We show that for tall matrix parameters, like projection matrices in the MLP layers, the Muon update can have row norms that are arbitrarily non-uniform. This can lead to a self-reinforcing feedback loop whereby neurons receive persistently small updates and eventually do not contribute meaningfully to network outputs. This problem is effectively mitigated by an additional row normalization step, but current methods do this in a way that moves the Muon update geometry away from the polar factor of the momentum matrix, which we find is undesirable. We propose Aurora, an optimizer that enforces row-uniformity of matrix parameter updates while respecting Muon's polar factor geometry. Aurora outperforms Muon in our pre-training experiments and, when combined with existing methods, achieves state-of-the-art performance among spectral optimizers on the optimizer track of the modded-nanoGPT speedrun. Additionally, we find that Aurora's empirical gains over Muon scale with the MLP expansion factor, suggesting that Aurora may allow for effective training of very wide MLP layers.
Near 1310 nm photonic-crystal surface-emitting lasers (PCSELs) are attractive narrow-beam sources for optical communication and sensing, but their final design refinement is costly. Small geometry changes simultaneously shift the band-edge resonance, cavity leakage, far-field div…
Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance. Here we present a systematic, compute-aware study of BO that evaluates surro…
Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning. Their performance, however, critically depends on the accurate estimation of the underlying spectral subspace and can deteriorate substantially in the presence of n…
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate am…
SignMuon compresses the Muon update to one bit per parameter by taking its elementwise sign, providing the most direct way to run a matrix-aware optimizer under an extremely low communication budget. It outperforms SignSGD in practice, yet it can ascend even on a linear function.…
Fine-tuning Vision Transformers (ViTs) with low-rank adapters (LoRA) promises better communication efficiency under federated setup, yet existing aggregation strategies face fundamental limitations. Independently averaging these LoRA factors is mathematically inconsistent, introd…