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so we can control values by controlling data.

What do you mean? As in you would filter specific data from the posttraining step? What would you be trying to prevent the model from learning specifically?

We need to split "search" into more fine-grained concepts.

For example, "model has representation of the world and simulates counterfactual futures depending of its actions and selects action with the highest score over the future" is a one notion of search.

The other notion can be like this: imagine possible futures as a directed tree graph. This graph has set of axioms and derived theorems describing it. Some of the axioms/theorems are encoded in model. When model gets sensory input, it makes 2-3 inferences from combination of encoded theorems + input and selects action depending on the result of inference. While logically this situation is equivalent to some search over tree graph, mechanistically it looks like "bag of heuristics".  

"Feature multiplicity" in language models. 

This refers to the idea that there may be many representations of a 'feature' in a neural network. 

Usually there will be one 'primary' representation, but there can also be a bunch of 'secondary' or 'dormant' representations. 

If we assume the linear representation hypothesis, then there may be multiple direction in activation space that similarly produce a 'feature' in the output. E.g. the existence of 800 orthogonal steering vectors for code [LW · GW]. 

This is consistent with 'circuit formation' resulting in many different circuits / intermediate features [LW(p) · GW(p)], and 'circuit cleanup' happening only at grokking. Because we don't train language models till the grokking regime, 'feature multiplicity' may be the default state. 

Feature multiplicity is one possible explanation for adversarial examples. In turn, adversarial defense procedures such as obfuscated adversarial training or multi-scale, multi-layer aggregation may work by removing feature multiplicity, such that the only 'remaining' feature direction is the 'primary' one. 

Thanks to @Andrew Mack [LW · GW]  for discussing this idea with me

Really liked this post!

Just for my understanding:

You mention trans/cross-coders as possible solutions to the listed problems, but they also fall prey to issues 1 & 3, right?

Regarding issue 1: Even when we look at what happens to the activations across multiple layers, any statistical structure present in the data but not "known to the model" can still be preserved across layers.

For example: Consider a complicated curve in 2D space. If we have an MLP that simply rotates this 2D space, without any knowledge that the data falls on a curve, a Crosscoder trained on the pre-MLP & post-MLP residual stream would still decompose the curve into distinct features. Similarly, a Transcoder trained to predict the post-MLP from the pre-MLP residual stream would also use these distinct features and predict the rotated features from the non-rotated features.

Regarding issue 3: I also don't see how trans/cross-coders help here. If we have multiple layers where the {blue, red} ⊗ {square, circle} decomposition would be possible, I don't see why they would be more likely than classic SAEs to find this product structure rather than the composed representation.

A big reason for this is logistics, as how you are getting to the fight can actually hamper you a lot, and this especially bites hard on offense, because it's easier to get supplies to your area than it is to get supplies to an offensive unit.

ah. for 'at optimality' which you wrote, i don't imagine it to take place on that high of a macroscopic level (the one on which 'supplies' could be transported), i think the limit is more things that look to us like the category of 'angling rays of light just right to cause distant matter to interact in such away as to create an atomic explosion, or some even more destructive reaction we don't yet know about, or to suddenly carve out a copy of itself there to start doing things locally', and also i'm not imagining the competitors being 'solid' macroscopic entities anymore, but rather being patterns imbued (and dispersed) in a relatively 'lower' level of physics (which also do not need 'supplies'). (edit: maybe this picture is wrong, at optimality you can maybe absorb the energy of such explosions / not be damaged by them, if you're not a macroscopic thing)

(i'm just exploring what it would be like to be clear, i don't think such conflicts will happen because i still expect just one optimal-level-agent to come from earth)

Why understanding planning / search might be hard

It's hypothesized that, in order to solve complex tasks, capable models perform implicit search during the forward pass. If so, we might hope to be able to recover the search representations from the model. There are examples of work that try to understand search in chess models and Sokoban models [LW · GW]. 

However I expect this to be hard for three reasons. 

1. The model might just implement a bag of heuristics [LW · GW]. A patchwork collection of local decision rules might be sufficient for achieving high performance. This seems especially likely for pre-trained generative models [LW · GW].
2. Even if the model has a globally coherent search algorithm, it seems difficult to elucidate this without knowing the exact implementation (of which there can be many equivalent ones). For example, search over different subtrees may be parallelised [LW · GW] and subsequently merged into an overall solution.  
3. The 'search' circuit may also not exist in a crisp form, but as a collection of many sub-components that do similar / identical things. 'Circuit cleanup' only happens in the grokking regime, and we largely do not train language models till they grok. 

Well done for managing to push something out there. It's a good start, I'm sure you'll fill in some of the details with other posts over time.

? I don't know  Rosencranz.

I'm asking you  because you say "Is it the case that the tech would exist without him? I think that's pretty unclear" and this, in my view, depends a lot on the answers to those questions.

Is China doing well in the EV space a bad thing?

The opposite, it is good. But if Musk did not have any influence on it, this diminishes Musk's positive impact in this field, making his impact less positive.

What do we privilege, the preference of doctors or the welfare of patients?

What is more important, educators preferences or quality of children education?

I understand you intended these questions to be rhetorical, but the answers you think are obvious: did you arrive at them through "pure reason," or by looking at what "democratic consensus" actually ended up with?