arXiv:2609.10654v1 Announce Type: new Abstract: The Abstraction and Reasoning Corpus (ARC) benchmarks cognitive generalization, the ability to infer and apply abstract rules from limited examples. This paper presents a multi-stage rule-chaining framework that performs compositional reasoning across symbolic, structural, and conceptual levels. The framework integrates three complementary solvers: (1) a deterministic rule discovery module that induces atomic transformations through geometric, color, and object-based analysis; (2) a pattern-composition engine that reconstructs outputs via block merging, repetition, and spatial heuristics; and (3) a structural abstraction layer that infers hierarchical and nested relationships across grids. These solvers operate sequentially within a progressive fallback hierarchy, where each stage reuses prior reasoning traces to enhance interpretability and generalization. Training passed for 995 tasks out of 1000, further evaluated on 105 tasks out of 120 and solved 230 test tasks out of 240 ARC-AGI-2 tasks. The system achieved strong coverage across deterministic, compositional, and abstract categories, demonstrating an overall accuracy exceeding 95 percent. The proposed architecture bridges symbolic reasoning and pattern synthesis, providing interpretable insight into cognitive generalization. The results suggest that rule chaining and hierarchical composition can advance machine reasoning toward transparent, human-aligned abstraction without relying on task-specific tuning.
Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking