The most beautiful aspect to me is the flickering effect of the ill formed mandelbrot set, seems the distortion caused by convection streams of hot air...

"Smooth Mandelbrot set isn't real, it can't hurt you"

@thNumber

Жыл бұрын

screenshot moment

@wormball

Жыл бұрын

it is complex! (infinitely complex)

it would be interesting to see ML try and "rediscover" the formula to draw it, rather than trying to imitate the likeness of the set

if the goal is just to overfit on the mandelbrot set, you can use an ELM which you can fit to it in a single step set random weights, random bias with shapes (2, nodes) (nodes) and then create your X and y data the inputs n outputs, then create a "beta" by doing this (python sorta pseudocode) ``` beta = pinv(sigmoid(X@weights+bias))@y ``` where linalg could be either torch.linalg.pinv or numpy.linalg.pinv or equivelant for Moore-Penrose Inverse in whatever language/library and sigmoid could be any implementation of the sigmoid function. the @ symbol in python is made for dot products and should work in modern versions (i use 3.7+) (in numpy you can replace it with "X.dot(weights)+bias" if you want and same for torch) and X and y are the coordinates as a matrix (X shape is: however many datapoints, 2) (and y shape is: all the values if it's monochrome or: however many datapoints, 3) then you can inference this model for new data like ``` def predict(x): return sigmoid(x@weights+bias)@beta ``` where x is your coordinates as a vector, depending on the number of nodes it should be able to fit almost perfectly in a single step, and as always the more data points the better. the only cavaet is you need tons of memory bc you cant exactly batch it, though you can fit separate elms on separate batches and then average their predictions together as an ensemble

@EmergentGarden

2 жыл бұрын

Interesting, elm = extreme learning machine? I'll look more into this when I revisit the project.

@xefoam

2 жыл бұрын

@@EmergentGarden thats right! and im glad to hear

Trying to find the authors discussion of activation functions. Best I have ever seen

Awesome! What kind of data are you feeding the NN? Is it images of Mandelbrot sets? Or simply vectors of numerical inputs to the Mandelbrot function?

@randomsnow6510

2 жыл бұрын

the nn is quried on a set of inputs and the loss is the differance between that and what the mandlebrot set outputted

@valovanonym

Жыл бұрын

@@randomsnow6510 that's not the question Ilias asked. Plus the loss it very likely to be something else than just the difference (it's not even a distance), maybe mse?

That flickering, jiggling behavior actually looks neat.

It looks like it's burning, I like it.

It would be interesting to see if an RNN could learn the Mandelbrot iteration rule.

@DrSpooglemon

Жыл бұрын

If there was a way of working that out formulaically it would save a hell of a lot of processor cycles! Especially at deep zooms..

what do you mean with "can attempt to learn"?

how you visualise this,thanks in advance

1:56 At the same time you dont need a heater in your room :D

I think one improvement you could make would be how training points are selected. Say, give it 100 points at 0 iterations, 100 points at 1 iteration, 100 points at 2 iterations, 100 points at 3 iterations ... 100 points at 2000 iterations, and 500000 points that are actually in the set, or something like that.

10 months and until now only 13 comments. Realizing I'm into some niche stuff.

The interesting thing about the mandelbrot set, as with many other complex systems, is that they can be described with a very simple expression. As far as I can tell, the neural network here is not learning the mandelbrot set any more than I am if I were to tediously memorize a subset of it one number at a time (with, of course, a lot of rounding-error). Indeed, the neural network is *incredibly* inefficient at this task - 20 layers, 400 neurons each and we get a fuzzy visual copy of something which can be expressed with essentially three terms. It reminds me of the recent findings that neural networks with 175 billion parameters were only able to perform 3-digit arithmetic with 80% accuracy. Despite their inherent overwhelming complexity, they are generally unable to identify even the simplest rules underlying a set of observations. In some ways, this limitation is quite an interesting (but kind of obvious) characteristic of their learning behaviour.

Ahahaha, I'm actually trying to do the same thing. Just 3 layers, 16 neurons each. I get interesting color gradient, but the shape doesn't really look like Mandelbrot.

It's an interesting approach, but I think a better approach would be a CNN combined with an LLM and/or GANs. So, the LLM "understands" the functional relationship of the Mandelbrot algorithm, and the CNN can create/"understand" the pictorial constructions of the Mandelbrot set. Maybe the GANs can create new Mandelbrot-like sets or algorithms.

I'm am going to code this on my ti84 or I am going to die trying

You can provide the neural network access to use formulas to create the patterns, and it would found found the original calcualtion method z = z^2 + 1 / c with attempts. 9 letter is'nt that complex if you think about it.

i wonder if someone could simulate dementia with AI? like inputting music, removing neurons one by one and then showing the final result.

@Claudineionficinal

2 жыл бұрын

Yes, you cant really remove neurons but you can set his weights to zero to simulate a missing neuron. I wonder if it will try to atleast adapt or it will fuck it up permanently

@MisterSoundless

Жыл бұрын

What an interesting question! Look at Nexpo's 'The Disturbing Art of A.I.' video, in which he mentions an experiment testing just that, via slowly removing neurons from a Stable Diffusion network and looking at the resulting effect. The relevant part starts at around 15:50, and is quite short, but still interesting.

@filippograzioli3641

Жыл бұрын

It’s basically what dropout does :)

Congrats, you just overfit huge network on a complex shape... If you can't zoom in and make it render finer details, it's overfitting

i have a formula or you: z = z^2 + 1 / c

3:24 ITS, NOT IT'S. DO YOU HAVE THE WRONGEST GRAMMAR?