Diagnose Before Distillation: Efficient Multi-Teacher Reasoning Post-Training under Capability Conflict

Multi-teacher on-policy distillation offers an efficient way to consolidate specialized reasoning models into a single student, but choosing how teachers should be combined often requires costly student-training runs and downstream benchmark evaluation. This process becomes particularly unreliable when teachers encode conflicting specialization directions. We study whether lightweight activation diagnostics can identify such conflicts before full distillation and guide the choice of teacher-fusion strategy. Using mathematics, coding, general instruction following, and creative writing teachers fine-tuned from the same OLMo-2-1B base model, we compare centered activation-direction cosine, centered CKA, and centered neuron set Jaccard. Centered directional cosine reveals strong opposition between math and creativity (−0.52) and between code and creativity (−0.45), compared with weaker opposition between math and code (−0.24) and weak alignment between general and creativity (+0.10). In contrast, centered CKA remains within 0.76–0.84 and centered Jaccard within 0.49–0.55, providing little separation among teacher pairs. We then evaluate nine fusion strategies spanning prompt-level routing, token-level routing, probability-space mixing, compatibility-guided clustering, gradient projection, and gradient summation. Prompt-level routing achieves the strongest mathematical reasoning result, reaching 48.7% on GSM8K-chat, while math–code cluster fusion provides a more balanced trade-off, reaching 27.6% on IFEval and a 100% story-acquisition rate. Token-level routing and all-teacher gradient projection are substantially less effective. These results suggest a practical principle for efficient reasoning post-training: diagnose teacher compatibility before distillation, separate strongly conflicting teachers, and restrict direct fusion to relatively compatible subsets.