Genetic Notation for Prompts

Definition

An input $r$ is composed of a set of information ${\mathbb{I}}_r$ that is represented by a token sequence $\mathbf{x}=\{x_1,\dots ,x_n\}$ where $n$ is equal to the token length of $r$.

$r({\mathbb{I}}_r,\mathbf{x})$

Gene

A “gene”, $g$, can be considered some subset $g_i\subseteq \mathbf{x}$ such that:

$({\varphi }^{‘}(g_i)=I_{g,i})\subset {\mathbb{I}}_r$

Which in plain English means that we are able to use some set of tokens $g$ present in $\mathbf{x}$ to derive a piece of information $I_{g,i}$ .

Genotype

A genotype for a prompt is the exact content of the prompt $r_i$ itself. This is to say $\mathbf{x}$

Phenotype

Phenotype is the outcome obtained from some prompt. This would be determined to be the $o_i$ that is observed. Now we can have different levels of stringency here, same in biology. As there may be a set $o_i$ which denotes the outputs that when decoded produce some target information. For:

$o_i\in o,{\varphi }^{‘}(o_i)=I_{target}$

Mutation notation

A mutation is a perturbation of an input $r\to r_m$ where the token sequence $\mathbf{x}\to {\mathbf{x}}_m$. This means that the information accessible by the prompt is changed, ${\mathbb{I}}_r\to {\mathbb{I}}_{r,m}$ .