Multi-Teacher Ensemble Distillation: A Mathematical Framework for Probability-Domain Knowledge Aggregation

• URL: http://arxiv.org/abs/2601.09165v1
• Date: Wed, 14 Jan 2026 05:10:36 GMT
• Title: Multi-Teacher Ensemble Distillation: A Mathematical Framework for Probability-Domain Knowledge Aggregation
• Authors: Aaron R. Flouro, Shawn P. Chadwick,
• Abstract summary: We develop an axiomatic, operator-theoretic framework for multiteacher ensemble knowledge distillation.<n>Rather than prescribing a specific aggregation formula, we define five core axioms governing valid knowledge aggregation operators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Building on the probability-domain distillation framework of Sparse-KD, we develop an axiomatic, operator-theoretic framework for multi-teacher ensemble knowledge distillation. Rather than prescribing a specific aggregation formula, we define five core axioms governing valid knowledge aggregation operators, encompassing convexity, positivity, continuity, weight monotonicity, and temperature coherence. We prove the existence and non-uniqueness of operator families satisfying these axioms, establishing that multiple distinct aggregation mechanisms conform to the same foundational principles. Within this framework, we establish operator-agnostic guarantees showing that multi-teacher aggregation reduces both stochastic variance and systematic supervisory bias under heterogeneous teachers, while providing Jensen-type bounds, log-loss guarantees, and safety attenuation properties. For aggregation operators linear in teacher weights, we further establish classical ensemble variance-reduction results under standard independence assumptions, with extensions to correlated-error regimes. The framework provides theoretical grounding for multi-teacher distillation from diverse frontier models while admitting multiple valid implementation strategies.

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