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Optimization · Large Scale, Parallel and Distributed

Xinwen Zhang, Yihan Zhang, Hongchang Gao, Heng Huang

In recent years, decentralized optimization has gained significant attention for solving machine learning problems where data are distributed across multiple devices. However, existing decentralized optimization algorithms are primarily designed for single-level and two-level optimization tasks, limiting their application to more complex problems such as decentralized stochastic $K$-level optimization, where $K>2$. In this work, we propose a novel decentralized stochastic $K$-level variance-reduced gradient descent algorithm to address the significant computation and communication overhead caused by the multi-level structure in decentralized stochastic $K$-level optimization problems. Moreover, we propose a novel theoretical analysis to tackle the recursive dependence issue caused by the multi-level structure when establishing the convergence rate of our algorithm. Finally, the experimental results confirm the effectiveness of our proposed algorithm.

Optimization · Large Scale, Parallel and Distributed

Benjamin Thérien, Xiaolong Huang, Aaron Defazio, Irina Rish, Eugene Belilovsky

DiLoCo is a powerful framework for training large language models (LLMs) under networking constraints, allowing for increased parallelism and accelerator utilization in data center settings. A critical but often overlooked factor in DiLoCo’s behavior is the choice of inner optimizer, which shapes the pseudogradient used by the outer optimizer. Given the recent success of Muon relative to AdamW for data parallel (DP) training, in this work, we examine how Muon's normalized optimizer steps can affect the pseudogradient's quality. Empirically, we find that, relative to AdamW, Muon yields more \emph{directionally correct} pseudogradients as the number of workers ($K$) is increased. In our experiments pre-training language models, we conduct extensive hyperparameter tuning across 150M, 416M, 914M, 1.76B, and 3.1B models for DiLoCo, MuLoCo, AdamW DP, and Muon DP. Consistently across all scales, we find that with $K\geq1$ workers, MuLoCo (Muon inner optimizer DiLoCo) achieves superior performance to DiLoCo in absolute terms and for $K>2$ it outperforms DiLoCo relative to their data parallel baselines, while being compatible with quantization, streaming, and long synchronization intervals. At $K=1$, we find that MuLoCo can even outperform the data-parallel gold standard while having larger optimal and critical batch sizes.

Optimization · Large Scale, Parallel and Distributed

Insu Jang, Runyu Lu, Nikhil Bansal, Ang Chen, Mosharaf Chowdhury

Multimodal large language models (MLLMs) extend the capabilities of large language models (LLMs) by combining heterogeneous model architectures to handle diverse modalities like images and audio. However, this inherent heterogeneity in MLLM model structure and data types makes makeshift extensions to existing LLM training frameworks unsuitable for efficient MLLM training, especially in distributed training. In this paper, we present ModalGlue, an efficient distributed MLLM training framework that contemplates MLLM's unique characteristics in both model and data parallelization. ModalGlue introduces frozen-aware pipeline parallelism and workload-balanced context parallelism to improve MLLM training throughput. Our extensive evaluation shows that \name outperforms state-of-the-art solutions by $2.26\times$ on average in terms of MLLM training throughput.

Optimization · Large Scale, Parallel and Distributed

haoyuan liang, Zhiyu Ye, Jielong Tang, Yang Yang, Shilei Cao, Guowen Li, Fei Hu, Zhiwei Zhang, Haohuan Fu, Juepeng Zheng

As Multimodal Large Language Models (MLLMs) continue to be trained, the availability of public data diminishes, limiting the possibility for further training and adaptation. However, private data remains an underutilized yet valuable resource. Federated Learning (FL) enables decentralized training on private data, yet extending it to MLLMs is challenging: heterogeneous client modalities induce architectural incompatibility, and full-parameter fine-tuning of billion-scale models incurs prohibitive communication costs. Parameter-efficient methods like LoRA alleviate these issues but introduce aggregation inconsistency, as averaged low-rank updates fail to recover the true global update faithfully. To address these issues, we propose **UniFLoW**(Universal multi-modal Federated LoRA fine-tuning framework With Analytical Aggregation), a unified federated framework that leverages pre-trained large language models and a multi-modal Encoder architecture, and our proposed Federated Aggregating Analytical Low-Rank Adaption$FedA^2$-$LoRA$). UniFLoW effectively utilizes fragmented client-side multi-modal data while $FedA^2$-$LoRA$ ensuring consistent aggregation. And modality-specific encoders and a II stage training strategy ensure effective integration of diverse modalities without overfitting. Experiments on text, image, and speech demonstrate that **UniFLoW** enables scalable, communication-efficient, and aggregation-consistent federated fine-tuning, with $FedA^2$-$LoRA$ achieving state-of-the-art performance compared to existing FedLoRA approaches. We envision UniFLoW as a promising solution to the growing scarcity of public data.

