Critical time threshold for aggregation failure in non-recurrence-complete models

Determine whether there exists a critical time threshold t beyond which any non-recurrence-complete sequence model—defined as an architecture that cannot realize general hidden-state-dependent recurrent updates due to fully parallelizable forward or backward computation—fails to correctly aggregate inputs in long-horizon agentic settings such as software engineering agents.

Background

The paper formalizes recurrence completeness and true depth, arguing that architectures whose forward or backward passes are fully parallelizable cannot realize general hidden-state-dependent recurrences. It introduces input aggregation criticality as the practical manifestation of these limits: beyond some horizon, non-recurrence-complete models are predicted to fail at forming correct latent states when tasks require non-scannable, strictly serial integration.

Within this theoretical framing, the authors explicitly conjecture the existence of a critical time t after which non-recurrence-complete models can no longer aggregate inputs correctly, emphasizing implications for agentic systems (e.g., software engineering agents) that must integrate long streams of side-effect-laden observations.