I agree that a possible downside of talking about capabilities is that people might assume they are uncorrelated and we can choose not to create them. It does seem relatively easy to argue that deception capabilities arise as a side effect of building language models that are useful to humans and good at modeling the world, as we are already seeing with examples of deception / manipulation by Bing etc. 

I think the people who think we can avoid building systems that are good at deception often don't buy the idea of instrumental convergence either (e.g. Yann LeCun), so I'm not sure that arguing for correlated capabilities in terms of intelligence would have an advantage. 

The issue with being informal is that it's hard to tell whether you are right. You use words like "motivations" without defining what you mean, and this makes your statements vague enough that it's not clear whether or how they are in tension with other claims. (E.g. what I have read so far doesn't seems to rule out that shards can be modeled as contextually activated subagents with utility functions.) 

An upside of formalism is that you can tell when it's wrong, and thus it can help make our thinking more precise even if it makes assumptions that may not apply. I think defining your terms and making your arguments more formal should be a high priority. I'm not advocating spending hundreds of hours proving theorems, but moving in the direction of formalizing definitions and claims would be quite valuable. 

It seems like a bad sign that the most clear and precise summary of shard theory claims was written by someone outside your team. I highly agree with this takeaway from that post: "Making a formalism for shard theory (even one that’s relatively toy) would probably help substantially with both communicating key ideas and also making research progress." This work has a lot of research debt, and paying it off would really help clarify the disagreements around these topics. 

Thanks Daniel, this is a great summary. I agree that internal representation of the reward function is not load-bearing for the claim. The weak form of representation that you mentioned is what I was trying to point at. I will rephrase the sentence to clarify this, e.g. something like "We assume that the agent learns a goal during the training process: some form of implicit internal representation of desired state features or concepts". 

Thanks Daniel for the detailed response (which I agree with), and thanks Alex for the helpful clarification.

I agree that the training-compatible set is not predictive for how the neural network generalizes (at least under the "strong distributional shift" assumption in this post where the test set is disjoint from the training set, which I think could be weakened in future work). The point of this post is that even though you can't generally predict behavior in new situations based on the training-compatible set alone, you can still predict power-seeking tendencies. That's why the title says "power-seeking can be predictive" not "training-compatible goals can be predictive". 

The hypothesis you mentioned seems compatible with the assumptions of this post. When you say "the policy develops motivations related to obvious correlates of its historical reinforcement signals", these "motivations" seem like a kind of training-compatible goals (if defined more broadly than in this post). I would expect that a system that pursues these motivations in new situations would exhibit some power-seeking tendencies because those correlate with a lot of reinforcement signals. 

I suspect a lot of the disagreement here comes from different interpretations of the "internal representations of goals" assumption, I will try to rephrase that part better. 

The internal representations assumption was meant to be pretty broad, I didn't mean that the network is explicitly representing a scalar reward function over observations or anything like that - e.g. these can be implicit representations of state features$.$ I think this would also include the kind of representations you are assuming in the maze-solving post, e.g. cheese shards / circuits. 

Here is my guess on how shard theory would affect the argument in this post:

1. In my understanding, shard theory would predict that the model learns multiple goals from the training-compatible (TC) set (e.g. including both the coin goal and the go-right goal in CoinRun), and may pursue different learned goals in different new situations. The simplifying assumption that the model pursues a randomly chosen goal from the TC set also covers this case, so this doesn't affect the argument. 
2. Shard theory might also imply that the training-compatible set should be larger, e.g. including goals for which the agent's behavior is not optimal. I don't think this affects the argument, since we just need the TC set to satisfy the condition that permuting reward values in $S_{\text{ood}}$ will produce a reward vector that is still in the TC set. 

So think that assuming shard theory in this post would lead to the same conclusions - would be curious if you disagree.