Toy model: A multi-layer model doing Computation in Superposition

[danbraunai]

Migrated from: goodfire-ai/spd-gf#43
Original author: @leesharkey

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In Elhage et al. (2022) there is a section on computation in superposition, not just representation in superposition.

Previously, our resid-mlp model from the APD paper (Braun et al. (2025)) was supposed to exhibit a similar phenomenon. Follow Bhagat et al.'s post that studies this model, we're not confident that it exhibits the phenomenon that we wanted it to exhibit. In particular, we wanted it to exhibit computation in superposition.

Is there some straightforward change to the resid-mlp task or model such that it exhibits the phenomenon we want? It should:

• Be able to leverage sparsity in the input data such that it performs more computations than it has neurons while
• doing better than the 'naive' baseline of just implementing as many computations as it has neurons.