Definition
Plain language
Only ever moving in one direction — always up, or always down, never reversing.
As stated in the literature
A property of a function or relationship that is order-preserving (or order-reversing) throughout; in the Safety Paradox, attack success is proven monotonically increasing in the model's safety-classifier sharpness.
Also called: monotonicity, monotonically
Why it matters: Knowing a quantity moves in just one direction lets you reason confidently about trends without worrying about reversals.
For example, the total distance shown on a car's odometer is monotonic because it only ever goes up, never down.
Heard on the show
“Task gradient norm climbs monotonically with reward variance.”Episode 010 — When Reward Climbs But Reasoning Goes Generic: Diagnosing Template Collapse in Agentic RL