Cristian-Curaba

By scanning the graphical proof, I don't see any issue on the following generalization of the Mediator Determines Redund Theorem:
Let $X_1,\dots ,X_n,\Lambda$ and ${\Lambda }^{\prime }$ be random variables and let $X_1,\dots ,X_m$ be any not-empty subset of $X_1,\dots ,X_n$ that satisfy the following conditions:
    - $\Lambda$ Mediation: $X_1,\dots ,X_m$ are independent given $\Lambda$
    - ${\Lambda }^{\prime }$ Redundancy: $\forall j\in \{1,\dots ,m\}{\Lambda }^{\prime }\leftarrow X_j\to {\Lambda }^{\prime }$
Then ${\Lambda }^{\prime }\leftarrow \Lambda \to {\Lambda }^{\prime }$.

In the above, I've weaken the ${\Lambda }^{\prime }$ Redundancy hypothesis, requiring ... (read more)

Great work! I have a technical question.

My current understanding is as follows:

1.  If we have even one observable variable with agreement observation and for which the latent variables satisfy the exact naturality condition, we can then build the transferability function exactly.
2.  In the approximation case, if we have multiple observable variables that meet these same conditions, we can choose the specific variable (or set of variables, in the proofs you used a couple) that will minimize the ${ϵ}_{red}$ errors. We would not need to use all o... (read more)

TL;DR
If the narrow (but intelligent) AI can weakly interact with the environment, adapt from feedback and exfiltrate secretly, even once, it can learn how to translate from its ancient language to the environmental one by building samples of pairs. The crucial aspect is training the agent on an unknown/unconventional alphabet: the outputs are meaningless from the environmental point of view, limiting the environmental learning possibilities of the language.

The goal of the following comment is two-sided:
Let's assume that the narrow (but intelligent) AI can ... (read more)