数据驱动的机器学习无法达到符号级逻辑推理——缩放定律的极限
Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law
AI总结：
本文通过理论分析和实验证明，数据驱动的监督深度学习无法通过增加训练数据和时间达到符号级三段论推理的严谨性，并揭示了训练数据和方法上的根本限制。
摘要：
球面神经网络无需训练数据即可实现符号级三段论推理，这引发了一个问题：逻辑推理的缩放定律极限在哪里？即数据驱动的机器学习系统能否通过增加训练数据和训练时间达到同样的水平。我们展示了两个方法论上的限制，阻碍了监督深度学习达到符号级三段论推理：（1）训练数据无法区分所有24种有效的三段论推理类型；（2）从前提到结论的端到端映射在模式识别和逻辑推理的神经组件之间引入了矛盾的训练目标。除了理论分析，我们通过实验说明欧拉网络无法实现严谨的三段论推理。我们进一步挑战最新的ChatGPTs（GPT-5-nano和GPT-5），以确定三段论语句在四种表面形式（模式）下的可满足性：单词、双词、简单符号和长随机符号，结果表明表面形式影响推理性能，且ChatGPT GPT-5可能达到100%准确率但仍提供不正确的解释。由于经验训练过程在达到100%准确率后停止，我们得出结论：监督机器学习系统无法达到符号逻辑推理的严谨性。
英文摘要：
By promoting vectors to spheres and enabling explicit model construction, neural networks can perform symbolic-level syllogistic reasoning without training data. We identify two fundamental limitations that prevent conventional data-driven machine learning systems from achieving this capability: training data generated by the combination table cannot distinguish all 24 valid syllogism types, and end-to-end premise-to-conclusion mapping creates contradictory targets within neural components. Experiments with two representative conventional systems, GPT-5 using linguistic inputs and Euler Net using visual inputs, support this analysis. ChatGPT GPT-5 may reach 100% accuracy in syllogistic reasoning, but with hallucinations. Because the learning process terminates upon reaching 100% accuracy, the system cannot progress beyond empirical accuracy to symbolic level reasoning. Random test data reduced Euler Net's accuracy to 56%. Repeatedly expanding the training set increased its accuracy to 97%, with perfect performance on 8 syllogism types. However, because unintended inputs cannot be exhaustively covered, even 100% test accuracy does not imply symbolic-level reasoning. Since syllogistic reasoning underpins logical reasoning and human rationality, these results suggest that increasing data and training time alone cannot ensure symbolic level logical reasoning.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
