New Fisher information paper explains why LLM updates are sparse in post-training
cephaloform · x · 2026-10-15
A new paper studies why LLM parameter updates are so sparse during post-training, through the lens of Fisher information, connecting theory with empirical findings across RL, SFT, and on-policy distillation. YouJiacheng called it the most interesting paper he read this month: sparsity comes from on-policy sampling.
- On-policy sampling places probability mass on next tokens with similar parameter sensitivities (e.g. tea vs coffee after "She drank a cup of")
- Small sensitivity differences lead to small token-level Fisher, which implies a small diagonal model Fisher
- Expected gradients are bounded by the square root of the Fisher, so small Fisher concentrates learning on a sparse subset of parameters
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