The Capability Convergence Hypothesis: Capability from Access Structure, Not Scale

What the math gives to ML

The paper isolates a useful architectural principle: prediction can only exploit history through the query-time accessible state, regardless of how expressive the hidden representation is. Its data-processing bound turns an architectural bottleneck into a measurable quantity, and motivates combining a fixed-size compressive state with a query-dependent verbatim retrieval channel. The most actionable transfer is a budgeted hybrid recurrent/SSM backbone augmented by sparse attention or external memory, with the retrieval path activated when the state channel cannot preserve the required information. This is not merely a larger state: the two channels support qualitatively different operations, compression for long-range mixing and indexed access for exact facts.