GeoSD improves OOD reasoning generalization via geometric self-distillation

Researchers introduce GeoSD, a geometric self-distillation objective designed to prevent the out-of-distribution drift common in on-policy distillation. The method counters this by scaling teacher preferences with student overlap and penalizing prediction drift using Fisher-Rao distance.

• Uses Hellinger loss to attenuate supervision on tokens the student cannot yet support.
• Applies a proximal term measuring Fisher-Rao distance to limit deviation from recent checkpoints.
• Implements natural-gradient updates within the geometry of next-token distributions.
• Improves average OOD accuracy by 5.7-8.6 points across mathematical reasoning benchmarks.
• Maintains gains across model scales ranging from 1.7B to 32B parameters.

GeoSD preserves in-distribution performance while significantly enhancing generalization by keeping alternative predictions reachable at high-entropy states.