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HyperTransfer: Understanding the Equivalence between Base Optimizer and Hyperball

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

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

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