THE GRADIENT IS A COVARIANCE

Summary from the TLDR AI newsletter

Reinforcement learning, on-policy distillation, and supervised fine-tuning on near-policy data change only a small fraction of parameters. Small and sparse are different claims. The expected gradient is a covariance, the Fisher is a variance, and the Fisher caps the gradient for any reward. At one position, the Fisher is the variance of logit sensitivities: whatever moves every candidate together counts for nothing. None of this needs on-policy sampling - it needs a score centered under the sampling distribution.