NuMuon: Nuclear-Norm-Constrained Muon for Compressible LLM Training

The rapid progress of large language models (LLMs) is increasingly constrained by memory and deployment costs, motivating compression methods for practical deployment. Many state-of-the-art compression pipelines leverage the low-rank structure of trained weight matrices, a phenomenon often associated with the properties of popular optimizers such as Adam. In this context, Muon is a recently proposed optimizer that improves LLM pretraining via full-rank update steps, but its induced weight-space structure has not been characterized yet. In this work, we report a surprising empirical finding: despite imposing full-rank updates, Muon-trained models exhibit pronounced low-rank structure in their weight matrices and are readily compressible under standard pipelines. Motivated by this insight, we propose NuMuon, which augments Muon with a nuclear-norm constraint on the update direction, further constraining the learned weights toward low-rank structure. Across billion-parameter-scale models, we show that NuMuon increases weight compressibility and improves post-compression model quality under state-of-the-art LLM compression pipelines while retaining Muon's favorable convergence behavior.

SENTINEL: Stagewise Integrity Verification for Pipeline Parallel Decentralized Training

Decentralized training introduces critical security risks when executed across untrusted, geographically distributed nodes. While existing Byzantine-tolerant literature addresses data parallel (DP) training through robust aggregation methods, pipeline parallelism (PP) presents fundamentally distinct challenges. In PP, model layers are distributed across workers where the activations and their gradients flow between stages rather than being aggregated, making traditional DP approaches inapplicable. We propose SENTINEL, a verification mechanism for PP training without computation duplication. SENTINEL employs lightweight momentum-based monitoring using exponential moving averages (EMAs) to detect corrupted inter-stage communication. Unlike existing Byzantine-tolerant approaches for DP that aggregate parameter gradients across replicas, our approach verifies sequential activation/gradient transmission between layers. We provide theoretical convergence guarantees for this new setting that recovers classical convergence rates when relaxed to standard training. Experiments demonstrate successful training of up to 4B-parameter LLMs across untrusted distributed environments with up to 176 workers while maintaining model convergence and performance.

AsyncMesh: Fully Asynchronous Optimization for Data and Pipeline Parallelism

Data and pipeline parallelism are key strategies for scaling neural network training across distributed devices, but their high communication cost necessitates co-located computing clusters with fast interconnects, limiting their scalability. We address this communication bottleneck by introducing asynchronous updates across both parallelism axes, relaxing the co-location requirement at the expense of introducing staleness between pipeline stages and data parallel replicas. To mitigate staleness, for pipeline parallelism, we adopt a weight look-ahead approach, and for data parallelism, we introduce an asynchronous sparse averaging method equipped with an exponential moving average based correction mechanism. We provide convergence guarantees for both sparse averaging and asynchronous updates. Experiments on large-scale language models (up to \em 1B parameters) demonstrate that our approach matches the performance of the fully synchronous baseline, while significantly reducing communication overhead.