Theory · Learning Theory

QUOC TUNG LE, Anh Nguyen, Viet Anh Nguyen

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures like Vehicle Routing or Unit Commitment. By relaxing coupling constraints, LR enables parallel solving of subproblems and frequently yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical works showed promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\cO(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupled constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $\Omega(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Finally, we extend our framework to the problem of learning to warm-start sub-gradient ascent.

Optimization · Large Scale, Parallel and Distributed

Bing Liu, Boao Kong, Limin Lu, Kun Yuan, Chengcheng Zhao

Decentralized learning often involves a weighted global loss with heterogeneous node weights $\lambda$. We revisit two natural strategies for incorporating these weights: (i) embedding them into the local losses to retain a uniform weight (and thus a doubly stochastic matrix), and (ii) keeping the original losses while employing a $\lambda$-induced row-stochastic matrix. Although prior work shows that both strategies yield the same expected descent direction for the global loss, it remains unclear whether the Euclidean-space guarantees are tight and what fundamentally differentiates their behaviors. To clarify this, we develop a weighted Hilbert-space framework $L^2(\lambda;\mathbb{R}^d)$ and obtain convergence rates that are strictly tighter than those from Euclidean analysis. In this geometry, the row-stochastic matrix becomes self-adjoint whereas the doubly stochastic one does not, creating additional penalty terms that amplify consensus error, thereby slowing convergence. Consequently, the difference in convergence arises not only from spectral gaps but also from these penalty terms. We then derive sufficient conditions under which the row-stochastic design converges faster even with a smaller spectral gap. Finally, by using a Rayleigh-quotient and Loewner-order eigenvalue comparison, we further obtain topology conditions that guarantee this advantage and yield practical topology-design guidelines.

Optimization · Large Scale, Parallel and Distributed

Davide DAscenzo, Sebastiano Cultrera di Montesano

Training deep learning models on single-cell datasets with hundreds of millions of cells requires loading data from disk, as these datasets exceed available memory. While random sampling provides the data diversity needed for effective training, it is prohibitively slow due to the random access pattern overhead, whereas sequential streaming achieves high throughput but introduces biases that degrade model performance. We present scDataset, a PyTorch data loader that enables efficient training from on-disk data with seamless integration across diverse storage formats. Our approach combines block sampling and batched fetching to achieve quasi-random sampling that balances I/O efficiency with minibatch diversity. On Tahoe-100M, a dataset of 100 million cells, scDataset achieves more than two orders of magnitude speedup compared to true random sampling while working directly with AnnData files. We provide theoretical bounds on minibatch diversity and empirically show that scDataset matches the performance of true random sampling across multiple classification tasks.

Deep Learning · Large Language Models

Daniel Scalena, Leonidas Zotos, Elisabetta Fersini, Malvina Nissim, Ahmet Üstün

With the rise of reasoning language models and test-time scaling methods as a paradigm for improving model performance, substantial computation is often required to generate multiple candidate sequences from the same prompt. This enables exploration of different reasoning paths toward the correct solution, however, allocates the same compute budget for each prompt. Grounded on the assumption that different prompts carry different degrees of complexity, and thus different computation needs, we propose EAGer, a training-free generation method that leverages model uncertainty through token-wise entropy distribution to reduce redundant computation and concurrently improve overall performance. EAGer allows branching to multiple reasoning paths only in the presence of high-entropy tokens, and then reallocates the saved compute budget to the instances where exploration of alternative paths is most needed. We find that across multiple open-source models on complex reasoning benchmarks such as AIME 2025, EAGer can reallocate the budget without accessing target labels, achieving the best efficiency-performance trade-off in terms of reasoning length and Pass@k. When target labels are accessible, EAGer generates up to 65% fewer tokens (hence saving compute) and achieves up to 37% improvement in Pass@k compared to the Full Parallel Sampling. Our results show that EAGer consistently maximizes the efficiency-performance trade-off by enabling dynamic control over computation expenditure.

