发现图神经网络中学习到的传输机制可能只是临时依赖,而非真正必要。
Learned, Relied Upon, or Necessary? Separating Checkpoint Dependence from Task-Level Value in Sheaf GNNs
- 提出两种新评估方法:检查点依赖与协议相对替换
- 实验证明多数任务性能依赖固定检查点,重训练后仍可恢复
- 适用于评估图神经网络中传输机制是否真正重要
Sheaf GNN 中学习到的限制映射常被当作模型发现了有效边几何的证据。但参数变化或事后消融无法区分这种依赖是否真实有益。本文提出两个估计量:检查点依赖(固定预测器下的映射干预)与协议相对替换(重新训练匹配族以移除映射容量、边变异或持久边分配)。任务零定理表明,标签仅能识别传输分类方向,每个多维矩阵存在 $d^2-d$ 个不可见自由度。精确框架模型给出依赖与任务价值分离的边界。标签仅训练验证了预测分离;对公开的 NSD、DNSD 及 DSNN 实现的审计显示,真实图上同时存在可替换与不可替换的传输模式。所有五个 DNSD 基准均表现出固定检查点依赖。重训练后,破坏分配或共享映射控制在四组中恢复全性能;罗马帝国数据集仍保留 $.0675$ 的优势(相比持续重采样分配)和 $.0391$ 的优势(相比参数匹配共享映射),在十次官方划分中稳定存在。因此,学习到的映射可主导计算流程却不构成不可或缺的边几何。主张学习传输应结合检查点干预与匹配重训练。
原文摘要 · Abstract (English)
Learned restriction maps in sheaf graph neural networks are often treated as proof that the model has discovered useful edge geometry. That conclusion does not follow from parameter movement or from a post-hoc ablation: both can show how one checkpoint is organized while leaving open whether learned transport still helps after the rest of the model adapts. We separate these claims with two estimands. Checkpoint reliance intervenes on the maps of a fixed predictor; protocol-relative replacement retrains matched families that remove map capacity, edge variation, or persistent edge assignment. A task-null theorem shows why the claims can diverge: labels identify only the transported classifier directions, leaving $d^2-d$ invisible degrees of freedom in every full $d\times d$ map. An exact frame model then gives the boundary at which reliance becomes unreplaced task value. Label-only training realizes the predicted separation, while audits of public NSD, DNSD, and Directed Sheaf Neural Network (DSNN) implementations recover both replaceable and unreplaced transport regimes on real graphs. All five DNSD benchmarks exhibit fixed-checkpoint reliance. After retraining, assignment-breaking or shared-map controls recover Full performance on four; Roman-Empire retains a $.0675$ advantage over continually resampled assignment and a $.0391$ advantage over a parameter-matched shared map across ten official splits. Thus, a learned map can govern a fitted computation without constituting indispensable edge geometry. Claims of learned transport should pair checkpoint interventions with matched retraining.
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