Procedural Refinement by LLM-driven Algorithmic Debugging for ARC-AGI-2
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| Format: | Preprint |
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2026
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| _version_ | 1866911712634994688 |
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| author | Qiu, Yu-Ning Zou, Lin-Feng Wang, Jiong-Da Yuan, Xue-Rong Dai, Wang-Zhou |
| author_facet | Qiu, Yu-Ning Zou, Lin-Feng Wang, Jiong-Da Yuan, Xue-Rong Dai, Wang-Zhou |
| contents | In high-complexity abstract reasoning, a system must infer a latent rule from a few examples or structured observations and apply it to unseen instances. LLMs can express such rules as programs, but ordinary conversation-based refinement is largely outcome-level: it observes that an answer or output is wrong without formally re-checking which abstraction, relation, or transformation justified that outcome. We propose \emph{Abduction-Based Procedural Refinement} (ABPR), a neuro-symbolic refinement approach that couples an LLM with a Prolog meta-interpreter. ABPR treats each candidate program as an executable declarative hypothesis of the latent rule and reifies its SLD goal--subgoal resolution into compact proof-tree-style derivations, following Shapiro's algorithmic program debugging (APD). In this view, refinement is not merely code-level debugging, but semantic re-checking of the model's hypothesised rule. We evaluate ABPR primarily on ARC-AGI-2, a challenging few-shot abstract rule induction benchmark over grid transformations. ABPR with Gemini-3-Flash achieves 56.67\% Pass@2, while GPT-5.5 xHigh with ABPR reaches 98.33\% Pass@2 on the public evaluation set. Supplementary experiments on fill-in-the-blank I-RAVEN-X and A-I-RAVEN adaptations provide evidence that the same trace-guided framework extends beyond ARC-specific grid tasks to RAVEN-style relational and analogical abstraction. Repeated-run and sensitivity analyses show that parallel trace-guided search reduces stochastic variance as search breadth and total search depth increase. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Procedural Refinement by LLM-driven Algorithmic Debugging for ARC-AGI-2 Qiu, Yu-Ning Zou, Lin-Feng Wang, Jiong-Da Yuan, Xue-Rong Dai, Wang-Zhou Software Engineering Artificial Intelligence In high-complexity abstract reasoning, a system must infer a latent rule from a few examples or structured observations and apply it to unseen instances. LLMs can express such rules as programs, but ordinary conversation-based refinement is largely outcome-level: it observes that an answer or output is wrong without formally re-checking which abstraction, relation, or transformation justified that outcome. We propose \emph{Abduction-Based Procedural Refinement} (ABPR), a neuro-symbolic refinement approach that couples an LLM with a Prolog meta-interpreter. ABPR treats each candidate program as an executable declarative hypothesis of the latent rule and reifies its SLD goal--subgoal resolution into compact proof-tree-style derivations, following Shapiro's algorithmic program debugging (APD). In this view, refinement is not merely code-level debugging, but semantic re-checking of the model's hypothesised rule. We evaluate ABPR primarily on ARC-AGI-2, a challenging few-shot abstract rule induction benchmark over grid transformations. ABPR with Gemini-3-Flash achieves 56.67\% Pass@2, while GPT-5.5 xHigh with ABPR reaches 98.33\% Pass@2 on the public evaluation set. Supplementary experiments on fill-in-the-blank I-RAVEN-X and A-I-RAVEN adaptations provide evidence that the same trace-guided framework extends beyond ARC-specific grid tasks to RAVEN-style relational and analogical abstraction. Repeated-run and sensitivity analyses show that parallel trace-guided search reduces stochastic variance as search breadth and total search depth increase. |
| title | Procedural Refinement by LLM-driven Algorithmic Debugging for ARC-AGI-2 |
| topic | Software Engineering Artificial Intelligence |
| url | https://arxiv.org/abs/2603.20334 |