Interaction Locality in Hierarchical Recursive Reasoning
Yosuke Miyanishi, Tetsuro Morimura

TL;DR
This paper introduces interaction locality, a framework for measuring how information flow in hierarchical models remains within local regions or segments, revealing architectural patterns in recursive reasoning and embodied models.
Contribution
It proposes a task-geometry-aware framework for analyzing spatial information flow, applied to various models and benchmarks, highlighting differences in local-global information handling.
Findings
High-level recurrent states tend to write within nearby cells or segments.
Recursive updates accumulate local writes into broader structures.
Embodied models show locality primarily at module boundaries.
Abstract
Spatial reasoning requires both location-bound computation and location-invariant structure: agents must make local moves while preserving route, object, or constraint-level plans. We propose interaction locality, a task-geometry-aware framework for measuring whether information flow stays within nearby cells or semantic segments, or crosses them. We instantiate the framework with sparse-autoencoder feature ablations and finite-noise activation patching, with structural Jacobian and attention checks reported in the appendix, and apply it to HRM and TRM, two compact hierarchical and recursive reasoning models, on Maze-Hard, Sudoku Extreme, and ARC-AGI. Across these models, activation patching gives the clearest architectural fingerprint: high-level recurrent states tend to write information within nearby cells or same-segment units, while repeated recursive updates accumulate these local…
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