Optimization · Large Scale, Parallel and Distributed

Jiangwen Dong, Jiayu Li, Tianhang Zheng, Wanyu LIN

Edge-cloud collaborative inference is crucial for LLM-powered edge devices, as on-device models often lack the required reasoning capability, while cloud-only inference can be costly and slow under strict latency and token/API budgets. However, existing edge-cloud collaboration methods typically route input tasks based on their estimated difficulty. These static, coarse heuristics overlook subtask dependencies, missing opportunities for parallel execution and budget-adaptive routing. To this end, we propose HybridFlow, a resource-adaptive edge-cloud inference framework that enables parallel execution of interdependent subtasks. Specifically, we build a dependency-aware DAG for each input task, facilitating concurrent execution of subtasks once their dependencies are resolved, thereby reducing end-to-end latency. Additionally, we propose a dynamic benefit–cost utility model, optimizing the trade-off between accuracy, token/API cost, and latency in real-time. This dynamic routing minimizes unnecessary cloud usage while preserving reasoning quality. Across GPQA, MMLU-Pro, AIME24, and LiveBench-Reasoning, HybridFlow improves the cost-accuracy trade-off, reducing latency and cloud API usage while maintaining competitive accuracy.

Optimization · Large Scale, Parallel and Distributed

Jinrui Zhou, Haotian Xu, Xichong zhang, He Sun, Mingjun Xiao

Federated Learning (FL) enables decentralized clients to collaboratively train a global model without sharing raw data. However, most existing FL frameworks assume that clients train on static local datasets collected in advance or that the data follows a fixed underlying distribution, which limits their applicability in dynamic environments where data evolves over time. A parallel line of research, online FL, removes all assumptions and adopts an adversarial perspective, but this approach is often overly pessimistic and neglects the structured, partially predictable nature of real-world data dynamics. To bridge this gap, we propose SFedPO, a streaming federated learning framework that incorporates a prediction oracle to capture the temporal evolution of client-side data distributions. We theoretically analyze the convergence bounds of SFedPO and develop two practical sampling strategies: a Distribution-guided Data Sampling (DDS) strategy that dynamically selects training data under limited storage by balancing historical reuse and distribution adaptation, and a Shift-aware Aggregation Weights (SAW) mechanism that modulates global aggregation based on client-specific sampling behaviors. We further establish robustness guarantees under prediction errors. Extensive experiments demonstrate that SFedPO effectively adapts to streaming scenarios with distribution shifts and significantly outperforms existing methods.

Optimization · Large Scale, Parallel and Distributed

Chengjie Ma, Seungeun Oh, Jihong Park, Seong-Lyun Kim

Federated learning (FL) enables distributed model training, yet in heterogeneous deployments, Bandwidth-Constrained Clients (BCCs) often contribute inefficiently due to limited uplink bandwidth. In model-heterogeneous FL with fixed small sub-models, BCCs with sub-models may improve quickly in early rounds but become under-parameterized later, resulting in slow convergence and poor generalization. To address this challenge, we propose FedGMR, a federated learning framework centered around Gradual Model Restoration (GMR), where GMR progressively increases each client’s sub-model density during training, allowing BCCs to remain effective contributors throughout optimization. To make GMR practical under real-world heterogeneity, FedGMR is realized as an end-to-end workflow with asynchronous coordination and stable, mask-aware aggregation. We further establish convergence guarantees, showing that the aggregation error scales with the average sub-model density across clients and rounds, and that GMR provably narrows the gap toward full-model FL. Extensive experiments on FEMNIST, CIFAR-10, ImageNet-100, and StackOverflow demonstrate that FedGMR improves both convergence speed and final accuracy, especially under severe heterogeneity and non-IID data distributions.

General Machine Learning · Hardware and Software

Size Zheng, Xuegui Zheng, Hanshi Sun, Qi Hou, Wenlei Bao, Shiyu Li, Haojie Duanmu, Jin Fang, Chenli Xue, Chenhui Huang 等

The scaling of large language models (LLMs) is currently bottlenecked by the rigidity of distributed programming. While high-performance libraries like CuBLAS and NCCL provide optimized primitives, they lack the flexibility required for rapidly evolving model architectures. Conversely, existing tensor compilers fail to address the complex memory hierarchy of distributed clusters effectively. To bridge this gap, we propose DITRON, a scalable tile-level compiler that democratizes high-performance distributed kernel development. DITRON introduces a novel hierarchical programming abstraction spanning Core, Device, and Task levels to map tensor programs efficiently onto heterogeneous distributed hardware. This abstraction allows DITRON to support diverse parallelism strategies while abstracting away the complexity of inter-node and intra-node communication. Evaluated across large-scale clusters, DITRON achieves performance parity with or exceeding expert-tuned CUDA libraries, delivering speedups of 6%–30% on isolated kernels and 5%–30% on end-to-end inference in vLLM. Furthermore, DITRON demonstrates strong portability, achieving significant speedups on both NVIDIA and AMD platforms.

