Deriving the SVD (Single Value Decomposition) from scratch | Hacker News Reader

Deriving the SVD (Single Value Decomposition) from scratch

stillthinking.net

35 pointspcael18 comments

This is a decent derivation, if a little verbose, but I find myself doubting the disclaimer at the top:

> Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made.

If you're writing by hand and trying to avoid accusations of AI-generated content, it's really easy not to write bulleted lists where each item starts with a boldface summary like "A clean bijection in the middle." Or drive home a point with such pithy italicized mottos as "The complexity was never in the map. It was in the basis." If you didn't use AI in the writing here, you have trained yourself very well to write like an LLM.

So many shibboleths. Zero chance it's not AI.

Except anyone can use bullets.

And except the section title is basically me resuming what was seeing before:

Taking stock: what we managed to extract

So you want me to use what? Give me a break.

I was just about to type the same thing. There's no way this isn't AI-generated, I've had conversations with ChatGPT to learn about some matrix math and solving systems of equations, and this feels like a carbon copy of some of those conversations. Em-dashes galore, things "falling out" of other things, bullet points, "That last point is the heart of it.", "Both frames clean, no skew.", "Now here is the insight that makes the whole thing click.".

I am not giving you the benefit of the doubt even with your disclaimer at the top. Too many LLMisms to be a coincidence.

I read the article anyway so people don't complain about me complaining about AI slop, and I'll say this: Reading this article was like having someone explain really complex board game rules without first giving me motivation on why I would want to play or what I'm trying to achieve. What can I do with SVD? Maybe give me a concrete problem to solve, where SVD is helpful.

I recently worked on a toy 2D geometric constraint solver and it was super fun to implement from scratch. I had an AI to consult on various mathematical concepts (which in my opinion is one of the great uses of AI), and giving it a concrete problem to solve was extremely helpful to to cut through a lot of the notation noise. It of course also gave me the motivation to actually learn the concepts, or else I wasn't going to see lines and circles snap together using the constraints I had defined.

In any case, maybe you really did write this without any AI usage. I doubt it, but if that's really the case, I'd recommend a change of tone and writing style, because currently it is almost exactly 1:1 with a vanilla chatgpt session.

Yeah it's 100% bullshit. The biggest red flag here isn't the use of AI, it's the author thinking we're dumb enough not to be able to detect it easily. That itself is dumb and makes this whole article easy to disregard.

Let me give you an idea, just dont read it then. Im not monetizing anything btw.

No. Worse. You're wasting our time

Lol, its funny how people think they know about others peoples lives... and speaking of wasting time...

> Same transformation. Same map on every actual vector. But now it looks like an arbitrary tangle of scaling, shearing, and sign flips — you’d never guess it was just “stretch x by 3.”

I have a very hard time imagining a human writing this if they weren't intentionally attempting to sound like an LLM.

And,

> This is the engine behind image compression

SVD+truncate (or any other low rank approximation) is absolutely not used in any real image compression. Of course, it is a popular classroom project to demonstrate SVD. It's O(n^3) ffs.

Only AI would call SVD the "engine behind image compression", lol.

Im fully aware. But since you came here to criticize only, thanks.

Its one of the simple forms of lossy compression, so you could have just point out that constructively, but hey this is internet.

It would have been in a different tone had it been human written. In fact, if it had not been written with AI, there is no chance SVD gets called the fancy "engine behind image compression", the blog would have said exactly what you said in the comment above: "Its one of the simple forms of lossy compression, here's a simple before/after on a sample image" or whatever.

Im not trying anything. I just put as a joke. Im using AI to learn, but I wrote the structure and the references, and remodeled some parts with AI, yes, but I wrote the base input text by hand, in the sense AI would not be needed, but it helps me as English is not my first language.

What's with the title? Shouldn't it be singular instead of single?

Yes, obviously no LLM would make this mistake.

So at least the user who submitted it to HN was a human (or perhaps a very scheming LLM attempting to appear it?)

These day's I'm super-into information theory and entropy, so I liked the connection made at the end. I'm a visual person, and I found this schematic of SVD on the wikipedia page very insightful [1].

[1]: https://en.wikipedia.org/wiki/Singular_value_decomposition#/...

Slight mistake in equation (1) (or maybe it's supposed to be a narrative decision?), the inner product of Av_i with itself should end up being s_i^2 and not 1. The vectors u_i are orthonormal, but Av_i = s_i u_i, not just u_i.

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