用新算子统一抽象推理，小模型也能100%解题
Asterisk Operator
- 基于邻接结构并行传播构建统一推理框架
- 600万参数模型在ARC2上达100%准确率
- 适合研究神经符号推理与高效算法的学者
我们提出 extbf{星号算子}（$ extasteriskcentered$-算子），一种基于邻接结构并行传播（ASPP）的抽象推理统一框架。该算子将结构化推理任务形式化为由隐式关系图引导的局部并行状态演化过程。理论证明$ extasteriskcentered$-算子在保持局部计算约束的同时具备全局推理能力，提供了一种高效且收敛的抽象推理计算范式。通过严格的数学分析和在ARC2挑战及康威生命游戏上的全面实验，验证了该算子的通用性、收敛性与优越性能。我们提出的嵌入-星号蒸馏方法在仅使用600万参数的情况下，于ARC2验证集达到100%准确率，标志着神经符号推理的重大突破。
原文摘要 · Abstract (English)
We propose the \textbf{Asterisk Operator} ($\ast$-operator), a novel unified framework for abstract reasoning based on Adjacency-Structured Parallel Propagation (ASPP). The operator formalizes structured reasoning tasks as local, parallel state evolution processes guided by implicit relational graphs. We prove that the $\ast$-operator maintains local computational constraints while achieving global reasoning capabilities, providing an efficient and convergent computational paradigm for abstract reasoning problems. Through rigorous mathematical analysis and comprehensive experiments on ARC2 challenges and Conway's Game of Life, we demonstrate the operator's universality, convergence properties, and superior performance. Our innovative Embedding-Asterisk distillation method achieves 100\% accuracy on ARC2 validation with only 6M parameters, representing a significant breakthrough in neural-symbolic reasoning. \textbf{Keywords:} Abstract Reasoning, Adjacency Structure, Parallel Propagation, Asterisk Operator, Convergence, Universal Approximation
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