HORST: Composing Optimizer Geometries for Sparse Transformer Training
Transformer sparsification has hit a fundamental wall: standard optimizers cannot simultaneously push models toward sparsity and keep training stable. Adaptive methods naturally favor L-infinity geometry (stability), while sparsity demands L-1 bias. HORST solves this by composing optimizer steps as non-commutative operators, using hyperbolic mirror maps to inject sparsity pressure without sacrificing convergence. The result is a modular optimizer that works across vision and language tasks. For practitioners scaling transformers, this addresses a real bottleneck in efficient model deployment, bridging the gap between theoretical sparsity and practical training robustness.
Modelwire context
ExplainerThe non-commutativity point is the part worth sitting with: HORST is not simply blending two objectives but asserting that the order in which optimizer steps are applied materially changes the geometry of the loss landscape, which is a stronger and less obvious claim than standard multi-objective regularization.
The theoretical scaffolding here connects directly to the 'Improved Guarantees for Constrained Online Convex Optimization via Self-Contraction' paper covered the same day, which tightened regret bounds for constrained optimization under adversarial conditions. HORST is essentially asking a related question in a different register: not how to satisfy hard constraints online, but how to compose geometric pressures during gradient descent without losing convergence guarantees. Both papers signal that the optimization theory layer beneath modern training pipelines is receiving serious renewed attention, likely because scaling alone is no longer sufficient to paper over inefficiencies in sparse or constrained regimes.
The practical test is whether HORST's sparsity gains hold when applied to models above the 7B parameter range on standard language benchmarks like MMLU or HellaSwag. If published follow-up results stay confined to vision tasks or sub-1B language models, the convergence story for large-scale deployment remains unverified.
Coverage we drew on
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MentionsHORST · Transformers · Sparse Training
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