Solve any equation using gradient descent 

ta hell is that intro 💀

You're narration is like from 90s american television. I liked it very much.

WHY THE SCARY ASS INTRO????

Bro i was home alone and wanted to watch some math shit, i instantly closed yt when i saw the intro😂

The fact that there’s no quintic formula was proved by Galois before dying in a duel at 20

While being just a machine learning tutorial, this has an unsettling vibe that I find very unique for a educational channel, and honestly much more captivating. Keep it up!

The intro, the speaker's voice, and everything was beautiful in this video

Bizarre style, I love it.

that voice kinda gives the vintage vibes of it, it's like you watching a very old vid. good shit homie

Beautiful and very well made video, I personally loved the old tv vibe to this, not to disregard the instructive yet nicely explained method of gradient descent. Subscribed

I love this explanation, voice, simplicity. Im guessing the voice is a text to speech trained on old 60s videos?

Truly happy i found this gem of a chanel before it blows up

Amazing to hear a new algorithm to solve equations, even the non real ones! - Thanks for helping me understand!

Bro this video is so fire. I get so annoyed by the voices in my actual school videos that they make you watch and this is a huge step up from that it actually makes this seem like it’s a top secret information like you’re debriefing the first nuclear tests or something

This is just awesome stuff. Makes me want to study math. To be patient and learn the fundamentals that gets me to being able to understand and solve these equations. Fascinating.

Instead of squaring, you can raise to higher even powers(like 4,6,..etc), giving quicker convergence if i remember correctly.

fantastic video ur gonna blow up soon (this is a threat)

AWESOME Video! Thanks! Trying to put some basic understanding on this: "We seek a cubic polynomial approximation (ax^3 + bx^2 + cx + d) to cosine on the interval [0, π]." Let's say you want to represent the cosine function, which is a bit wavy and complex, with a much simpler formula-a cubic polynomial. This polynomial is a smooth curve described by the equation where a, b, c, and d are specific numbers (coefficients) that determine the shape of the curve. Now, why would we want to do this? Cosine is a trigonometric function that's fundamental in fields like physics and engineering, but it can be computationally intensive to calculate its values repeatedly. A cubic polynomial, on the other hand, is much simpler to work with and can be computed very quickly. So, we're on a mission to find the best possible cubic polynomial that behaves as much like the cosine function as possible on the interval from 0 to π (from the beginning to the peak of the cosine wave). To find the perfect a, b, c, and d that make our cubic polynomial a doppelgänger for cosine, we use a method that involves a bit of mathematical magic called "least squares approximation". This method finds the best fit by ensuring that, on average, the vertical distance between the cosine curve and our cubic polynomial is as small as possible. Imagine you could stretch out a bunch of tiny springs from the polynomial to the cosine curve-least squares find the polynomial that would stretch those springs the least. Once we have our cleverly crafted polynomial, we can use it to estimate cosine values quickly and efficiently. The beauty of this approach is that our approximation will be incredibly close to the real deal, making it a nifty shortcut for complex calculations.

Nice video. Next step is designing a suitable neural network (choose number of hidden layers, and nodes of each layer, as well as an activation function), and use gradient descent to “learn” the node values, such that the neural network f.ex. produces a regression function to a set of points.

Great video! The visualizations were very helpful to my understanding. Will you be making more machine learning videos in the future?

Yes, solving the equation x^5 + x = y for x in terms of y is much more complex than solving quadratic equations because there is no general formula for polynomials of degree five or higher, due to the Abel-Ruffini theorem. This means that, in general, we can't express the solutions in terms of radicals as we can for quadratics, cubics, and quartics. However, we can still find solutions numerically or graphically. Numerical methods such as Newton's method can be used to approximate the roots of this equation for specific values of y. If we're interested in a symbolic approach, we would typically use a computer algebra system (CAS) to manipulate the equation and find solutions.

There's something about the way you talk and edit the video together that actually makes it interesting. I can't put my finger on it. Maybe it's how novel it is? I don't know, but PLEASE make more videos like this. It's amazing, and I actually understood it completely (rare for someone so bad at math lol)

Thank you for the video!! Took some time to grasp the second example. No surprise. This gradient descent optimization is at the heart of machine learning.

simple , straight forward and good vibes. i love it

Excellent explanation, immediately subscribed 😁

A perfect video to watch at 2 am, especially the intro... now I will have a ton of time to think about this algorithm because there is no way i will sleep 😂 but seriously, very much interesting. I will delve deeper into it 👍

bro i came to watch math at night but your freaking intro scared the shiiiiiii out of me 😭

I like it! This demonstrates a good method! It should be noted that these principles also apply to similar methods which may have more desirable convergence properties such as Newton-Raphson methods.

