Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization\/whitening based methods. While yielding substantial performance gains, a fundamental question arises: can we develop new paradigms beyond orthogonalization, pushing the efficiency frontier further? We present \\textbf{Adaptively Rotated Optimization (ARO}, a new matrix optimization framework that treats gradient rotation as a first class design principle. ARO accelerates LLM training by performing normed steepest descent in a rotated coordinate system, where the rotation is determined by a novel norm-informed policy. This perspective yields update rules that go beyond existing orthogonalization and whitening optimizers, improving sample efficiency in practice. To make comparisons reliable, we propose a rigorously controlled benchmarking protocol that reduces confounding and bias. Under this protocol, ARO consistently outperforms AdamW (by 1.3 $\\sim$1.35$\\times$) and orthogonalization methods (by 1.1$\\sim$1.15$\\times$) in LLM pretraining at up to 8B activated parameters, and up to $8\\times$ overtrain budget, without evidence of diminishing returns. Finally, we discuss how ARO can be reformulated as a symmetry-aware optimizer grounded in rotational symmetries of residual streams, motivating advanced designs that enable computationally efficient exploitation of cross-layer\/cross module couplings.<\/p>\n","protected":false},"excerpt":{"rendered":"
Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization\/whitening based methods. While yielding substantial performance gains, a fundamental question arises: can we develop new paradigms beyond orthogonalization, pushing the efficiency frontier further? We present \\textbf{Adaptively Rotated Optimization (ARO}, a new matrix optimization framework that treats gradient rotation 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