This paper considers the design of optimal fixed-step first-order methods for high-dimensional minimization of $L$-smooth convex functions. For optimizing worst-case performance measured via suboptimality of the final function value (relative to the initial squared distance to a minimizer), we provide an algebraic proof of the optimality of the optimized gradient method (OGM) and establish its uniqueness among all fixed-step first-order methods. For the alternative measure of final squared gradient norm (relative to initial suboptimality), we prove the OGM-G method is optimal and uniquely so among fixed-step first-order methods. Finally, for the setting measuring the final squared gradient norm (relative to the initial squared distance to a minimizer), we show the recently proposed Lemniscate method is optimal and uniquely so. Our proofs rely on algebraic reductions for lower bound arguments rather than traditional information-theoretic bounds, which were previously only able to establish OGM's optimality but not uniqueness.
Benjamin Grimmer, Sunghyeon Jo, Chanwoo Park· 0 citations
Low-resource authorship style transfer (LAST) aims to rewrite text into the style of an arbitrary target author using only a few reference examples while preserving the original meaning. Existing methods often struggle to achieve both high style fidelity and semantic preservation because they compress diverse references into a single static author embedding, which averages out context-dependent stylistic variation, and rely on hidden representations for style control, which entangle style with content. We propose HyperStyler, a novel architecture that decouples LAST into style selection and style realization. Stylo-navigator predicts style coordinates by jointly modeling the source context and target-author references, and Stylo-hypernet realizes them via dynamic parameter modulation instead of hidden-state injection. Our experiments on Reddit, Blog, and News datasets demonstrate that HyperStyler consistently outperforms prior methods including LLM-based approaches and generalizes robustly across domains. Notably, HyperStyler achieves superior performance with as few as 2.4% additional parameters over T5-large, while being over 1.8x faster than LLMs at inference.
Jongkyung Shin, Minguk Jeon, Chanwoo Park et al.· 0 citations
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