arXiv subjects

Ziqing Wen

Publications and source records attributed to Ziqing Wen.

10 recordsLinked to original sources

arXiv2026

Solution-space heterogeneity shapes federated learning dynamics across partial differential equations

Federated scientific machine learning enables institutions to train neural surrogates without centralizing local physical data, yet studies of partial differential equations (PDEs) lack a transferable definition of non-independent and identically distributed data. Existing protocols partition coordinates, coefficients, boundary conditions, or geometries according to equation-specific rules. Here, we introduce solution-space PDE-Dirichlet, a protocol that converts continuous supervised responses into reusable solution bins and quantifies the realized separation between clients through optimal transport over the geometry of these bins. We derive an exact inverse relation between population allocation heterogeneity and the Dirichlet concentration, and we establish conditions under which response heterogeneity induces gradient disagreement, local-update dispersion, and parameter divergence. Across seven controlled and public PDE tasks, three neural-operator families, and five random seeds, a lower concentration consistently increases the realized solution distance and optimization heterogeneity. The degradation in final error is task dependent: the largest effect occurs for low-viscosity Burgers, reaching 4.157 percentage points under the most heterogeneous setting, whereas additional communication or smoother dynamics can reduce the final gap despite persistent parameter separation. These results distinguish a reproducible geometric mechanism from task-dependent generalization outcomes and provide a common basis for evaluating non-IID federated PDE learning.

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arXiv2026

GWT: Scalable Optimizer State Compression for Large Language Model Training

Training large language models (LLMs) requires substantial memory, a significant fraction of which is consumed by the moment states maintained by adaptive optimizers such as Adam. Existing memory-efficient approaches commonly compress parameters or gradients through low-rank projections, which may discard information outside the selected subspace or incur additional costs from subspace construction and singular value decomposition (SVD). We introduce \textbf{Gradient Wavelet Transform (GWT)}, an SVD-free framework that applies a multilevel Haar transform to matrix gradients. GWT maintains first- and second-moment states only for the compact approximation coefficients, while retaining all detail coefficients transiently in each update. We show that the orthogonal transform preserves the complete current gradient and establish gradient alignment and a stationary-point guarantee for smooth objectives under bounded preconditioning and a directly verifiable coarse-momentum coherence condition. Experiments on language-model pre-training and downstream fine-tuning show that GWT reduces estimated model-and-optimizer-state memory by up to 52\% while maintaining competitive or improved model quality. On LLaMA-3B pre-training, GWT achieves $1.9\times$ the throughput of 8-bit Adam and is compatible with multiple optimizer families, including Adam, Adam-mini, and Muon.

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arXiv2026

FOAM: Blocked State Folding for Memory-Efficient LLM Training

Large language models (LLMs) have demonstrated remarkable performance due to their large parameter counts and extensive training data. However, their scale leads to significant memory bottlenecks during training, especially when using memory-intensive optimizers like Adam. Existing memory-efficient approaches often rely on techniques such as singular value decomposition (SVD), projections, or weight freezing, which can introduce substantial computational overhead, require additional memory for projections, or degrade model performance. In this paper, we propose Folded Optimizer with Approximate Moment (FOAM), a method that compresses optimizer states by computing block-wise gradient means and incorporates a residual correction to recover lost information. Theoretically, FOAM achieves convergence rates equivalent to vanilla Adam under standard non-convex optimization settings. Empirically, FOAM eliminates up to 90\% of the memory overhead of optimizer states and accelerates convergence. Furthermore, FOAM is compatible with other memory-efficient optimizers, delivering performance and throughput that match or surpass both full-rank and existing memory-efficient baselines. Code is available at https://github.com/zqOuO/FOAM.

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arXiv2026

Unveiling High-Probability Generalization in Decentralized SGD

Decentralized stochastic gradient descent (D-SGD) is an efficient method for large-scale distributed learning. Existing generalization studies mainly address expected results, achieving rates limited to $\mathcal{O}\left(\frac{1}{δ\sqrt{mn}}\right)$, where $δ$ is the confidence parameter, $m$ the number of workers, and $n$ the sample size. When $m=1$, D-SGD reduces to traditional SGD, whose optimal high-probability generalization bound is $\mathcal{O}\left(\frac{1}{\sqrt{n}}\log (1/δ)\right)$. This discrepancy reveals a gap between high-probability guarantees for SGD and those for D-SGD. To close this, we develop a high-probability learning theory for D-SGD, aiming for the optimal $\mathcal{O}\left(\frac{1}{\sqrt{mn}}\log (1/δ)\right)$ rate. We refine bounds for D-SGD using pointwise uniform stability in distributed learning-a weaker notion than uniform stability-and analyze them across convex, strongly convex, and non-convex settings. We also provide high-probability results for gradient-based measures in non-convex cases where only local minima exist, and derive optimization error and excess risk bounds. Finally, accounting for communication overhead, we analyze generalization bounds for local models within time-varying frameworks.

