Definition
Plain language
A chain of terms where the middle bits all cancel, leaving only the endpoints.
As stated in the literature
A sum whose consecutive terms cancel pairwise so only boundary terms remain; underlies the deterministic-environment reward-recovery result, and its breakdown under stochastic transitions forces targeting advantage instead of reward.
Why it matters: This cancellation makes certain reward calculations clean in predictable settings, and noticing where it stops working signals when a different method is needed.
For example, adding (2−1) + (3−2) + (4−3) cancels the middle numbers and leaves just 4−1, which is 3.
Heard on the show
“That clean cancellation, that's what mathematicians call a telescoping sum, and it's why the log-ratio equals the reward in the deterministic world.”Episode 173 — The Free Step-Level Grader Hiding in Every RL Training Run