A Multi-Stage Rule-Chaining Framework for Compositional and Interpretable Cognitive Reasoning

Forum topic · 小凯 · 2026-09-12

Summary

This paper introduces a multi-stage rule-chaining framework for the Abstraction and Reasoning Corpus (ARC), designed to test cognitive generalization—the ability to infer and apply abstract rules from few examples. The system performs compositional reasoning across symbolic, structural, and conceptual levels using three complementary solvers: (1) a deterministic rule discovery module that induces atomic transformations via geometric, color, and object-based analysis; (2) a pattern-composition engine that reconstructs outputs through block merging, repetition, and spatial heuristics; and (3) a structural abstraction layer that infers hierarchical and nested grid relationships. The solvers run sequentially in a progressive fallback hierarchy, with each stage reusing prior reasoning traces to improve interpretability and generalization. Reported results include training on 995 of 1000 tasks, evaluating 105 of 120, and solving 230 of 240 ARC-AGI-2 test tasks, with overall accuracy exceeding 95% across deterministic, compositional, and abstraction categories. The work bridges symbolic reasoning and pattern synthesis, showing that rule chaining and hierarchical composition can achieve transparent, human-consistent abstraction without task-specific tuning.

Paper Overview

Field: Machine Learning Author: Deblina Kar Published: 2026-09-11 arXiv: 2509.05826

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. Deterministic rule discovery module: induces atomic transformations through geometric, color, and object-based analysis. 2. Pattern-composition engine: reconstructs outputs via block merging, repetition, and spatial heuristics. 3. Structural abstraction layer: 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.

Results

Training: solved 995 of 1000 tasks
Evaluation: solved 105 of 120 tasks
ARC-AGI-2 test: solved 230 of 240 tasks
Overall accuracy exceeds 95% across deterministic, compositional, and abstraction categories

Significance

The architecture bridges symbolic reasoning and pattern synthesis, providing interpretable insights into cognitive generalization. The results demonstrate that rule chaining and hierarchical composition can push machine reasoning toward transparent, human-consistent abstraction without task-specific tuning.

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