Unifying Local Communications and Local Updates for LLM Pretraining

Communication-efficient pre-training of LLMs is increasingly important as training draws on compute distributed across clusters, data centers, and lower-bandwidth links. Many practical methods reduce communication frequency but still rely on synchronous All-Reduce operations that maintain identical model states and tie progress to global collectives. This can become a bottleneck when bandwidth or worker speed is heterogeneous. We introduce GASLoC, a novel decentralized pre-training algorithm that generalizes the notion of communication acceleration to the recently popular "outer optimizer" to allow a practical gossip-based training framework that is compatible with adaptive optimizers, allows for local optimizer steps, and can utilize sparse randomized peer communication. Empirically, on a number of standard LLM training tasks, we demonstrate that GASLoC outperforms state-of-the-art decentralized algorithms in single step per communication setting for a number of topologies and, unlike existing decentralized methods in the LLM setting, it allows to obtain performance competitive with DiLoCo when utilizing multiple local steps. In the heterogeneous bandwidth setting we demonstrate the advantage of GASLoC showing that it can significantly outperform DiLoCo.

Learned Subspace Compression for Communication-Efficient Pipeline Parallelism

Pipeline parallelism enables training of large language models that exceed single-device memory, yet inter-stage activation communication becomes the dominant bottleneck when trained on low-bandwidth networks. Recent work in this area has proposed using fixed orthogonal projections to compress activations. However, this still results in a significant performance degradation and requires a number of non-standard adaptations to constrain the optimization. A natural alternative is to learn a low rank projection for each pipeline stage, however maintaining the necessary orthogonality of these projectors during training remains a challenge. We present Manifold Aware Projection Learning (MAPL), a method that treats inter-stage compression as a learnable orthogonal projection under explicit Stiefel manifold (orthogonal matrices) constraints. Rather than prescribing a fixed global subspace, MAPL lets each pipeline stage discover and continuously adapt its own task-optimal compression subspace via manifold-constrained steepest descent. To recover token-specific signals at stage boundaries, we introduce per-stage factorized anchor embeddings that allow for full-rank activation reconstruction with negligible communication overhead. We further show that we can incorporate residual vector quantization after projection with a streaming codebook synchronization protocol that amortizes dictionary communication. Across LLaMA models from 150M to 1B parameters we show that MAPL can be easily applied to the existing pipeline and can achieve high compression with neglibile performance degradation with a drastically improved tradeoffs in performance vs. compression compared to Subspace Networks.

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

Covenant-72B: Pre-Training a 72B LLM with Trustless Peers Over-the-Internet

Recently, there has been increased interest in globally distributed training, which has the promise to both reduce training costs and democratize participation in building large-scale foundation models. However, existing models trained in a globally distributed manner are relatively small in scale and have only been trained with whitelisted participants. Therefore, they do not yet realize the full promise of democratized participation. In this report, we describe Covenant-72B, an LLM produced by the largest collaborative globally distributed pre-training run (in terms of both compute and model scale), which simultaneously allowed open, permissionless participation supported by a live blockchain protocol. We utilized a state-of-the-art communication-efficient optimizer, SparseLoCo, supporting dynamic participation with peers joining and leaving freely. Our model, pre-trained on approximately 1.1T tokens, performs competitively with fully centralized models pre-trained on similar or higher compute budgets, demonstrating that fully democratized, non-whitelisted participation is not only feasible, but can be achieved at unprecedented scale for a globally distributed pre-training run.

Efficient Refusal Ablation in LLM through Optimal Transport

Safety-aligned language models refuse harmful requests through learned refusal behaviors encoded in their internal representations. Recent activation-based jailbreaking methods circumvent these safety mechanisms by applying orthogonal projections to remove refusal directions, but these approaches treat refusal as a one-dimensional phenomenon and ignore the rich distributional structure of model activations. We introduce a principled framework based on optimal transport theory that transforms the entire distribution of harmful activations to match harmless ones. By combining PCA with closed-form Gaussian optimal transport, we achieve efficient computation in high-dimensional representation spaces while preserving essential geometric structure. Across six models (Llama-2, Llama-3.1, Qwen-2.5; 7B-32B parameters), our method achieves up to 11% higher attack success rates than state-of-the-art baselines while maintaining comparable perplexity, demonstrating superior preservation of model capabilities. Critically, we discover that layer-selective intervention (applying optimal transport to 1-2 carefully chosen layers at approximately 40-60% network depth) substantially outperforms full-network interventions, revealing that refusal mechanisms may be localized rather than distributed. Our analysis provides new insights into the geometric structure of safety representations and suggests that current alignment methods may be vulnerable to distributional attacks beyond simple direction removal.

