DMuon: Efficient Distributed Muon Training with Near-Adam Overhead

Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads. The matrix-aware updates offer a compelling alternative to conventional element-wise optimization, particularly as model architectures continue to grow in scale and heterogeneity. Yet contemporary distributed training infrastructure built around the assumption of element-wise optimizers is poorly matched to matrix-level optimizers such as Muon, whose updates couple entire weight matrices and require costly Newton-Schulz iterations. Vanilla Muon implementations incur more than 2x the cost of forward and backward passes. To close this gap, we present DMuon, an open-source distributed Muon implementation that integrates into existing training pipelines as a drop-in module, with no framework-level modifications. Across both embodied foundation model and large language model (LLM) training workloads, DMuon achieves a 1.48x-3.01x speedup in end-to-end step time and a 6.85x-163.00x speedup in optimizer-step time, bringing per-step latency to near-AdamW levels and enabling efficient scaling in our model training.

WALL-WM: Carving World Action Modeling at the Event Joints

WALL-WM is a World Action Model that shifts video-action learning from chunk-centric optimization to event-grounded Vision-Language-Action pretraining, using semantically coherent action events as the atomic unit of learning. Existing WAMs commonly initialize from multimodal or video foundation models and then optimize fixed-length action chunks conditioned directly on the current observation and instruction. Although convenient, this chunk-centric formulation creates a fundamental granularity mismatch. Language describes semantic goals and events, vision evolves through continuous scene dynamics, and actions operate at control-level timescales; forcing all three into the same fixed-length prediction window turns VLA training into short-horizon correlation fitting. WALL-WM addresses this mismatch by organizing both supervision and data around semantic events. Specifically, it pairs event-grounded VLA pretraining with a data ecosystem built from event-level captions and cluster-balanced sampling, enabling scalable learning over diverse behaviors, scenes, and task structures. From the same event-pretrained backbone, WALL-WM supports two complementary inference modes. The event mode consumes next-event descriptions and enables variable-length execution chunks, while the unified mode uses a VLM with Staircase Decoding to condition conventional fixed-length chunk inference while preserving a gradient-continuous VLA path. Together with Muon-optimizer-based large-scale pretraining infrastructure, WALL-WM provides a practical scale-up recipe for general-purpose WAMs. Experiments show that WALL-WM generalizes broadly across language, scenes, and tasks, achieving state-of-the-art performance in large-scale real-world generalization evaluation.

Wall-OSS-0.5 Technical Report

Large-scale Vision-Language-Action (VLA) pretraining is increasingly adopted as the foundation for robot policies, yet the evidence for pretrained VLAs is almost invariably reported after task-specific fine-tuning. This leaves a foundational question unanswered: does VLA pretraining itself yield executable robot behavior, or does it merely furnish a better initialization for downstream policy learning? We present Wall-OSS-0.5, an open-source 4B VLA built upon a 3B VLM backbone augmented with action-generation components, designed so that pretrained robotic capability is directly measurable on physical hardware. The model is pretrained across more than 20 embodiments, processing over one million robot trajectories per epoch alongside a grounded multimodal corpus. We adopt a gradient-bridged co-training recipe in which three objectives play distinct and complementary roles: discrete action prediction routes strong VLM-native gradients into the backbone, multimodal prediction preserves grounded vision-language understanding, and continuous flow matching serves as the deployment-time action interface. Before task-specific fine-tuning, the pretrained checkpoint achieves non-trivial zero-shot real-robot behavior, completing several tasks, including a held-out deformable manipulation task, at high task progress on a 17-task suite. After fine-tuning, the same checkpoint serves as a stronger adaptation prior, reaching 60.5% average task progress on 15 real-robot tasks and outperforming π_0.5 by 17.5%. Multimodal evaluations further confirm that action training does not erode grounded vision-language competence: the model preserves broad vision-language ability while strengthening embodied grounding. Together, these results reposition VLA pretraining from an initialization strategy to a directly testable, already useful source of robot capability.

Explore Reinforced: Equilibrium Approximation with Reinforcement Learning

Current approximate Coarse Correlated Equilibria (CCE) algorithms struggle with equilibrium approximation for games in large stochastic environments but are theoretically guaranteed to converge to a strong solution concept. In contrast, modern Reinforcement Learning (RL) algorithms provide faster training yet yield weaker solutions. We introduce Exp3-IXrl - a blend of RL and game-theoretic approach, separating the RL agent's action selection from the equilibrium computation while preserving the integrity of the learning process. We demonstrate that our algorithm expands the application of equilibrium approximation algorithms to new environments. Specifically, we show the improved performance in a complex and adversarial cybersecurity network environment - the Cyber Operations Research Gym - and in the classical multi-armed bandit settings.

Tree Search for Simultaneous Move Games via Equilibrium Approximation

Neural network supported tree-search has shown strong results in a variety of perfect information multi-agent tasks. However, the performance of these methods on partial information games has generally been below competing approaches. Here we study the class of simultaneous-move games, which are a subclass of partial information games which are most similar to perfect information games: both agents know the game state with the exception of the opponent's move, which is revealed only after each agent makes its own move. Simultaneous move games include popular benchmarks such as Google Research Football and Starcraft. In this study we answer the question: can we take tree search algorithms trained through self-play from perfect information settings and adapt them to simultaneous move games without significant loss of performance? We answer this question by deriving a practical method that attempts to approximate a coarse correlated equilibrium as a subroutine within a tree search. Our algorithm works on cooperative, competitive, and mixed tasks. Our results are better than the current best MARL algorithms on a wide range of accepted baseline environments.