发表机构
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机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究TabPFN在复杂表格几何上的内部行为，用曲折持久同调将其层表示视为点云，构建合成表格任务基准。发现其内部表示几何拓扑与数据集级可靠性相关，复杂几何有双重拓扑特征，相关描述符与多种指标有关，能诊断可靠性及运行状态。
AI 中文摘要
TabPFN是一种基于变压器的表格预测基础模型，通过依赖支持集和查询输入进行推理，无需特定任务训练。尽管其实验性能强劲，但其在结构复杂表格几何上的内部行为仍了解不足。我们使用曲折持久同调研究此行为，将TabPFN层表示视为演化的点云。构建了具有已知真实概率和不同内在拓扑的合成表格任务控制基准。发现TabPFN内部表示几何的拓扑与数据集级可靠性密切相关，例如零阶同调群\(H_0\)碎片化计数与控制任务中的平均绝对残差正相关，且在大样本量的高分辨率扭曲圆案例研究中这种关联增强。更复杂的几何结构会引发双重拓扑特征：\(H_1\)环活动增加和\(H_0\)碎片化增加，同时\(H_1\)持久性变短。这些描述符与贝叶斯误差、平均绝对残差和过度自信相关。结果表明曲折持久同调可诊断推断的上下文任务几何的可靠性，并提供TabPFN在拓扑压力状态下运行时的上下文级视图。
英文摘要
TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs. Despite its strong empirical performance, its internal behavior on structurally difficult tabular geometries remains poorly understood. We study this behavior using zigzag persistent homology, treating TabPFN layer representations as evolving point clouds. We construct a controlled benchmark of synthetic tabular tasks with known true probabilities and varied intrinsic topology, including warped circles, tori, spheres, Hopf links, trefoil knots, and Swiss rolls. Across these tasks, we find that the topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability; for example, the zeroth homology group $H_0$ fragmentation count correlates positively with mean absolute residual across controlled tasks, and this association strengthens in a high-resolution warped circle case study at large sample size. Harder geometries induce a dual topological signature: increased $H_1$ loop activity and increased $H_0$ fragmentation, while the $H_1$ persistence becomes shorter-lived. These descriptors correlate with Bayes error, mean absolute residuals, and overconfidence. Our results suggest that zigzag persistence diagnoses the reliability of the inferred in-context task geometry and provides a context-level view of when TabPFN operates in topologically stressed regimes.
