Theoretical Guarantees for LT-TTD: A Unified Transformer-based Architecture for Two-Level Ranking Systems

Modern recommendation and search systems typically employ multi-stage ranking architectures to efficiently handle billions of candidates. The conventional approach uses distinct L1 (candidate retrieval) and L2 (re-ranking) models with different optimization objectives, introducing critical limitations including irreversible error propagation and suboptimal ranking. This paper identifies and analyzes the fundamental limitations of this decoupled paradigm and proposes LT-TTD (Listwise Transformer with Two-Tower Distillation), a novel unified architecture that bridges retrieval and ranking phases. Our approach combines the computational efficiency of two-tower models with the expressivity of transformers in a unified listwise learning framework. We provide a comprehensive theoretical analysis of our architecture and establish formal guarantees regarding error propagation mitigation, ranking quality improvements, and optimization convergence. We derive theoretical bounds showing that LT-TTD reduces the upper limit on irretrievable relevant items by a factor that depends on the knowledge distillation strength, and prove that our multi-objective optimization framework achieves a provably better global optimum than disjoint training. Additionally, we analyze the computational complexity of our approach, demonstrating that the asymptotic complexity remains within practical bounds for real-world applications. We also introduce UPQE, a novel evaluation metric specifically designed for unified ranking architectures that holistically captures retrieval quality, ranking performance, and computational efficiency.