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Life sciences · Preprint
arXiv · September 9, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint presents Muon-C, a theoretically motivated optimization algorithm that modifies the Muon optimizer for convolutional kernels. In a single benchmark on CIFAR-10 flow matching, it reports faster convergence and better final FID scores than baseline methods, but the work lacks peer review, independent replication, and characterization of variance or statistical significance.
Preprint. Convolutional neural networks on CIFAR-10 flow matching task.. Intervention: Muon-C optimizer: represents kernel momentum as frequency-wise channel-transfer matrices, polarizes blocks independently, uses critical Fourier grid.. Compared with: Unfolded Muon optimizer and Adam optimizer..
Muon-C achieves 9.87 FID at 40k iterations on CIFAR-10 flow matching, compared with 22.26 for unfolded Muon and 51.31 for Adam. Muon-C reaches final quality using 0.62× and 0.64× model FLOPs relative to unfolded Muon and Adam, respectively. Under equal tuning budgets, Muon-C achieves 3.42 FID.
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This is a preprint describing a novel optimizer algorithm with computational experiments on CIFAR-10, lacking peer review, independent validation, or clinical/biological application.
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Muon replaces matrix momentum with an approximately orthogonal polar direction, but its geometry depends on the matrix representation. For convolution, standard unfolding describes a local patch map rather than the convolution operator. We introduce Muon-C, an operator-aligned optimizer that represents kernel momentum as frequency-wise channel-transfer matrices, polarizes these blocks independently, and uses a critical Fourier grid to return updates exactly to the original finite kernel support. We show that the new geometry arises from combining the block partition and Fourier coordinates. The exact-polar direction is a linear minimization oracle under the critically sampled convolution norm. Its worst-case guarantee relative to the continuous convolution-operator norm is never weaker than unfolding and is strictly stronger for $3\times3$ kernels. On CIFAR-10 flow matching with matched applied-update RMS, Muon-C reaches 9.87 FID at 40k iterations, compared with 22.26 for unfolded Muon and 51.31 for Adam. It reaches their final quality using $0.62\times$ and $0.64\times$ their model FLOPs, respectively. Under equal tuning budgets, Muon-C achieves 3.42 FID. Gains persist across data scales and transfer to classification across convolutional architectures.
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