D08 — Prompt Paraphrase Robustness

This framework asks: Does the circuit’s behavior depend on surface-level prompt wording, or on the underlying semantic structure?

A circuit explanation should be robust to paraphrase: if the task is “identify the indirect object,” the circuit should work regardless of whether the prompt says “Then, Mary gave a drink to” or “After that, Mary handed a drink to.” Sensitivity to surface form suggests the circuit is exploiting template-specific cues rather than implementing the claimed algorithm.

Counterfactual consistency measures this by evaluating the circuit across a battery of semantically equivalent prompt variants and quantifying how much behavior varies. Low variance indicates a robust mechanism; high variance reveals template overfitting.

Theoretical grounding

Source	Year	Key contribution
Wang et al., “Interpretability in the Wild”	2022	IOI with multiple templates (ABBA/BABA variants)
Geiger et al., “Causal Abstraction for Faithful Model Interpretability”	2023	Intervention consistency across input distributions
Conmy et al., “Towards Automated Circuit Discovery”	2023	ACDC sensitivity to prompt distribution
Hanna et al., “How does GPT-2 compute greater-than?“	2023	Template robustness for year comparison

Core concept

Given a set of paraphrases ( {x_1, \ldots, x_K} ) for the same underlying task instance, robustness is measured by the coefficient of variation of the circuit’s task metric:

[ \text{CV} = \frac{\sigma_M}{\mu_M} = \frac{\text{std}(M(C, x_1), \ldots, M(C, x_K))}{\text{mean}(M(C, x_1), \ldots, M(C, x_K))} ]

where ( M(C, x_k) ) is the circuit’s faithfulness score (logit diff, KL, etc.) on paraphrase ( k ). Low CV indicates that the circuit implements a template-invariant computation. Alternatively, the consistency score compares the worst-case paraphrase to the best-case:

[ \text{Consistency} = \frac{\min_k M(C, x_k)}{\max_k M(C, x_k)} ]

Instruments under D08

Counterfactual Consistency (34_counterfactual_consistency.py)

Evaluates circuit faithfulness across multiple prompt template variants for each task, reporting per-template scores and their variance.

What it establishes: Whether the circuit captures template-invariant structure. What it does not establish: Which specific template features the circuit is sensitive to (requires further ablation).

Usage:

uv run python 34_counterfactual_consistency.py --tasks ioi sva

Reading the scores

Pattern	What it means
CV < 0.05	Highly robust — circuit is template-invariant
CV 0.05–0.15	Mostly robust with minor template sensitivity
CV > 0.3	Template-dependent — circuit exploits surface cues
Consistency > 0.9	Worst case is close to best case
One template fails dramatically	Circuit relies on a specific positional pattern