superposition-as-constrained-optimization
IN premise — summaries/2026/08/24/elhage-2022-toy-models-superposition-chunk-13.md
Created 2026-08-25T02:58:00+00:00
The Sachan follow-up (Redwood Research) formalizes superposition as a constrained optimization problem: minimize reconstruction error subject to a sparsity/orthogonality budget, providing a principled prediction of when polysemanticity emerges.
Summary
Instead of treating superposition as a mysterious byproduct of training, this reframes it as the natural outcome of a simple tradeoff: the model tries to capture as much information as possible while keeping its internal representations sparse and distinct. The practical upshot is that you can now predict when a single neuron will start juggling multiple concepts based on the model's size and budget, rather than just discovering it empirically.