Continuous Function

Legacy Concept Lab

Transformer Circuits, Induction Heads & Mechanistic Interpretability

These frameworks study GPT-style models, including Llama-3 and Claude-3, by identifying concrete circuits

Concept 13 of 100RepresentationsPhase 5
Open DemoAll Foundations
#13CircuitsRepresentations
key equation
rl+1=rl+Wlattnrl+Wlmlprlr_{l+1} = r_l + W^{\text{attn}}_l r_l + W^{\text{mlp}}_l r_l
Phase 5: Representation & interpretabilityConcept 13 of 100

Why It Matters for Modern Models

  • These frameworks study GPT-style models, including Llama-3 and Claude-3, by identifying concrete circuits
  • Inform safety research (locating deception-related circuits) and architecture design

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Interactive visualizations of how QK and OV matrices implement algorithms like induction
  • Broader taxonomies of circuit motifs beyond a few toy examples

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
rl+1=rl+Wlattnrl+Wlmlprlr_{l+1} = r_l + W^{\text{attn}}_l r_l + W^{\text{mlp}}_l r_l

Decompose transformer computations into linear components on the residual stream:

rl+1=rl+Wlattnrl+Wlmlprlr_{l+1} = r_l + W^{\text{attn}}_l r_l + W^{\text{mlp}}_l r_l

Induction heads: specific attention heads implement an algorithm:

[A][B]…[A]→[B][A][B]\dots[A] \rightarrow [B]

by attending from the final [A] token to previous [A] tokens and copying the subsequent token's representation.

The sudden appearance of these heads is tied to a phase transition in in-context learning.

Canonical Papers

A Mathematical Framework for Transformer Circuits

Elhage et al.2021Anthropic
Read paper →

In-Context Learning and Induction Heads

Olsson et al.2022Anthropic
Read paper →

Connections

Prerequisites

⊗Attention◎Embeddings⊕Superposition⚲Probing

Enables

🔍Sparse Autoencoders🔬Circuit Discovery📝ICL

Next Moves

Explore this concept from different angles — like a mathematician would.

Semantic Connections

≈ Analogy
🔬Circuits→Circuit Discovery◎Algorithmic feature→Embeddings
🔄 Same Technique
⊗Copy via attention→Attention🔬Ablation studies→Circuit Discovery
⚠️ Breaks When
ΘFeature learning dominates→NTK