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Life sciences · Preprint
arXiv · August 12, 2026
Posted before peer review. The findings may change or fail to hold.
MOON is a novel multi-task learning optimization algorithm that manipulates gradients under matrix geometry rather than Euclidean space. The preprint reports theoretical convergence rates and empirical improvements across benchmarks, but has not undergone peer review and presents no clinical or applied validation.
Preprint. Intervention: MOON: Multi-Objective OrthoNormalized Updates, performing gradient manipulation under spectral–nuclear norm geometry with orthonormalized manipulated gradient for parameter updates..
Convergence of averaged Pareto-stationarity measure at O(T^−1/2) in deterministic setting Convergence rate of O(T^−1/4) under stochastic gradients MOON consistently improves both optimization efficiency and final multi-task performance across various benchmarks
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This is an unrefereed arXiv preprint presenting a novel optimization algorithm with theoretical convergence analysis and empirical validation, but lacks peer review and clinical or applied evidence.
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Multi-objective optimization (MOO) has demonstrated significant success in multi-task learning by mitigating task conflicts through gradient manipulation. However, most existing methods flatten model parameters into vectors and perform gradient manipulation under Euclidean geometry, thereby overlooking the matrix structure prevalent in modern architectures such as Transformers. In this paper, we show that gradient manipulation in Euclidean space does not generally yield the steepest descent direction under matrix geometry, potentially limiting optimization efficiency. Drawing from the theory of steepest descent for matrix-valued parameters, we propose MOON (Multi-Objective OrthoNormalized Updates), which performs gradient manipulation under spectral--nuclear norm geometry and uses the orthonormalized manipulated gradient for parameter updates. Theoretically, for smooth non-convex objectives, we establish convergence of the averaged Pareto-stationarity measure at rates of $\mathcal{O}(T^{-1/2})$ in the deterministic setting and $\mathcal{O}(T^{-1/4})$ under stochastic gradients. Empirical results across various benchmarks show that MOON consistently improves both optimization efficiency and final multi-task performance. Our code is available at https://github.com/KunlinLyu/MOON.
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