Chapter 5: How to Describe?

post by ld97 · 2020-03-02T10:07:03.166Z · LW · GW · None comments

A quick reminder about rules: We have a network of objects and two different parts of it activated at the same time. The connection between them hasn't established yet. If we try to increase the strength of the signal or reduce the activation threshold - we will receive a complete mess as an output. Our goal is to create a mechanism that will work only using existing information about the network.

Now I will add some mathematics to describe our problem with more formal language. There won't be any complicated stuff. We've been already using it all this time, but haven't used this terminology.

First of all, let's rename our network of objects to Knowledge Graph. If "graph" sounds scary to you, or you feel like "oh, it was that thing from discrete mathematics," - don't worry. I will quickly explain what it is and why our network is a graph.

The graph is a set of vertices and edges between them. Imagine circles and lines connecting them.
Vertices are circles. Lines are edges.
In our network, vertices are objects. Connections between them are edges.
We were talking about graphs all the time you are reading this sequence. But didn't call them so. And most of the time, we were talking about Oriented Weighted Graph.
Oriented means that instead of lines, we will use arrows. They show us how the signal can travel among the graph. If we have an arrow from the vertex (object), the signal can go from vertex-sender to vertex-receiver.
Weighted means that every arrow will have some number on top of it. In our case, it will be connection strength.

Graph theory is about finding some common rules for structures that can be described with vertices and edges. It answers questions like:
How can ve travel between vertices using edges?
Can we color vertices by some rule? For example, can we color graph the way no neighbors (connected vertices) won't have the same color?
And etc.

Here comes the trickiest part of all this stuff. Remember, how did we define objects? The strongly coupled subnetworks of neurons. Inside they are also graphs! So we have a Graph of graphs. And vertices of inner graphs can have their own "independent" connections. And that's why we can split the object "Special Relativity" to "relativity" and "special" parts, that have separate connections and meanings. We can travel to neighbors that are "around" objects or Go Deeper and explore "subobjects."

We have a Knowledge Graph, that can be described mathematically as a graph there each object also can be a graph. Because of these words sound very complex, and I've given you a promise that there won't be any too complicated stuff, let's forget about it and return to our well-known world with circles and arrows. So, let's not thinking about it. But thinking IS about it. Please don't keep it in mind. Damn, I love this language, my native one don't have such mindblowing potential.

To connect two objects that are not neighbors, we need to find a way for the signal. It will jump from one object to another, and we need something that will show it the direction.
I couldn't resist a rhyming "graph" and "path":

A task we solving is well-known
In Theory of graphs,
To make connections between zones
We need to find a path.

That's how we can describe our problem using graph theory. We are trying to create some mechanism that will help signal to find the path in our Knowledge Graph.

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