Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918474803052544 |
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| author | Kalinowski, Alexander |
| author_facet | Kalinowski, Alexander |
| contents | 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 |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index Kalinowski, Alexander Machine Learning 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 |
| title | Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.26984 |