ICLR26 Paper Defines 'Interpretive Equivalence': Comparing Neural Network Algorithms Without Full Interpretation
burny_tech · x · 2026-09-18
Alan Sun and Mariya Toneva's ICLR26 paper (arXiv:2603.30002) tackles a fundamental mechanistic interpretability question: can we determine whether two neural networks implement the same underlying algorithm without fully interpreting either?
- Core concept: "interpretive equivalence" — two interpretations are equivalent if all their possible implementations are equivalent.
- Method: treat a high-level mechanism as a family of consistent model implementations, generate alternatives via causal interventions on behaviorally irrelevant components, then compare representation spaces.
- Under causal-abstraction assumptions, they derive upper and lower bounds linking representational distance to interpretive distance, bridging circuits, causal abstractions, and representation geometry.
- Case studies on Transformers plus a Congruity test lay groundwork for rigorous MI evaluation and automated, generalizable interpretation.
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