This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision |
| uiai [2026/03/17 10:27] – [Definition: Counterfactual action] pedroortega | uiai [2026/03/17 10:30] (current) – [Definition: Third-party action] pedroortega |
|---|
| o_t = w\,\dot{a}_{t+1}\,v. | o_t = w\,\dot{a}_{t+1}\,v. |
| $$ | $$ |
| | |
| | {{ :uiai-third-party.png?600 |}} |
| |
| **Diagram note.** | **Diagram note.** |
| The intended picture is that inside a long world-written observation token, there is an embedded block $\dot{a}_4$ that occupies an $\mathcal{A}$-position under the tokenization convention, even though on-path it is still written by the world and therefore appears as evidence. | The diagram illustrates a third party action. Inside a long observation token $o_3$, one can identify an embedded block $\dot{a}_4$ that is interpreted as a third-party action. Because it is written by the world, it counts as evidence. |
| |
| It is not hard to see that, for a given potential index $k$, the counterfactual action $\dot{a}_{t+1}$ and the third-party action $\dot{a}_{t+1}$ are the same random block: the difference is only whether the gate sampled $\gamma_k = 1$ (counterfactual, not observed) or $\gamma_k = 0$ (third-party, observed) at position $k$. The precise distinction between the different types of $\mathcal{A}$-tokens is important; we will also refer to them as //factual// (first-person, agent-generated), //counterfactual//, and //third-party// $\mathcal{A}$-tokens. | It is not hard to see that, for a given potential index $k$, the counterfactual action $\dot{a}_{t+1}$ and the third-party action $\dot{a}_{t+1}$ are the same random block: the difference is only whether the gate sampled $\gamma_k = 1$ (counterfactual, not observed) or $\gamma_k = 0$ (third-party, observed) at position $k$. The precise distinction between the different types of $\mathcal{A}$-tokens is important; we will also refer to them as //factual// (first-person, agent-generated), //counterfactual//, and //third-party// $\mathcal{A}$-tokens. |