Separately parameterized high/low recurrent modules

Determine whether a high/low recurrent-state architecture with separately parameterized high- and low-level recurrent modules provides benefits beyond the shared-module high/low configuration evaluated in the paper.

Background

The paper evaluates a matched high/low recurrent-state design in which the same recurrent body updates both states. That shared-module hierarchy produces no consistent aggregate benefit and substantially degrades MATH500 performance.

The authors explicitly limit this conclusion to the shared-module setting and note that the separately parameterized modules used by HRM-Text were not tested, leaving their potential benefit unresolved.

References

This conclusion is specific to the shared-module setting. It does not rule out benefits from the separately parameterized H and L modules used by HRM-Text. A closer HRM-Text-style variant with distinct modules for the two update streams is still under evaluation and is not included in the present comparison.

— Towards Looped Models Done Right, Part I: Topology, Input Injection, Recurrent-State Design  (2610.23036 - Huang et al., 16 Oct 2026) in Section 3, subsection “Finding 2: A shared-module H/L hierarchy provides no consistent benefit”