Quantum Conversations

Overview

Do the things we don't say (but perhaps that we thought) affect what we say (or think!) in the future? Modern (standard) LLMs output sequences of tokens, one token at a time. However, in order to emit a single token at timestep $t$, a model carries out a selection by taking a draw over the $V$ possible tokens in the vocabulary. The "chosen" token, $x_t$, will tend to be one of the more probable tokens, but (particularly when the model temperature is high) it might not be the most probable token-- and occasionally the chosen token might even be a lower probability token. Given that we are currently at timepoint $t$, our core question is: do humans "keep around" some representation of the history of "what could have been outputted" rather than solely storing the sequence of previously outputted tokens?

Approach

Given a model, $M$, and a sequence of tokens, $x_1, x_2, ..., x_t$, we want to examine the probability of outputting each possible token (there are $V$ of them) at time $t+1$. We can then store the full "history" of outputted token probabilities as a $V \times t$ matrix. In principle, we could consider the full set of branching paths that could have been taken. However, for a sequence of $t$ tokens, this would require storing $V^t$ possible paths. This is intractable, even for relatively short sequences ($V$ is on the order of 100,000, and $t$ is on the order of thousands). Here we approximate the set of possible paths using particle filters. Then for $n$ particles, we need to store a $V \times t \times n$ tensor.

We can then ask: given an observed sequence of tokens from a human conversation or narrative, can we better explain the token-by-token probabilities using that full tensor (e.g., by accounting for tokens not emitted), or is "all" of the predictive power carried solely by the single observed sequence?