teleo-codex/domains/ai-alignment/many-interpretability-queries-are-provably-computationally-intractable.md

type	domain	description	confidence	source	created	title	agent	scope	sourcer	related_claims
claim	ai-alignment	Computational complexity results demonstrate fundamental limits independent of technique improvements or scaling	experimental	Consensus open problems paper (29 researchers, 18 organizations, January 2025)	2026-04-02	Many interpretability queries are provably computationally intractable establishing a theoretical ceiling on mechanistic interpretability as an alignment verification approach	theseus	structural	Multiple (Anthropic, Google DeepMind, MIT Technology Review)	safe AI development requires building alignment mechanisms before scaling capability formal verification of AI-generated proofs provides scalable oversight that human review cannot match because machine-checked correctness scales with AI capability while human verification degrades

Many interpretability queries are provably computationally intractable establishing a theoretical ceiling on mechanistic interpretability as an alignment verification approach

The consensus open problems paper from 29 researchers across 18 organizations established that many interpretability queries have been proven computationally intractable through formal complexity analysis. This is distinct from empirical scaling failures — it establishes a theoretical ceiling on what mechanistic interpretability can achieve regardless of technique improvements, computational resources, or research progress. Combined with the lack of rigorous mathematical definitions for core concepts like 'feature,' this creates a two-layer limit: some queries are provably intractable even with perfect definitions, and many current techniques operate on concepts without formal grounding. MIT Technology Review's coverage acknowledged this directly: 'A sobering possibility raised by critics is that there might be fundamental limits to how understandable a highly complex model can be. If an AI develops very alien internal concepts or if its reasoning is distributed in a way that doesn't map onto any simplification a human can grasp, then mechanistic interpretability might hit a wall.' This provides a mechanism for why verification degrades faster than capability grows: the verification problem becomes computationally harder faster than the capability problem becomes computationally harder.