Capability from Access Structure, Not Scale: Lower Bounds and Pre-Registered Tests for Hybrid Sequence Models

Short summary

The paper proposes the Capability Convergence Hypothesis: under fixed inference budgets, representational convergence does not guarantee capability convergence. Capability instead converges toward access-complete hybrid architectures combining compressive O(1)-state channels with scalable verbatim-index channels. Pre-registered experiments confirm predicted performance gaps between architectures, with one prediction failing and reported transparently.

• •Capability Convergence Hypothesis: representational convergence from scale does not imply capability convergence under fixed budgets
• •Identifies three resource walls (Shannon, horizon, circuit) that only access-complete hybrid architectures can cross
• •Pre-registered experiments confirm most predictions, with one failure reported transparently

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