D05 — Top-K Accuracy

This framework asks: Does the circuit preserve the model’s most confident predictions?

Top-K accuracy provides a discrete, human-interpretable faithfulness measure: does the circuit’s output ranking agree with the full model’s top predictions? While KL divergence (D03) and CE delta (D04) capture continuous distributional differences, top-K accuracy answers the practical question of whether the circuit gets the “right answer” — where “right” means agreeing with the full model’s top choices.

This metric is especially informative for tasks with multiple valid completions. A circuit may have moderate KL divergence but perfect top-5 accuracy, indicating it captures the core mechanism while differing only in probability mass allocation among low-ranked tokens.

Theoretical grounding

Source	Year	Key contribution
Wang et al., “Interpretability in the Wild”	2022	Accuracy-based metrics alongside logit diff
Conmy et al., “Towards Automated Circuit Discovery”	2023	Top-1 accuracy as circuit quality threshold
Goldowsky-Dill et al., “Localizing Model Behavior”	2023	Ranking preservation under intervention
Olsson et al., “In-context Learning and Induction Heads”	2022	Token prediction accuracy for induction tasks

Core concept

Let ( \text{top}_K^{\text{full}}(x) ) be the set of K highest-probability tokens under the full model, and ( \text{top}_K^{\text{circuit}}(x) ) the same under the circuit. Top-K accuracy is:

[ \text{Acc}@K = \frac{1}{N} \sum_{i=1}^{N} \frac{|\text{top}_K^{\text{full}}(x_i) \cap \text{top}_K^{\text{circuit}}(x_i)|}{K} ]

For the special case ( K=1 ), this reduces to exact-match accuracy: does the circuit predict the same top token as the full model? Weighted variants incorporate rank correlation (Kendall’s ( \tau )) over the top-K set:

[ \tau_K = \text{KendallTau}\bigl(\text{rank}_K^{\text{full}},; \text{rank}_K^{\text{circuit}}\bigr) ]

Instruments under D05

Output Variants — Top-K Mode (21_output_variants.py)

Evaluates top-1, top-5, and top-10 agreement between circuit and full model outputs, plus rank correlation within the top-K set.

What it establishes: Whether the circuit preserves the model’s discrete predictions. What it does not establish: Probability calibration — two distributions can agree on ranking but differ in confidence.

Usage:

uv run python 21_output_variants.py --tasks ioi sva --metric topk

Reading the scores

Pattern	What it means
Top-1 accuracy > 95%	Circuit reproduces the model’s best guess
Top-5 accuracy > 90%	Core ranking structure preserved
Top-1 high but top-10 low	Circuit captures dominant mode, misses alternatives
Rank correlation > 0.9	Fine-grained ordering within top-K preserved
Top-K drops sharply with K	Circuit is narrow — captures one mechanism only