Absolutely love the audio!!!! How do I get access to it?

Gradient descent is finding optimal minimum point of the function f(x), not finding solution of f(x)=0. However, optimal point of any f(x) is exactly the solution of f'(x) (derivative function of f(x)). So, in case your function has only one variable, to find the solution of f(x)=0, you can replace the derivative term with f(x) and so on. If your function has more than one variable, you can't replace, cause there's only one function has been given, so you do not know that function is depends on which variable (as mentioned above, if you have one variable, f(x) is derivative function depends on x when you use Gradient Descent to find solution). So, the solution is using Least Square Approximation method as the video has shown. Function f^2(variable) always has optimal minimum point. If minimum point's value is 0, it is the solution. If not, GD still finds optimal minimum point, but it is not the solution.

i thought my screen got dust, but unique style. Nice!

What is the voiceover? Thanks,

Am I getting this right? On your first example, our objective from the problem is solving for the values of x in x^5 + x = 3, but then you changed the problem to finding the roots (zeroes) of x^5 + x - 3 = 0 now. I'm bad at the higher math stuff but ain't this two things different? Apologies for the mistake if I made something but the reason seems so arbitrary, or should I just not think of it? Moreover, that method you did on squaring the entire equation, should I always do that? Because that seems really arbitrary too, especially that we're looking at a 5th degree polynomial so I thought this entire process would produce five solutions for us.

this video is bizarre but in a good way

Great explanation Edgar!

But how do you choose this "learning rate"? Like in your x^5 example, if you would have chosesn 0.025, then you will never get a solution, as your solver will spiral to infinity? If you know your solution has a 0, could you use the "reseduial" (value of previous evaluation) to guess how far you need to step? Perhaps paired with a relaxation factor?

Why squaring the function? do we always need to square the function to solve it via gradient descent?

This is just newton’s method

really nice video Edgar! subbed! thank you

Dig that initial distinction between formulas/expressions and algorithms. Made something click.

Is that the Kingdom Hearts menu item noise at 4:05?

there's a lot of limitations related to gradient descent though, such as determining appropriate initial conditions and hyperparameters and convergence problems... but for simple well-behaved polynomials its definitely fine, although Newton's method would achieve faster convergence

Yes - interesting. I've been considering the idea of minimizing f^2 by gradient descent for solving f = 0 but never actually implemented it. Is that a common technique in numerical computing? I think, I haven't seen it in textbooks yet (but maybe my memory is wrong). How does it compare to e.g. Newton iteration convergence wise? Maybe one could also try to minimize the indefinite integral F of f instead of f^2, if that is easily computable - which it is in the case of polynomials. Might be interesting to explore, if that leads to a good (i.e. fast) algorithm.

Great vid, really impressive editing.

Awesome vid, instant sub

Well done, thanks!

I adore the vibe of the video

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Would a sixth degree polynomial in x be referred to as "x hexed"? Really like the video.

Excellent, more!

Want to know how you made this video animation?

excellently explained video

Best into so far

Okay but why don't you explain why this method doesn't work sometimes for particular degrees depending on the function

what text to speech do you use

thanks sir !

Very good presentation. Not sure what superscript "T" is, first appearing @8:05 in the update formula.

love the old aesthetic you're going for.

genuinely curious why you put that in the intro

Broo this is a cool video! Could you share the source code for the video animations

We are taught this in high school class 12.

The second example would have been solved better by linear regression.

It is really nice

oh its good , but i thought i will be able to apply it in my exams lol

Put another way: One can "solve any equation" by numerical methods, i.e. a computer with a properly coded algorithm.

Isn't it Newton Raphson method?

Use Newton method, it's quiker!

I hear Kingdom Hearts Menu selection sound😮

this clip is from the 70`s?

I've found gradient descent to work very badly for polynomials.

TIL "x quartered" is a thing you can say

Your psychosis demon explains gradient decent

Ok now solve the navier stokes equations

multivariable newton’s method

Wow genial

The voice sounded like Carl Sagan. Are you using an AI generated voice?

what is that intro bruh

The clickbait here is so absurd. Obviously this cannot solve non convex problems.

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