Federated parameter-efficient fine-tuning (PEFT) enables communication-efficient adaptation of large pretrained models on decentralized edge data, but it remains fragile under non-IID client heterogeneity. In low-rank adaptation (LoRA), different clients may learn locally useful but spectrally misaligned update subspaces, causing high-variance aggregation and poor global transfer. We propose TRISHUL, a spectral-control framework for robust federated PEFT. TRISHUL follows the FL no-raw-data-sharing setting but does not itself provide formal privacy guarantees. TRISHUL uses shared frozen multi-head low-rank bases to obtain algebraically exact aggregation of compact core updates, applies nuclear norm proximal shrinkage to suppress client-specific high-rank spectral components before upload, and allocates adaptation heads non-uniformly across layers using a concave water filling budget rule derived from pretrained layer capacity. Because shrinkage is performed only on small core matrices, TRISHUL adds negligible computation and no extra per-round communication over the underlying multi-head PEFT protocol. Across vision and language benchmarks, including CIFAR-100, SVHN, 20 Newsgroups, MRQA, and GLUE with LLaMA3.2-1B, TRISHUL improves convergence, stability, and final performance over federated LoRA baselines, with greater gains under stronger heterogeneity.
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.