Interaction Locality in Hierarchical Recursive Reasoning

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 writes into broader solution structure. This pattern holds across maze paths, Sudoku constraints, and ARC-AGI object neighborhoods, with the strongest concentration in TRM. To test whether interaction locality extends beyond toy-yet-challenging grid benchmarks, we also apply it to MTU3D, a large-scale embodied 3D scene-grounding model. In this MTU3D setting, causal spatial locality appears primarily at the transition where visual scene features are handed to the downstream grounding module, rather than uniformly throughout the visual encoder. This contrast suggests that the local-to-global handoff observed in HRM and TRM is tied to explicit recursive reasoning dynamics, while embodied 3D models may concentrate causal spatial structure at module boundaries. Interaction locality turns the intuitive local-execution/global-planning story into a reproducible measurement framework for recursive and embodied spatial reasoning.

한 줄 요약

**[공간 추론 / Interaction Locality]** Sparse autoencoder ablation·activation patching으로 HRM·TRM의 정보 흐름이 인접 cell·동일 segment 내에 집중됨을 측정, Maze·Sudoku·ARC-AGI·MTU3D에서 local-to-global handoff가 recursive reasoning에 고유함을 시연.

핵심 기여도

공간 추론이 location-bound 계산과 location-invariant 구조를 동시 요구 — 에이전트가 local move를 하면서 route·object·constraint 수준 plan 보존해야 함 진단.
Interaction locality 제안 — task-geometry-aware 프레임워크로 정보 흐름이 인접 cell·semantic segment 내에 머무는지 또는 cross하는지를 측정.
프레임워크를 sparse autoencoder feature ablation과 finite-noise activation patching으로 instantiate, structural Jacobian·attention check를 appendix에 보고.
HRM·TRM(compact hierarchical·recursive reasoning model)을 Maze-Hard·Sudoku Extreme·ARC-AGI에 적용 — high-level recurrent state가 인접 cell·same-segment unit에 정보 write, 반복 recursive update로 broader solution structure 누적 패턴 발견.

핵심 아이디어

Hierarchical recursive reasoning 모델의 local-execution/global-planning 직관은 sparse autoencoder ablation·activation patching이라는 재현 가능 측정 도구로 정량화 가능하며, interaction locality라는 task-geometry-aware metric으로 모델·task·module 단위의 정보 흐름 fingerprint를 비교할 수 있다.

기술적 접근법

**방법론**: Interaction locality — task-geometry-aware 측정 프레임워크.
**핵심 기법**: (1) Sparse autoencoder feature ablation으로 정보 흐름 측정, (2) Finite-noise activation patching, (3) Structural Jacobian·attention check 보조, (4) HRM·TRM을 Maze-Hard·Sudoku Extreme·ARC-AGI 적용, (5) 대규모 embodied 3D scene-grounding 모델 MTU3D에도 적용해 module boundary 분석.

주요 결과

HRM·TRM 모두 high-level recurrent state가 인접 cell·same-segment unit에 정보 write, recursive update로 broader structure 누적 — TRM에서 가장 강한 concentration.
패턴이 maze path·Sudoku constraint·ARC-AGI object neighborhood 전반에 일관.
MTU3D에서 causal spatial locality가 visual encoder 전반이 아닌 visual feature가 downstream grounding module에 전달되는 transition에 주로 나타남.
Recursive reasoning의 local-to-global handoff는 explicit recursive dynamics에 결부, embodied 3D 모델은 module boundary에 집중.

의의 및 한계

**의의**: Interaction locality라는 재현 가능 측정 프레임워크로 직관을 정량화, recursive reasoning과 embodied 3D 모델의 정보 흐름 fingerprint 대조, mechanistic interpretability의 spatial reasoning 확장. **한계**: HRM·TRM·MTU3D 한정으로 다른 모델 일반화는 추가 검증, sparse autoencoder ablation 자체의 가정 의존성, 측정 결과의 해석은 task geometry 사전 정의에 의존.

실용적 활용

Recursive reasoning 모델의 mechanistic 분석.
공간 추론 모델 디자인의 진단 도구.
Embodied AI·grounding 시스템의 module 경계 검증.