Recursive Meta-Distillation: An Axiomatic Framework for Iterative Knowledge Refinement
This foundational work provides a theoretical basis for understanding stability and failure modes in iterative distillation, which is incremental as it builds on existing axiomatic frameworks for single-stage settings.
The paper tackles the lack of mathematical understanding of recursive knowledge distillation by introducing an axiomatic framework that formalizes it as a sequence of probability-distribution operators, proving that anchored recursive distillation induces geometric convergence to base teacher distributions under mild assumptions.
Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.