Deep Learning · Large Language Models

Guoxia Wang, Shuai Li, Congliang Chen, Jinle Zeng, Jiabin Yang, Dianhai Yu, Yanjun Ma, Li Shen

Loss spikes remain a persistent obstacle in large-scale language model pretraining. While previous research has attempted to identify the root cause of loss spikes by investigating individual factors, we observe that, in practice, such spikes are typically triggered by the confluence of heterogeneous factors. Empirically, loss spikes may arise from a combination of data outliers, hardware or transient computational faults, numerical precision issues, and hyperparameter settings. Regardless of the underlying cause, these spikes manifest as unstable optimizer updates, as abnormal gradients contaminate both first- and second-moment states. In this paper, we propose a principled gradient-centric remedy: AdaGC, an adaptive per-tensor gradient clipping scheme that mitigates such contamination by bounding gradient norms relative to a tensor-wise exponential moving average of their historical clipped values. AdaGC is optimizer-agnostic, introduces negligible memory overhead, and reduces communication costs compared to GlobalGC, particularly in hybrid-parallel distributed training environments. Experiments on Llama-2 7B, Mixtral 8×1B, and ERNIE 10B-A1.4B demonstrate that AdaGC robustly eliminates training instabilities, consistently reducing spike scores to zero for all models and improving downstream accuracy over GlobalGC by 1.32\%, 1.27\%, and 2.48\%, respectively. Furthermore, AdaGC seamlessly integrates with optimizers such as Muon and Lion, consistently yielding higher average accuracy and zero spike scores.

Optimization · Large Scale, Parallel and Distributed

Demyan Yarmoshik, Nhat Trung Nguyen, Alexander Rogozin, Alexander Gasnikov

This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while local variables are subject to coupled and node-specific constraints. Such problem formulations arise in machine learning applications, including federated learning and multi-task learning, as well as in resource allocation and distributed control. We analyze this problem under smooth and non-smooth assumptions, considering both strongly convex and general convex objective functions. Our main contribution is an optimal algorithm for the smooth, strongly convex regime, whose convergence rate matches established lower complexity bounds. We further provide near-optimal methods for the remaining cases.

Optimization · Large Scale, Parallel and Distributed

Qiyuan Chen, Xian Wu, Yi Wang, Xianhao Chen

Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose *Hybrid-Order Split Federated Learning* (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.

Deep Learning · Large Language Models

Harman Singh, Xiuyu Li, Kusha Sareen, Monishwaran Maheswaran, Sijun Tan, Xiaoxia (Shirley) Wu, Junxiong Wang, Alpay Ariyak, Qingyang Wu, Samir Khaki 等

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, for example by independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is _verification_: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at **pairwise self-verification**. Leveraging this insight, we introduce **V1**, a framework that unifies generation and verification through efficient pairwise ranking. V1 comprises two components: **V1-Infer**, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and **V1-PairRL**, an RL framework that **jointly trains** a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests) and math reasoning (AIME, HMMT) benchmarks, V1-Infer improves Pass@1 by up to 10\% over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, V1-PairRL achieves 7-9\% test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7\% over standard RL.

Optimization · Large Scale, Parallel and Distributed

Yijiang Li, Emon Dey, Zilinghan Li, Krishnan Raghavan, Ravi Madduri, Kibaek Kim

Federated learning~(FL) across multiple HPC facilities faces stochastic \emph{admission delays} from batch schedulers that dominate wall-clock time. Synchronous FL suffers from severe stragglers, while asynchronous FL accumulates stale updates when queues spike. We propose \fedqueue{}, a queue-aware FL protocol that incorporates scheduler delays directly into training and aggregation, which (i) predicts per-facility queue delays online to budget local work, (ii) applies cutoff-based admission that buffers late arrivals to bound staleness, and (iii) performs staleness-aware aggregation to stabilize heterogeneous local workloads. We prove the convergence for non-convex objectives at rate $\mathcal{O}(1/\sqrt{R})$ under bounded staleness, and show that the admission controls yield bounded staleness with high probability under queue-prediction error. Real-world cross-facility deployment of \fedqueue{} shows 20.5\% improvement over baseline algorithms. Controlled queue simulations demonstrate robust improvement over the baselines; in particular, about 34\% reduction in time to reach a target accuracy level under high queue variance and non-IID partitions.

