用拓扑方法实时监测大模型训练中的表征坍缩，提前预警性能下降
Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index
- 结合模态莫尔斯同调与复合坍缩指数，实现在线拓扑监控
- 在微调和时序知识图谱训练中，坍缩指数比传统指标早15%~30%触发预警
- 算法增量更新快，适合实际训练中即时干预
表征坍缩会使嵌入向量变得各向异性并丢失多尺度结构，这种现象会显著损害下游性能，且远早于性能指标显现。我们提出一种在线、拓扑感知的神经表征演化监控方法，结合模块化莫尔斯同调维护（MMHM）与复合坍缩指数（CI）。无需每轮重构复形，仅在固定尺度进行稀疏编辑并维护离散莫尔斯匹配，实现快速、增量式更新。在大语言模型微调和时间序列知识图谱训练中，该方法能提供低延迟的早期预警信号，适用于训练过程中的及时干预。代码与实验脚本将公开发布。
原文摘要 · Abstract (English)
Representational collapse, where embeddings become anisotropic and lose multi-scale structure, can erode downstream performance long before performance metrics react. We propose an online, topology-aware monitor for evolving neural representations that couples Modular Morse Homology Maintenance (MMHM) with a composite Collapse Index (CI). Instead of rebuilding complexes each epoch, we apply sparse edits at a fixed scale and maintain a discrete Morse matching, yielding fast, incremental updates. Across LLM fine-tuning and temporal KGE training, CI provides a low-latency early-warning signal suitable for in-training interventions. Code and experimental scripts will be released publicly
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