Transformer as an Euler Discretization of Score-based Variational Flow
Despite the Transformer's dominance across machine learning, its architecture remains largely heuristic and lacks a unified theoretical foundation. We introduce Score-based Variational Flow (SVFlow), a continuous-time dynamical system for representation learning in which the state evolves according to a variational posterior-weighted average of conditional log-likelihood scores, and provide a principled basis for regularization through variational consistency. We show that forward Euler discretization of spherical SVFlow exactly recovers the Transformer architecture. Multi-head attention approximates SVFlow vector field via a vMF kernel-smoothed posterior, while MoE/FFN approximates it in...
| Authors | Huadong Liao |
|---|---|
| Primary category | cs.LG |
| Published | 26 April 2026 |
| Last updated at source | 26 April 2026 |
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