Language Models

RL training for LLMs frequently suffers from training collapse due to exploding gradient variance in long-horizon tasks. We derive the Optimal Token Baseline (OTB) from first principles, proving that updates should be weighted inversely to their accumulated uncertainty (Realized Energy). Our computationally free Logit-Gradient Proxy eliminates training collapse, matches N=32 performance with just N=4, and reduces token consumption by 62-66%.

Definitive mathematical formulations for rollout correction methods in VeRL, progressing from REINFORCE to PPO to Decoupled PPO. Handles policy mismatch, temporal lag, replay buffers, and off-policy algorithms with importance sampling and rejection sampling techniques.

An information-theoretic analysis showing that scalar advantage formulations learn ≤ log₂(B) bits per episode, while per-timestep advantages preserve full reward entropy.

The relentless push for faster inference creates a dangerous training-inference mismatch that silently kills RL with LLMs. We reveal the vicious cycle—particularly acute in reasoning and agentic RL—and show that sequence-level importance sampling is the principled solution.