Think Through a Bottleneck: Hourglass Reasoning for Rigorous Induction

The problem is that self-refinement fails to improve few-shot inductive reasoning in large language models because simply prompting explicit rule verbalization is ineffective. The method introduces Hourglass reasoning, which enforces strict context isolation between stages, using a frozen LLM as a meta-constructor to pass only a compressed symbolic state (schema φ and rule T) across stage boundaries. Experimental evidence shows Hourglass raises ARC-AGI-2 best-of-5 accuracy by up to 14 points, nearly doubles GPT-5.5 Verilog synthesis accuracy on ChipBench from 31% to 58%, and reverses the harmful effect of explicit verbalization on BBEH-Linguini with Gemini 3.1 Pro. This matters because it demonstrates that the structural flow of information through isolated reasoning stages, not the language used, drives rigorous inductive reasoning in frozen LLMs.