arXiv cs.CL· Jacob Russin, Joonhwa Kim, Ellie Pavlick, Michael J. Frank·· 11 小时前AI 评分38
人类与神经网络中的几何推理与代数推理
Geometric and algebraic inference in humans and neural networks
AI 导读
研究将人类推理形式化为几何策略与代数策略：前者通过逐步塑造表征几何结构让后续推理变廉价，后者在推理时灵活关注上下文中的新关系但需额外计算。在传递性推理任务中，人类、从头训练的神经网络和 LLM 均表现出这两种策略的对立特征，关系熟悉时几何策略占优，需在上下文中做全新推理时代数策略出现。对神经网络的因果干预显示，两种策略分别依赖表征几何与选择性注意机制，并复现了人类类似神经生物学损伤的影响。
正文 · 原文
Abstract:Humans possess a remarkable ability to draw inferences from limited data. While some inferences are made intuitively from past experience, others require online reasoning based on novel information given in context. Here, we formalize these strategies, which we term geometric and algebraic inference, and study their computational tradeoffs in humans and neural networks. The geometric strategy gradually shapes representational geometry to reflect underlying relational structure, making subsequent inference cheap. The algebraic strategy flexibly attends to and reasons over novel relations given in context, but costs additional computation at inference time. We identify opposing signatures of these two strategies in transitive inference, a domain widely studied across species, and characterize the conditions under which each is observed. Our framework predicts that the geometric strategy should be dominant when relations are familiar, whereas the algebraic should emerge to support de novo inferences drawn in context. Multiple experiments demonstrate these opposing signatures in humans, neural networks trained from scratch, and large language models (LLMs). Causal interventions in the neural networks reveal that the geometric and algebraic strategies depend on representational geometry and selective attention mechanisms, respectively, and reproduce the effects of analogous neurobiological disruptions in humans. Our framework unifies these effects with disparate phenomena, including content effects observed in human and LLM reasoning and data-distribution effects observed in machine learning. Our findings reconcile competing views of cognitive flexibility that emphasize either representational geometry or algebraic manipulation by showing that each can have unique strengths, and can characterize different aspects of both human and neural network behavior.
| Comments: | Equal contribution: J. Russin, J. Kim. Joint senior authors: E. Pavlick, M. J. Frank. 99 pages (17 main text, 13 references, 69 appendix), 5 figures, 45 supplementary figures, 9 supplementary tables. Code: this https URL, this https URL, this https URL |
| Subjects: | Neurons and Cognition (q-bio.NC); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG) |
| Cite as: | arXiv:2611.00387 [q-bio.NC] |
| (or arXiv:2611.00387v1 [q-bio.NC] for this version) | |
| https://doi.org/10.48550/arXiv.2611.00387 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jacob Russin [view email]
[v1]
Fri, 30 Oct 2026 21:07:44 UTC (3,865 KB)
来源：arXiv cs.CL · arxiv.org