HyperTransfer: Understanding the Equivalence between Base Optimizer and Hyperball

2026-09-07

AI Summary

研究通过建立基准优化器与超球优化器的等价性，提出HyperTransfer方法，仅使用初始化和学习率调度即可复制基准优化器的动力学特性。

Abstract

Hyperball optimizers constrain parameter norms and update only their directions, establishing a distinct paradigm for neural network optimization. Although this geometry appears fundamentally different from that of conventional Base Optimizers, which update both parameter norms and directions, we show that the two paradigms are dynamically equivalent for scale-invariant networks. Building on this equivalence, we propose HyperTransfer, which constructs a Hyperball optimizer that reproduces the dynamics of a target Base Optimizer using only its initialization and learning-rate schedule, without running the target optimizer itself. We further derive the inverse mapping and extend the framework to non-scale-invariant networks. Experiments show that both HyperTransfer and the inverse mapping produce loss trajectories nearly identical to those of their targets, suggesting that Hyperball dynamics are governed primarily by the induced effective learning-rate schedule and optimizer state.

Problem

• Base Optimizer
• Hyperball
• scale-invariant networks

Innovation

• HyperTransfer
• dynamic equivalence
• scale-invariant networks
• effective learning-rate schedule