# Papadimitriou et al 2020 - Brain computation by assemblies of neurons

Talk for papadimitriou2020brain

We want to get from a very simple model of the brain to thoughts and logic. We present a very basic model of the brain, which consists of neurons, which fire (or not) at each timestep with some probability, and receive activations from their neighbors. (Think of Conway's game of life).

We want to show that thought, as we understand, can arise by such processes.

Important details:

- only at most \(k\) neurons fire at each step.
- the top \(k\) neurons will fire

## 1. convergence theorem: given a stimulus, eventually only the same set of neurons will be firing

- if you are in the top-\(k\) at one step, you will be more likely to fire in the next round

## 2. phenomena that can be modeled:

- projection: stimulus is reflected in set of firing neurons
- association: simultaneous stimulus result in neuron representations coming together and firing together

## 3. assembly calculus

- we have a system where we can project, associate, pattern-complete, and merge assemblies
- how powerful is this system? Turing complete

## 4. language

- stimulus mapped to assemblies, which can be hierarchically fed to higher assemblies (?)
- mimics sentence-constituent structure