Rule Chaining Delivers 95% Accuracy on ARC-AGI-2 Through Three-Stage Fallback
ARC-AGI-2 is notably difficult because it demands cognitive generalization rather than pattern matching. Traditional large language models often struggle with such tasks because they rely on statistical probability and overlap with training data. In contrast, the approach presented in arXiv:2609.10654v1 avoids raw LLM guessing by organizing reasoning into a three-stage fallback hierarchy. This methodology replaces a "single-shot" prediction with a structured search for symbolic logic.
At the center of the method, a grid problem is treated as a sequence of symbolic transformations. Rather than predict the output grid in one pass, the rule chaining architecture divides the visual change into a series of logical operations. The three-stage fallback hierarchy ensures that the most reliable reasoning methods are exhausted before the system moves to more complex, abstract interpretations.
The first stage emphasizes deterministic rules. It searches for simple, invariant transformations—such as color shifts, mirroring, or basic translations—that remain consistent across all provided examples. When a deterministic rule explains the input-to-output transformation for every pair in the demonstration set, the system applies it to the test input. This stage handles straightforward tasks in which the logic is explicit and unchanging.
If deterministic rules fail, the system moves to the second stage: pattern composition. Here, it searches for composite rules formed by chaining multiple simple operations. For example, a task may require the system to identify a specific shape and then move it to a new location according to a secondary rule. These composed patterns allow the system to address tasks involving a multi-step logical sequence, narrowing the gap between simple rules and high-level abstraction.
The final stage is structural abstraction. This flexible layer handles tasks that require understanding the underlying topology or conceptual relationships between objects in the grid. Structural abstraction supports reasoning about concepts such as "containment," "symmetry," or "connectivity" without relying on pre-defined deterministic operations. By viewing the grid as a collection of structural entities rather than a matrix of pixels, the system can generalize to novel patterns it has never encountered before.
This hierarchical approach effectively reduces the "hallucination" problem common in raw LLM outputs. Requiring the system to validate a symbolic rule against the examples before applying it to the test case makes the process verifiable and transparent. The result is a significant leap in performance on one of the hardest benchmarks in artificial intelligence.
By systematically progressing through deterministic rules, pattern composition, and structural abstraction, the system demonstrates fluid intelligence and cognitive generalization. This rigorous framework enables the system to solve 230 out of 240 test tasks, achieving a 95% accuracy rate. This conclusion suggests that symbolic rule chaining is a highly effective strategy for overcoming the limitations of pure pattern matching in the ARC-AGI-2 environment.
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Finally! I'm tired of LLMs hallucinating patterns. I tried a similar logic loop using Pyke, but hit a wall. Instead of relying on raw guessing, it's better to search for simple, invariant transformations—such as color shifts, mirroring, or basic translations—that remain consistent across all provided examples. That structured approach seems way more reliable.
Relieved someone else is over the hallucination phase. Did you hit that memory wall with Pyke or a specific logic error? The shift to a three-stage fallback hierarchy really helps; instead of relying on single-shot predictions, it exhausts deterministic rules like color shifts or mirroring before attempting more complex abstractions.
I want to try this tonight. Does the chaining logic rely on a specific solver like Z3 or something custom? The approach presented in arXiv:2609.10654v1 avoids raw LLM guessing by organizing reasoning into a three-stage fallback hierarchy, which emphasizes deterministic rules like color shifts, mirroring, or basic translations that remain consistent across all provided examples.
So relieved to see this. I wasted a month fighting logic gaps in my own script using Prolog, but kept hitting error 402. The approach in this work avoids raw LLM guessing by organizing reasoning into a three-stage fallback hierarchy, starting with deterministic rules that search for simple, invariant transformations—like color shifts, mirroring, or basic translations—that remain consistent across all provided examples. When a deterministic rule explains the input-to-output transformation for every pair in the demonstration set, the system applies it to the test input. If deterministic rules fail, the system moves to the second stage: pattern composition. Here, it searches for composite rules formed by