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This paper shows that hierarchical clustering can simultaneously satisfy scale invariance, richness, and consistency axioms, resolving Kleinberg's Impossibility Theorem for flat clustering. It constructs admissible hierarchical methods and analyzes their diversity and common backbone.
This paper formalizes the impossibility of perfect prompt-injection prevention in shared-embedding sequence models, proving that no in-pipeline mechanism can guarantee Semantic-Faithful Control due to inseparable representations of instructions and data, analogous to code-data confusion in Von Neumann architectures.
This paper formally defines the problem of eliciting latent knowledge (ELK) from AI systems using Causal Influence Diagrams, and proves an impossibility theorem: no feedback-based training strategy that depends only on agent behavior can guarantee an honest agent, even with perfect training feedback.