Memory

Memory is the formation of: $\mathcal{M}=[M_S,M_L,M_A]$ $M_S$ - Shot term memory, verbose and full context $M_L$ - Long term memory, summaries of conversation topics $M_A$ - Attentive/Archivist memory, information fed to the model by archivist

Short term memory

$M_S$ - Shot term memory, verbose and full context

For $k$ being the current numeration of the conversation and $n$ being the length of short term memory-

$M_{S,k}={\sum }_{i=k}^{k-n}\{r_i,o_i\}$

$M_{S,k}{\subset }_{i=k}^{i=k-n}\{r_i,o_i\}$

This may be modified such that only $r_i$ or $o_i$ is included in the output, in order to prevent redundant information. This is as $o_i\mapsto r_{i+1}$ quite neatly and it is expected that ${\mathbb{I}}_{i,j}\cup {\mathbb{I}}_{i=1}\approx {\mathbb{I}}_{i,j}\cap {\mathbb{I}}_{i=1}$ when performing a language model chain.

Long term memory

$M_L$ - Long term memory, Conciseand Relevant summary of a conversation. Note: ${\varphi }_{summarize}$ may be any arbitrary function to summarize, not just a language model call.

This is derived from some arbitrary summarization function upon the prior conversation. The exact algorithm and function for implementing this may vary.

${\mathcal{M}}_{L,k}={\varphi }_{summarize}(\{[r_1,o_1],\dots ,[r_k,o_k]\})$

For cases where the summarization function produces a larger corpus than it’s input than this is considered an expansion and the summarization function is defined as ${\varphi }_{expand}$. This is a meta-cognitive effect that should be considered similar to a person’s ability to narrativize some basic facts into a larger story that contains far more information. Which is a function that expands upon $I_{target}\in {\mathbb{I}}_{1\to k}$.

${\varphi }_{expand}({\mathbb{I}}_{1\to k})=o({\mathbb{I}}_{expand})$

Where

${\mathbb{I}}_{expand}\cap {\mathbb{I}}_{1\to k}=I_{target}$

Attentive Memory

$M_A$ - Attentive/Archivist memory, information fed to the model by Archivist

This is the set of information not present in $\mathcal{S},{\mathcal{M}}_{\mathcal{S}},{\mathcal{M}}_{\mathcal{L}}$ or $\mathcal{P}$ that is considered relevant to $I_{target}$.

In order to perform these operations a variety of options are available.