Mathspp: mathematics and programming

Pt En In this post I will show you how I got a neural network to write digits that look like they've been handwritten. In fact, the digits you can see in the first image of this post where generated by said neural network. The code that did all this is here . It all started when I read, some time ago, about this funny way in which you could use neural networks: you are going to train a neural network to take a vector of size $N$ as input, and you are going to teach your network to do nothing. That is, you are going to teach your neural network to behave as the identity function... but with a twist! If your input size is $N$, somewhere in the middle of the network you want to have a layer with less than $N$ neurons! If this happens, you can think that your vector $x$ that is going in, first has to be squeezed through that tight layer, and then it expands again to be the output of the network. If now you slice your network in half, the part of the network from the...

Pt En In this previous post I shared some code and animations of an algorithm that created random mazes. I shared it with you and I got some feedback on Facebook, saying that even the stupidly large mazes I gave you were really easy to solve (I think this link can show you what I am talking about). So it was about time I got you some new mazes! And this time, I don't think they are as easy to solve as the old ones. The mazes I am sharing today were created by code found in this GitHub repo . The README will tell you to run the wilson_generator.py file. You can also download the (windows) executable that is zipped inside the wilsonExe rar. (please notice that in both cases, you can use the wilsonconfig.ini file to change the size of the maze) The way our algorithm works is really simple. It will start a random walk on the top left corner of the window. Whenever the random walk intersects itself (creating a loop), it removes the loop from the walk, and then c...