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Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…

Machine Learning · Computer Science 2025-02-27 Siyuan Yu , Wei Chen , H. Vincent Poor

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each…

Machine Learning · Computer Science 2024-08-23 Yukun Zhang

Current LLM alignment methods are readily broken through specifically crafted adversarial prompts. While crafting adversarial prompts using discrete optimization is highly effective, such attacks typically use more than 100,000 LLM calls.…

Machine Learning · Computer Science 2025-03-04 Simon Geisler , Tom Wollschläger , M. H. I. Abdalla , Johannes Gasteiger , Stephan Günnemann

We introduce the Semantic Density Effect (SDE): the empirical finding that prompts carrying higher semantic information per token consistently produce more accurate, focused, and less hallucinated outputs across all major LLM families. SDE…

Computation and Language · Computer Science 2026-04-21 Amr Ahmed

We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance.…

Optimization and Control · Mathematics 2023-08-21 Elizabeth Collins-Woodfin , Courtney Paquette , Elliot Paquette , Inbar Seroussi

The tension between data privacy and model utility has become the defining bottleneck for the practical deployment of large language models (LLMs) trained on sensitive corpora including healthcare. Differentially private stochastic gradient…

Machine Learning · Computer Science 2025-07-31 Afshin Khadangi , Amir Sartipi , Igor Tchappi , Ramin Bahmani , Gilbert Fridgen

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

Machine Learning · Statistics 2024-10-29 Daniel Soudry , Elad Hoffer , Mor Shpigel Nacson , Suriya Gunasekar , Nathan Srebro

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Machine Learning · Statistics 2026-01-09 James Rice

Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for discriminative training of probabilistic generative models belonging to the exponential family. In this work, we introduce and justify this algorithm as a stochastic…

Machine Learning · Computer Science 2017-04-05 Andres R. Masegosa

Differentially private stochastic gradient descent (DP-SGD) adds noise to gradients in back-propagation, safeguarding training data from privacy leakage, particularly membership inference. It fails to cover (inference-time) threats like…

Cryptography and Security · Computer Science 2023-09-20 Minxin Du , Xiang Yue , Sherman S. M. Chow , Tianhao Wang , Chenyu Huang , Huan Sun

Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We…

Artificial Intelligence · Computer Science 2026-02-04 Yichen Han , Yuhang Han , Siteng Huang , Guanyu Liu , Zhengpeng Zhou , Bojun Liu , Yujia Zhang , Isaac N Shi , Lewei He , Tianyu Shi

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…

Machine Learning · Computer Science 2025-12-15 Sotirios Nikoloutsopoulos , Iordanis Koutsopoulos , Michalis K. Titsias

Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…

Optimization and Control · Mathematics 2023-10-03 Valentin Leplat , Daniil Merkulov , Aleksandr Katrutsa , Daniel Bershatsky , Olga Tsymboi , Ivan Oseledets

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training…

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep…

Machine Learning · Computer Science 2022-10-14 Mingrui Liu , Zhenxun Zhuang , Yunwei Lei , Chunyang Liao

Large Language Models (LLMs) have reshaped natural language processing, powering applications from multi-hop retrieval and question answering to autonomous agent workflows. Yet, prompt engineering -- the task of crafting textual inputs to…

Computation and Language · Computer Science 2025-01-31 Li Yin , Zhangyang Wang

Large language models (LLMs) exhibit strong capabilities as decision-making agents by interleaving reasoning and actions, as seen in ReAct-style frameworks. Yet, their practical deployment is constrained by high inference costs and large…

Machine Learning · Computer Science 2026-05-28 Jun Liu , Zhenglun Kong , Peiyan Dong , Changdi Yang , Tianqi Li , Hao Tang , Geng Yuan , Wei Niu , Wenbin Zhang , Pu Zhao , Xue Lin , Dong Huang , Yanzhi Wang

Decentralized training enables learning with distributed datasets generated at different locations without relying on a central server. In realistic scenarios, the data distribution across these sparsely connected learning agents can be…

Machine Learning · Computer Science 2025-02-27 Sakshi Choudhary , Sai Aparna Aketi , Kaushik Roy

On-policy self-distillation (SD) improves LLM reasoning by using teacher-side privileged information (PI) to turn sparse verifier outcomes into dense token-level supervision. Existing methods usually assume trusted PI, such as reference…

Computation and Language · Computer Science 2026-05-28 Jiazhen Huang , Xiao Chen , Xiao Luo , Yong Dai , Senkang Hu , Yuzhi Zhao

Considering generating samples with high rewards, we focus on optimizing deep neural networks parameterized stochastic differential equations (SDEs), the advanced generative models with high expressiveness, with policy gradient, the leading…

Machine Learning · Computer Science 2024-06-27 Xiangxin Zhou , Liang Wang , Yichi Zhou
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