Under GDPO, every printed windowed IM configuration and the no-window configuration exceeds the GDPO base in average accuracy on both MATH-500 and Countdown. Increasing sharpness from 0.5 to 2 at window 10 raises Countdown average accuracy from 61.3% to 66.2%, while MATH-500 averages remain nearly flat; removing the window lowers the d=1.5 averages relative to window 10.

dataset: MATH-500 · configuration: GDPO (base) · generationLengthTokens: 128

dataset: MATH-500 · configuration: GDPO (base) · generationLengthTokens: 256

dataset: MATH-500 · configuration: GDPO (base) · generationLengthTokens: 512

dataset: MATH-500 · configuration: GDPO (base) · generationLengthTokens: average

dataset: Countdown · configuration: GDPO (base) · generationLengthTokens: 128

dataset: Countdown · configuration: GDPO (base) · generationLengthTokens: 256

dataset: Countdown · configuration: GDPO (base) · generationLengthTokens: 512

dataset: Countdown · configuration: GDPO (base) · generationLengthTokens: average

dataset: MATH-500 · configuration: GDPO+IM d=0.5 w=10 · generationLengthTokens: 128

dataset: MATH-500 · configuration: GDPO+IM d=0.5 w=10 · generationLengthTokens: 256

dataset: MATH-500 · configuration: GDPO+IM d=0.5 w=10 · generationLengthTokens: 512

dataset: MATH-500 · configuration: GDPO+IM d=0.5 w=10 · generationLengthTokens: average