Foundation Lab

Logit Lens: Probing Intermediate Representations

First simple tool for "seeing inside" transformers—reveals layer-by-layer computation

Concept 46 of 100RepresentationsPhase 5

#46Logit LensRepresentations

key equation

\text{logits}^{(l)} = W_U \cdot h^{(l)}

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 46 of 100Logit LensRepresentations / Phase 5: Representation & interpretability

Current question

The unembedding matrix acts as a "universal probe"—no training required, just matrix multiply

\text{logits}^{(l)} = W_U \cdot h^{(l)}

PredictionCommit before tracing the equation.

Ask what should change under a concrete input, then trace that expectation through the equation.

EvidenceCompare the equation and source.

Use the key equation and canonical papers as the available witnesses, without implying that a runnable panel exists.

InvariantName what survives notation changes.

The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.

Next moveContinue through the atlas.

Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.

First simple tool for "seeing inside" transformers—reveals layer-by-layer computation
Shows that early layers often predict related tokens, later layers refine to the final answer
Foundation for activation patching and circuit analysis techniques

What is still poorly explained in textbooks and papers:

The unembedding matrix acts as a "universal probe"—no training required, just matrix multiply
Not all layers show sensible tokens: some layers store information in non-token-interpretable ways
Tuned lens (learned affine per layer) often works better than raw logit lens

If you want intuition first, start with the key equation and cited sources. Come back here for the full walkthrough.

Key Equation

\text{logits}^{(l)} = W_U \cdot h^{(l)}

Logit lens applies the unembedding matrix to intermediate residual stream states:

\text{logits}^{(l)} = W_U \cdot h^{(l)}

where $W_U$ is the unembedding matrix and $h^{(l)}$ is the residual stream at layer $l$ .

This reveals what token the model would predict if it "stopped" at layer $l$ :

p^{(l)}(\text{token}) = \text{softmax}(\text{logits}^{(l)})

The progression $p^{(0)} \to p^{(L)}$ shows how the prediction evolves through the network.

nostalgebraist2020LessWrong

Choose the next question to carry this object forward.