Legacy Concept Lab

Automated Circuit Discovery: Patching, Attribution & Decomposition at Scale

Moves mechanistic interpretability from "one-off archaeology" to repeatable pipeline—essential for scaling to frontier models

Concept 28 of 100RepresentationsPhase 5
#28Circuit DiscoveryRepresentations
key equation
ΔE=L(xcleando(E=ecorr))L(xclean)\Delta_E = \left| L(x_{\text{clean}}\mid \text{do}(E=e_{\text{corr}})) - L(x_{\text{clean}}) \right|
Phase 5: Representation & interpretabilityConcept 28 of 100

Why It Matters for Modern Models

  • Moves mechanistic interpretability from "one-off archaeology" to repeatable pipeline—essential for scaling to frontier models
  • 2024-2025 trend: ACDC (slow patching) → EAP (faster approximation) → CD-T (decomposition in seconds)—speed is the bottleneck
  • Enables target selection for steering, safety interventions, debugging—you need to find the circuit before you can edit it
  • After SAEs (#27), this shows how to build feature-level circuits automatically, not just head/neuron circuits
  • Bridges to automated red-teaming and interpretability evaluations at scale—necessary for AI safety pipelines

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Activation patching is causal; attribution patching is linearized causal—approximation can be useful even when unfaithful pointwise
  • Metric choice is everything—some metrics create degenerate gradients (zero-gradient at optimum), automated methods inherit these failures
  • Circuits are not unique—many sparse subgraphs can reproduce behavior, pruning reveals a mechanism not the mechanism
  • Speed-faithfulness tradeoff is fundamental—slow patching is accurate, fast approximations trade correctness for scalability
  • Circuit discovery is hypothesis testing—you're testing "does this subgraph explain behavior X" not discovering ground truth

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
ΔE=L(xcleando(E=ecorr))L(xclean)\Delta_E = \left| L(x_{\text{clean}}\mid \text{do}(E=e_{\text{corr}})) - L(x_{\text{clean}}) \right|

Automated circuit discovery turns mechanistic interpretability into a search/scoring/pruning problem over the model's computational graph, moving from hand-crafted case studies to scalable pipelines.

Activation patching as causal intervention (edge/node ablation):

ΔE=L(xcleando(E=ecorr))L(xclean)\Delta_E = \left| L(x_{\text{clean}}\mid \text{do}(E=e_{\text{corr}})) - L(x_{\text{clean}}) \right|

This measures causal effect: replace edge EE with value from corrupted run, measure impact on loss.

Attribution patching (first-order/Taylor approximation):

L(xcleando(E=ecorr))L(xclean)+(ecorreclean)ecleanLL(x_{\text{clean}}\mid \text{do}(E=e_{\text{corr}})) \approx L(x_{\text{clean}}) + (e_{\text{corr}}-e_{\text{clean}})^\top \frac{\partial}{\partial e_{\text{clean}}}L

Linearized causal estimate—faster than full patching, but approximation can be unfaithful.

Edge scoring + pruning (circuit extraction):

sE=ΔEL,then keep top-k edgess_E = |\Delta_E L|, \quad \text{then keep top-}k\text{ edges}

Rank edges by importance, prune to minimal circuit that preserves behavior.

Canonical Papers

Towards Automated Circuit Discovery for Mechanistic Interpretability

Conmy et al.2023NeurIPS
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Attribution Patching Outperforms Automated Circuit Discovery

Syed et al.2024BlackBoxNLP / ACL
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Efficient Automated Circuit Discovery in Transformers using Contextual Decomposition

Hsu et al.2025ICLR
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Connections

Next Moves

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