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arXiv2026

Revealing Modular Gradient Noise Imbalance in LLMs: Calibrating Adam via Signal-to-Noise Ratio

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers such as Adam(W) provide per-parameter adaptivity, they do not explicitly account for module-level gradient heterogeneity, resulting in slower convergence, suboptimal performance, or training instability. Existing approaches typically rely on manually tuned module-specific learning rates or specific optimization strategies, which are computationally costly and difficult to generalize across tasks or models. To establish a more principled approach, we first analyze the noise-damping behavior of Adam in high-noise modules and introduce \textbf{Module-wise Learning Rate Scaling via SNR (MoLS)}. MoLS estimates module-level SNRs to scale Adam updates, allowing automated module-wise learning rate allocation without manual tuning. Empirical results through multiple LLM training benchmarks demonstrate that MoLS improves convergence speed and generalization, achieving performance comparable to carefully tuned module-specific learning rates, while remaining compatible with memory-efficient training algorithms.

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arXiv2026

Stability and Generalization for Decentralized Markov SGD

Stochastic gradient methods are central to large-scale learning, yet their generalization theory typically relies on independent sampling assumptions. In many practical applications, data are generated by Markov chains and learning is performed in a decentralized manner, which introduces significant analytical challenges. In this work, we investigate the stability and generalization of decentralized stochastic gradient descent (SGD) and stochastic gradient descent ascent (SGDA) under Markov chain sampling. Leveraging a stability-based framework, we characterize how Markovian dependence and decentralized communication jointly influence generalization behavior. Our analysis captures the effects of network topology, Markov chain mixing properties, and primal-dual dynamics. We establish non-asymptotic generalization bounds for both algorithms, extending existing results on Markov stochastic gradient methods to decentralized and minimax settings.

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arXiv2026

Local Gradient Regulation Stabilizes Federated Learning under Client Heterogeneity

Federated learning (FL) enables collaborative model training across distributed clients without sharing raw data, yet its stability is fundamentally challenged by statistical heterogeneity in realistic deployments. Here, we show that client heterogeneity destabilizes FL primarily by distorting local gradient dynamics during client-side optimization, causing systematic drift that accumulates across communication rounds and impedes global convergence. This observation highlights local gradients as a key regulatory lever for stabilizing heterogeneous FL systems. Building on this insight, we develop a general client-side perspective that regulates local gradient contributions without incurring additional communication overhead. Inspired by swarm intelligence, we instantiate this perspective through Exploratory--Convergent Gradient Re-aggregation (ECGR), which balances well-aligned and misaligned gradient components to preserve informative updates while suppressing destabilizing effects. Theoretical analysis and extensive experiments, including evaluations on the LC25000 medical imaging dataset, demonstrate that regulating local gradient dynamics consistently stabilizes federated learning across state-of-the-art methods under heterogeneous data distributions.

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arXiv2024

Federated Prediction-Powered Inference from Decentralized Data

In various domains, the increasing application of machine learning allows researchers to access inexpensive predictive data, which can be utilized as auxiliary data for statistical inference. Although such data are often unreliable compared to gold-standard datasets, Prediction-Powered Inference (PPI) has been proposed to ensure statistical validity despite the unreliability. However, the challenge of `data silos' arises when the private gold-standard datasets are non-shareable for model training, leading to less accurate predictive models and invalid inferences. In this paper, we introduces the Federated Prediction-Powered Inference (Fed-PPI) framework, which addresses this challenge by enabling decentralized experimental data to contribute to statistically valid conclusions without sharing private information. The Fed-PPI framework involves training local models on private data, aggregating them through Federated Learning (FL), and deriving confidence intervals using PPI computation. The proposed framework is evaluated through experiments, demonstrating its effectiveness in producing valid confidence intervals.

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arXiv2024

Score-based Generative Models with Adaptive Momentum

Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to transform noise into data. However, existing denoising methods such as Langevin dynamic and numerical stochastic differential equation solvers enjoy randomness but generate data slowly with a large number of score function evaluations, and the ordinary differential equation solvers enjoy faster sampling speed but no randomness may influence the sample quality. To this end, motivated by the Stochastic Gradient Descent (SGD) optimization methods and the high connection between the model sampling process with the SGD, we propose adaptive momentum sampling to accelerate the transforming process without introducing additional hyperparameters. Theoretically, we proved our method promises convergence under given conditions. In addition, we empirically show that our sampler can produce more faithful images/graphs in small sampling steps with 2 to 5 times speed up and obtain competitive scores compared to the baselines on image and graph generation tasks.

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arXiv2024

Accelerating Federated Learning by Selecting Beneficial Herd of Local Gradients

Federated Learning (FL) is a distributed machine learning framework in communication network systems. However, the systems' Non-Independent and Identically Distributed (Non-IID) data negatively affect the convergence efficiency of the global model, since only a subset of these data samples are beneficial for model convergence. In pursuit of this subset, a reliable approach involves determining a measure of validity to rank the samples within the dataset. In this paper, We propose the BHerd strategy which selects a beneficial herd of local gradients to accelerate the convergence of the FL model. Specifically, we map the distribution of the local dataset to the local gradients and use the Herding strategy to obtain a permutation of the set of gradients, where the more advanced gradients in the permutation are closer to the average of the set of gradients. These top portion of the gradients will be selected and sent to the server for global aggregation. We conduct experiments on different datasets, models and scenarios by building a prototype system, and experimental results demonstrate that our BHerd strategy is effective in selecting beneficial local gradients to mitigate the effects brought by the Non-IID dataset, thus accelerating model convergence.

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