Optimization · Large Scale, Parallel and Distributed

Aleksandar Armacki, Ali Sayed

Convergence in high-probability (HP) has attracted increasing interest, due to implying exponentially decaying tail bounds and strong guarantees for individual runs of an algorithm. While many works study HP guarantees in centralized settings, much less is understood in the decentralized setup, where existing works require strong assumptions, like uniformly bounded gradients, or asymptotically vanishing noise. This results in a significant gap between the assumptions used to establish convergence in the HP and the mean-squared error (MSE) sense, and is also contrary to centralized settings, where it is known that $\mathtt{SGD}$ converges in HP under the same conditions on the cost function as needed for MSE convergence. Motivated by these observations, we study the HP convergence of Decentralized $\mathtt{SGD}$ ($\mathtt{DSGD}$) in the presence of light-tailed noise, providing several strong results. First, we show that $\mathtt{DSGD}$ converges in HP under the same conditions on the cost as in the MSE sense, removing the restrictive assumptions used in prior works. Second, our sharp analysis yields order-optimal rates for both non-convex and strongly convex costs. Third, we establish a linear speed-up in the number of users, leading to matching, or strictly better transient times than those obtained from MSE results, further underlining the tightness of our analysis. To the best of our knowledge, this is the first work that shows $\mathtt{DSGD}$ achieves a linear speed-up in the HP sense. Our relaxed assumptions and sharp rates stem from several technical results of independent interest, including a result on the variance-reduction effect of decentralized methods in the HP sense, as well as a novel bound on the MGF of strongly convex costs, which is of interest even in centralized settings. Finally, we provide experiments that validate our theory.

Optimization · Large Scale, Parallel and Distributed

Youhe Jiang, Fangcheng Fu, Taiyi Wang, Guoliang He, Eiko Yoneki

Serving Large Language Models (LLMs) can benefit immensely from parallelizing both the model and input requests across multiple devices, but incoming workloads exhibit substantial spatial and temporal heterogeneity. Spatially, workloads comprise heterogeneous requests with varying compute and memory demands. Temporally, workload composition varies over time. Nevertheless, existing systems typically assume spatially uniform and temporally stable workloads, employing a homogeneous, static model deployment. This mismatch between the assumption and real-world spatial-temporal heterogeneity results in suboptimal performance. We present OServe, an LLM serving system with heterogeneous and flexible model deployment that addresses both spatial and temporal heterogeneity. First, OServe introduces a novel workload-aware scheduling algorithm that optimizes heterogeneous model deployments according to real-time workload characteristics. Second, OServe proposes an efficient workload-adaptive switching method that migrates model deployments in response to predicted workload changes. Experiments on real-world traces show that OServe improves performance by up to 2$\times$ (average: 1.5$\times$) compared to state-of-the-art serving systems.

General Machine Learning · Representation Learning

yan wubin, Wei Ma, Shixiang Wan, Dongchen Li, Shaoshun Kang, Qing Yang, Dongliang Xu

Connectionist models and symbolic models have long embodied two divergent paradigms: the former excel at differentiable representation learning yet struggle with transparency, while the latter deliver explicit rule-based reasoning but resist gradient-based optimization. We introduce Arboreal Neural Networks (ArbNN), a neural–symbolic framework that unifies these paradigms both computationally and conceptually. At the design level, ArbNN departs fundamentally from prior neuralized-tree models through a depth-aware routing mechanism and a topology-informed softmax aggregation, which together enable one-shot full-path gradient propagation and consequently achieving rapid and well-conditioned optimization dynamics and high parallel inference efficiency. At the conceptual level, ArbNN reveals that decision-tree branching and self-attention routing are two realizations of the same conditional computation primitive. We prove a structural isomorphism between a decision tree and a single-query attention head, enabling a differentiable architecture that faithfully preserves symbolic decision logic. The defining property of ArbNN is Bidirectional Fidelity, ensuring that the neural module can be compiled from—and losslessly decompiled back into—a symbolic tree, yielding both ordering consistency in ranking behavior and explicit, auditable interpretability via reconstructed if–else rules. ArbNN further supports GBDT-based initialization, allowing it to inherit strong inductive biases and integrate seamlessly with existing production workflows. Empirically, ArbNN achieves state-of-the-art performance on various public tabular benchmarks and delivers consistent gains under temporal distribution shift in large-scale industrial credit-risk systems. To support realistic evaluation, we additionally contribute TabCredit, a feature-rich, temporally partitioned dataset built from millions of real-world loan applications. Together, these results demonstrate that ArbNN forms a unified, reversible, and practically deployable bridge between symbolic reasoning and neural computation for high-stakes tabular domains.