Important Note: Since writing this, there's been a lot of exciting work on understanding superposition via training sparse autoencoders to take features out of superposition. I recommend reading up on that work, since it substantially changes the landscape of what problems matter here.

This is the fifth post in a sequence called 200 Concrete Open Problems in Mechanistic Interpretability. Start here, then read in any order. If you want to learn the basics before you think about open problems, check out my post on getting started. Look up jargon in my Mechanistic Interpretability Explainer

Motivating papers: Toy Models of Superposition, Softmax Linear Units

Background

If you're familiar with polysemanticity and superposition, skip to Motivation or Problems.

Neural networks are very high dimensional objects, in both their parameters and their activations. One of the key challenges in Mechanistic Interpretability is to somehow resolve the curse of dimensionality, and to break them down into lower dimensional objects that can be understood (semi-)independently.

Our current best understanding of models is that, internally, they compute features: specific properties of the input, like "this token is a verb" or "this is a number that describes a group of people" or "this part of the image represents a car wheel". That early in the model there are simpler features, are later used to compute more complex features by being connected up in a circuit (example shown above (source)). Further, our guess is that features correspond to directions in activation space. That is, for any feature that the model represents, there is some vector corresponding to it. And if we dot product the model's activations with that vector, we get out a number representing whether that feature is present.(these are known as decomposable, linear representations)

This is an extremely useful thing to be true about a model! An even more helpful thing to be true would be if neurons correspond to features (ie the output of an activation function like ReLU). Naively, this is natural for the model to do, because a non-linearity like ReLU acts element-wise - each neuron's activation is computed independently (this is an example of a privileged basis). Concretely, if a neuron can represent feature A or feature B, then that neuron will fire differently for feature A and NOT feature B, vs fea...