HORST: Composing Optimizer Geometries for Sparse Transformer Training
This addresses the challenge of training sparse transformers, offering a principled optimizer that improves performance over standard methods, particularly at high sparsity.
HORST introduces a modular optimizer that combines adaptive methods' stability with an L1 sparsity bias via a hyperbolic mirror map, consistently outperforming AdamW across sparsity levels in transformer training on vision and language tasks.
Sparsifying transformers remains a fundamental challenge, as standard optimizers fail to simultaneously encourage sparsity and maintain training stability. Effective adaptive optimizers exhibit an implicit $L_{\infty}$ bias favoring stability, yet, sparsity requires an $L_1$ bias. To integrate sparsity, we propose a composition of optimizer steps, which we cast as non-commutative operators to analyze and combine their optimization geometry in a principled way. This yields HORST (Hyperbolic Operator for Robust Sparse Training), a modular optimizer that inherits stability from adaptive methods while inducing $L_1$ sparsity bias through a hyperbolic mirror map. Our experiments demonstrate its utility for sparse training of transformers on both vision and language tasks. HORST consistently and significantly outperforms AdamW baselines across all sparsity levels, with large gains at higher sparsity.