# When Rank Rises as LLMs Degrade

arXiv: https://arxiv.org/abs/2610.09647 · HTML: https://mlsanity.com/paper/2610.09647/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index](https://mlsanity.com/paper/2604.26984/) (2026)

## Abstract (arXiv)

Post-training adapts language models in non-stationary environments. Practitioners monitor representation health with RankMe and related spectral statistics, often assuming that rank falls when representations degrade. We show that this assumption is unsafe for LLM post-training. In a controlled study of Qwen3-0.6B with four degradation modes and three seeds, data duplication worsens held-out loss by 75% relative to healthy while increasing both original and centred RankMe; the latter changes by 13.5 pooled standard deviations. Covariance effective rank rises to nearly twice its healthy value. This failure is spectral dispersion rather than collapse, so a one-sided monitor rates the worst checkpoint as the healthiest. By contrast, a learning-rate misconfiguration lowers centred RankMe and k95, while uncentred RankMe is inconsistent across seeds. Direction is therefore a property of the regime-statistic pair and cannot be fixed by recalibration alone. We also distinguish two often-conflated statistics: RankMe normalises singular values, whereas covariance effective rank normalises eigenvalues. On raw intermediate-layer states in the pretrained model, massive activations pin the latter near 1 out of dimension d while RankMe retains usable range. We then test a two-sided, multichannel sequential monitor with separate calibration and test data. In a pre-registered shared-prefix, leave-one-seed-out evaluation, it detects all three damage regimes in every fold 10 to 60 steps after the fork and separates dispersion from downward-rank damage by firing direction. However, it never precedes held-out probe loss, and calibration with two seeds produces false alarms on the held-out healthy seed. Spectral monitoring can diagnose failure regimes, but it does not warn earlier than held-out loss, and validity claims require held-out healthy data.