Spectral Flow Probe: A Real-Time Geometric Diagnostic Toolkit for LLM Training

Large language models trained with reinforcement learning (DPO, GRPO) suffer a previously invisible failure mode: Participation Ratio (PR) collapse. We release Spectral Flow Probe (SFP), a lightweight Python toolkit that adds less than 2 seconds per checkpoint to detect this collapse in real time. Key findings across 3 model sizes (0.6B-4B) and 2 RL methods: PR collapse is universal, a shared danger window at step ~100 where collapse initiates, and standard metrics (loss, reward) are completely blind to the collapse. SFP provides four modules: Auditor, Monitor, Planner, and Regularizer. This paper extends the Representational Budget Theory framework (Zhang, 2026; DOI: 10.5281/zenodo.19585083).