated at z=exp(it). The algebra of convolutions and products is exactly the same in all three cases.
Re: Convolution Is Fancy Multiplication
#84Earlier quoted context omitted.
> Convolution is digit-based multiplication, It really isn't, and I don't understand the level of confusion that leads to this assertion. Is it because the elementary school algorithm for multiplication decomposes a number in it's decimal places before multiplying? > so why not start with that? Because it would be wrong, misguided, and it would fail to demonstrate the logic behind convolution. Let's take a step back…
Ref comment https://news.ycombinator.com/item?id=25195046 about this. Further to that, if you replace x with complex variable z^-1, you get what is usually called the z-transform. Set z to a specific complex root of unity exp(i2pi/N) and you have your discrete FT. One of the algorithms for multiplying large arbitrary precision numbers uses multiplication of the discrete transform of the digit sequences (in a differen…
Correction: exp(i2πm/N) .. which gives you Fourier coefficients at m.
Re: Convolution Is Fancy Multiplication
#85And multiplication is a fancy addition
Addition is a repetition of vector
Re: Convolution Is Fancy Multiplication
#86Earlier quoted context omitted.
The etymology is the same in English. To convolve : to roll together : writhe. Convolution : a form or shape that is folded in curved or tortuous windings.
That confuses the hell out of me. I first encountered it as a young gamedev hobbyist, doing image post-processing in OpenGL. One kind of kernel makes images blurry, one (attempts to) make them sharp. It doesn't bring folding to mind at all. And in FP, "fold" means "reduce". How much of dyscalculia is just one person thinking an analogy is completely obvious and the other person thinking it makes no sense?
> One kind of kernel makes images blurry, one (attempts to) make them sharp.
Any kernel with positive values will blur the image, and the effect will be quite similar to Gaussian blur (by the Central Limit Theorem).
It's kernels with positive and negative coefficients that may "enhance" or "sharpen" the image.
Re: Convolution Is Fancy Multiplication
#87Re: Convolution Is Fancy Multiplication
#88I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterExplained, Paul's Math Notes, 3Blue1Brown's YouTube Channel, Ben Eater's YouTube channel, and the entire body of high quality MOOCs are just available for free over the Internet is probably one of my favorite accomplishments of the human race in the 21st century…
because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject.
I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well in math and got encouraged to go become an elementary school teacher because, basically, sexism is alive and well and the world goes "Oh, I know what a woman who can't cut it in college is qualified for: Dealing with small kids all day!"
So a lot of elementary school teachers are women who suck at math and were also never told 'Get over it and get a degree you want.' Instead, they were told 'Oh, go teach kiddies. That's what you are qualified for.'
And I know this is a gender difference in terms of the world treating men and women differently -- a social difference, not a biological one -- because I'm a woman who is good at math (or was at one time) and was married to a man who was terrible at it. No one ever told him (a career soldier) "Oh, go become an elementary school teacher!"
Instead, he got his wife to tutor him in college math even though he found it so difficult he threw his pencil across the room one day when I showed him the right way to do it and then I told him "You can be nice or go find another tutor."
Re: Convolution Is Fancy Multiplication
#89Just because its funny, here is the obligatory reminder that deep convolutional networks are actually implemented as correlation, not convolution.
True, its just the lack of mirroring that differs, which is a linear operation and hence, the network can be considered too have learned the mirrored kernels, but it matters for initialization(bilinear init for conv^T sampling is still incorrectly mirrored in pytorch), and every time someone has put the images of the kernels in a paper its better than even odds they show the correlation, not convolution kernls.
Re: Convolution Is Fancy Multiplication
#90Earlier quoted context omitted.
I wholeheartedly agree on the point about decentralizing and modernizing education, and thank you for reminding me of this. We still have a massive bias towards academic institutions to work against, but the fact that knowledge is so easily accessible, and of such a high quality, is pretty amazing.
Why do you think academic institutions are something to work against to? I'm in academia and here everybody is enthralled and really happy about the explosion of high-quality, freely available learning resources. The only kind of complain that I have ever heard (and very rarely so) is because some of this material is supported by videos in a platform with shitty terms of service.
it's the bias that has to be worked against, not the institution