Celo2: Towards Learned Optimization Free Lunch

Learned optimizers are powerful alternatives to hand-designed update rules like Adam, yet they have seen limited practical adoption since they often fail to meta-generalize beyond their training distribution and incur high meta-training cost. For instance, prior work, VeLO, scaled meta-training to 4,000 TPU months ($\sim$10$\times$ GPT-3 compute) to meta-train a general-purpose optimizer but it failed to generalize beyond 600M parameters tasks. In this work, we present a surprising finding: by crafting a simple normalized optimizer architecture and augmenting meta-training, it becomes feasible to meta-train a performant general-purpose learned update rule on a tiny fraction of VeLO compute, 4.5 GPU hours to be precise. Our learned update rule scales stably to a billion-scale pretraining task (GPT-3 XL 1.3B) which is six orders of magnitude larger than its meta-training distribution. Furthermore, it shows strong performance across diverse out-of-distribution tasks and is compatible with modern optimization harness that includes orthogonalization, distinct update rules for input-output and hidden weights, and decoupled weight decay. In all, this work paves the way for practically applicable learnable optimization algorithms, unlocking exploration of richer meta-training and data curation recipes to further improve performance.

Stabilizing Native Low-Rank LLM Pretraining

Foundation models have achieved remarkable success, yet their growing parameter counts pose significant computational and memory challenges. Low-rank factorization offers a promising route to reduce training and inference costs, but the community lacks a stable recipe for training models from scratch using exclusively low-rank weights while matching the performance of the dense model. We demonstrate that Large Language Models (LLMs) can be trained from scratch using exclusively low-rank factorized weights for all non-embedding matrices without auxiliary "full-rank" guidance required by prior methods. While native low-rank training often suffers from instability and loss spikes, we identify uncontrolled growth in the spectral norm (largest singular value) of the weight matrix update as the dominant factor. To address this, we introduce Spectron: Spectral renormalization with orthogonalization, which dynamically bounds the resultant weight updates based on the current spectral norms of the factors. Our method enables stable, end-to-end factorized training with negligible overhead. Finally, we establish compute-optimal scaling laws for natively low-rank transformers, demonstrating predictable power-law behavior and improved inference efficiency relative to dense models.

Understanding and Exploiting Weight Update Sparsity for Communication-Efficient Distributed RL

Reinforcement learning (RL) is a critical component for post-training large language models (LLMs). However, in bandwidth-constrained distributed RL, scalability is often bottlenecked by the synchronization of policy weights from trainers to inference workers, particularly over commodity networks or in decentralized settings. While recent studies suggest that RL updates modify only a small fraction of model parameters, these observations are typically based on coarse checkpoint differences. We present a systematic empirical study of weight-update sparsity at both step-level and multi-step granularities, examining its evolution across training dynamics, off-policy delay, and model scale. We find that update sparsity is consistently high, frequently exceeding 99% across practically relevant settings. Leveraging this structure, we propose PULSE (Patch Updates via Lossless Sparse Encoding), a simple yet highly efficient lossless weight synchronization method that transmits only the indices and values of modified parameters. PULSE is robust to transmission errors and avoids floating-point drift inherent in additive delta schemes. In bandwidth-constrained decentralized environments, our approach achieves over 100x (14 GB to ~108 MB) communication reduction while maintaining bit-identical training dynamics and performance compared to full weight synchronization. By exploiting this structure, PULSE enables decentralized RL training to approach centralized throughput, reducing the bandwidth required for weight synchronization from 20 Gbit/s to 0.2 Gbit/s to maintain high GPU utilization.

Heterogeneous Low-Bandwidth Pre-Training of LLMs

Pre-training large language models (LLMs) increasingly requires distributed compute, yet bandwidth constraints make it difficult to scale beyond well-provisioned datacenters-especially when model parallelism forces frequent, large inter-device communications. We study whether SparseLoCo, a low-communication data parallel method based on infrequent synchronization and sparse pseudo-gradient exchange, can be combined with low-bandwidth pipeline model parallelism via activation and activation-gradient compression. We introduce a heterogeneous distributed training framework where some participants host full replicas on high-bandwidth interconnects, while resource-limited participants are grouped to jointly instantiate a replica using pipeline parallelism with subspace-projected inter-stage communication. To make the recently introduced subspace pipeline compression compatible with SparseLoCo, we study a number of adaptations. Across large-scale language modeling experiments (178M-1B parameters) on standard pretraining corpora, we find that activation compression composes with SparseLoCo at modest cost, while selective (heterogeneous) compression consistently improves the loss-communication tradeoff relative to compressing all replicas-especially at aggressive compression ratios. These results suggest a practical path to incorporating low-bandwidth model parallelism and heterogeneous participants into LLM pre-training.

When Data Falls Short: Grokking Below the Critical Threshold

In this paper, we investigate the phenomenon of grokking, where models exhibit delayed generalization following overfitting on training data. We focus on data-scarce regimes where the number of training samples falls below the critical threshold, making grokking unobservable, and on practical scenarios involving distribution shift. We first show that Knowledge Distillation (KD) from a model that has already grokked on a distribution (p1) can induce and accelerate grokking on a different distribution (p2), even when the available data lies below the critical threshold. This highlights the value of KD for deployed models that must adapt to new distributions under limited data. We then study training on the joint distribution (p1, p2) and demonstrate that while standard supervised training fails when either distribution has insufficient data, distilling from models grokked on the individual distributions enables generalization. Finally, we examine a continual pretraining setup, where a grokked model transitions from p1 to p2, and find that KD both accelerates generalization and mitigates catastrophic forgetting, achieving strong performance even with only 10% of the data. Together, our results provide new insights into the mechanics of grokking under knowledge transfer and underscore the central role of KD in enabling generalization in low-data and evolving distribution settings.