发表机构
Jheronimus Academy of Data Science; Eindhoven University of Technology（杰罗尼穆斯数据科学学院; 埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于庞加莱双曲几何的时间参数图元学习框架，以动态表示MLP训练轨迹，捕捉网络自组织演化，实现内在可解释性。
AI 中文摘要
内在可解释性仍然是一个具有挑战性的问题，特别是在多层感知器（MLPs）需要在优化环境中进行动态重新训练的情况下。本文研究了如何在非欧几里得空间中表示和研究MLPs及其训练动力学；我们的表示采用了庞加莱双曲几何模型。我们旨在捕捉其加权拓扑和自组织随时间演化的几何形态。与仅将分析限制在单一检查点（如已建立的基于度量的可解释性方法）不同，我们构建了时间参数图，即MLPs优化/训练过程中随时间T步的快照。这反映了神经网络不仅在其权重中编码信息，而且在其训练过程中所描绘的轨迹中也编码信息的观点。借鉴许多复杂网络可以在隐藏度量空间中嵌入，其中距离对应于连接可能性的思想，我们提出了一个基于几何和时间图的元学习框架，用于获得底层神经参数图的动态双曲表示。我们的模型将时间参数图嵌入庞加莱模型球中，并从中学习，同时保持对快照内神经元排列的等变性和对过去快照排列的不变性。通过这种方式，该方法保持了随时间的功能等价性，并恢复了网络潜在的演化几何。在回归和分类任务上使用训练好的MLPs进行的实验显示了强大的元网络性能，并伴有双曲时间表示。这揭示了网络结构在特定训练环境下如何随时间涌现，从而提供了对网络自组织的洞察。
英文摘要
Intrinsic explainability remains a challenging problem, particularly in contexts where multilayer perceptrons (MLPs) require dynamic re-training within an optimization environment. This paper investigates how MLPs and their training dynamics can be represented and studied in non-Euclidean spaces; our representation features the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting the analysis to single checkpoints---as per established measure-based explainability methods---we construct temporal \textit{parameter graphs}, i.e., snapshots over time $T$ steps of the optimization/training process for MLPs. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based metalearning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter graphs in the Poincaré model ball, and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, the approach preserves functional equivalence over time and recovers the latent evolving geometry of the network. Experiments on regression and classification tasks with trained MLPs show strong meta-network performance, accompanied by hyperbolic temporal representations. This reveals how the network structure emerges over time under specific training environments, thus providing insights into the network's self-organization.
CommentsPublished as a main conference paper at ICLR 2026. 10 Main Pages, 22 pages of supplementary material
