kana VS WaveFunctionCollapse

usig modern web technologies to develop high performance scientific applications. We built a highly optimized, interactive and exploratory application for single-cell data analysis[1]. it runs purely in the browser with no backend and scales upto 200K cells. similar efforts include the biowasm project [2].

[1] https://github.com/jkanche/kana

Thank you! And yes, I agree. I was looking at uh https://github.com/mxgmn/WaveFunctionCollapse and wondering if that were applicable here :)

Have a good day!

Intuitively, it measures the difference between two probability distributions. It's not symmetric, so it's not quite that, but in my opinion, it's good intuition.

As motivation, say you're an internet provider, providing internet service to a business. You naturally want to save money, so you perhaps want to compress packets before they go over the wire. Let's say the business you're providing service to also compresses their data, but they've made a mistake and do it inefficiently.

Let's say the business has, incorrectly, determined the probability distribution for their data to be $q(x)$. That is, they assign probability of seeing symbol $x$ to be $q(x)$. Let's say you've determined the "true" distribution to be $p(x)$. The entropy, or number of bits, they expect to transmit per packet/symbol will be $-\sum p(x) lg(q(x))$. Meaning, they'll compress their stream under the assumption that the distribution is $q(x)$ but the actually probability of seeing a packet, $x$, is $p(x)$, which is why the term $p(x) lg(q(x))$ shows up.

The number of bits you're transmitting is just $-\sum p(x) lg(p(x))$. Now we ask, how many bits, per packet, is the savings of your method over the businesses? This is $-\sum p(x) lg(q(x)/p(x))$, which is exactly the Kullback-Leibler divergence (maybe up to a sign difference).

In other words, given a "guess" at a distribution and the "true" distribution, how bad is it between them? This is the Kullback-Leibler distribution and why it shows up (I believe) in machine learning and fitness functions.

As a more concrete example, I just ran across a paper talking [0] about using WFC [1] to asses how well it, and other algorithms, do when trying to create generative "super mario brothers" like levels. Take a 2x2 or 3x3 grid, make a library of tiles, use that to generate a random level, then use the K-L divergence to determine how well your generative algorithm has done compared to the observed distribution from an example image.

[0] https://arxiv.org/pdf/1905.05077.pdf

[1] https://github.com/mxgmn/WaveFunctionCollapse

Reminds me of wave function collapse - a programmatic way to generate mazes.

I am using WFC to generate the terrain, with pretty much a copy-paste implementation of the original WFC implemented into Unity.

If you still want to go the WFC route, the original WFC repository is a great place to start. There's also a (relatively barebones looking) Godot plugin you could take a look at.

wave function collapse studies - this is done with the https://github.com/mxgmn/WaveFunctionCollapse algorithm after I saw https://github.com/CodingTrain/Wave-Function-Collapse mention it. done in P5! IG https://www.instagram.com/ronivonu/

There’s an interesting approach similar to this called [Wave Function Collapse](https://github.com/mxgmn/WaveFunctionCollapse) (no relation to wfc in physics idea besides inspiration). It can infer the probabilistic constraints from one input example, and it seems to generalize quite well. Here’s a [little demo](https://oskarstalberg.com/game/wave/wave.html)