Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
Superposition, Sparse Features & Monosemanticity
Frontier LMs heavily rely on superposition: neurons implement many overlapping features
#11SuperpositionRepresentations
key equation
\min_{A, s_i} \sum_i \|h_i - A s_i\|_2^2 + \lambda \|s_i\|_1Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 11 of 100SuperpositionRepresentations / Phase 5: Representation & interpretability
Current question
Simple geometric story for why superposition is useful (capacity vs interference trade-offs)
\min_{A, s_i} \sum_i \|h_i - A s_i\|_2^2 + \lambda \|s_i\|_1Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.
Why It Matters for Modern Models
- Frontier LMs heavily rely on superposition: neurons implement many overlapping features
- Monosemantic dictionaries being applied to Claude-class models for interpretability & safety
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Simple geometric story for why superposition is useful (capacity vs interference trade-offs)
- Interactive views of how sparse autoencoders carve up activation space into overlapping feature directions
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Features are represented not by one neuron each, but as sparse directions in activation space. Formalized via dictionary learning:
where are activations, columns of are features, and are sparse codes.
Sparse autoencoders applied to transformer MLP activations recover relatively interpretable, "monosemantic" features.