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We study the learning dynamics of a multi-pass, mini-batch Stochastic Gradient Descent (SGD) procedure for empirical risk minimization in high-dimensional multi-index models with isotropic random data. In an asymptotic regime where the…

Machine Learning · Statistics 2026-02-19 Zhou Fan , Leda Wang

Quantization is an effective way to reduce the memory cost of large-scale model training. However, most existing methods adopt fixed-precision policies, which ignore the fact that optimizer-state distributions vary significantly across…

Machine Learning · Computer Science 2026-04-10 Minglu Liu , Cunchen Hu , Liangliang Xu , Fengming Tang , Ruijia Wang , Fu Yu

Gradient dynamics play a central role in determining the stability and generalization of deep neural networks. In this work, we provide an empirical analysis of how variance and standard deviation of gradients evolve during training,…

Machine Learning · Computer Science 2025-09-09 Vincent-Daniel Yun

It has been proven that, compared to using 32-bit floating-point numbers in the training phase, Deep Convolutional Neural Networks (DCNNs) can operate with low precision during inference, thereby saving memory space and power consumption.…

Artificial Intelligence · Computer Science 2022-10-03 Binyi Wu , Bernd Waschneck , Christian Georg Mayr

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Statistics Theory · Mathematics 2023-09-06 Youssef Marzouk , Zhi Ren , Sven Wang , Jakob Zech

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Machine Learning · Computer Science 2019-12-06 Gauthier Gidel , Francis Bach , Simon Lacoste-Julien

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Machine Learning · Computer Science 2019-10-17 Mohammad Amin Nabian , Hadi Meidani

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

Machine Learning · Computer Science 2025-08-06 Paz Fink Shustin , Shashanka Ubaru , Małgorzata J. Zimoń , Songtao Lu , Vasileios Kalantzis , Lior Horesh , Haim Avron

We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered…

Computational Physics · Physics 2018-05-09 Yinhao Zhu , Nicholas Zabaras

Designing a deep neural network (DNN) with good generalization capability is a complex process especially when the weights are severely quantized. Model averaging is a promising approach for achieving the good generalization capability of…

Machine Learning · Computer Science 2020-02-04 Sungho Shin , Yoonho Boo , Wonyong Sung

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…

Machine Learning · Statistics 2022-03-28 Sebastian Goldt , Madhu S. Advani , Andrew M. Saxe , Florent Krzakala , Lenka Zdeborová

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has…

Information Theory · Computer Science 2020-06-24 Yuqing Du , Sheng Yang , Kaibin Huang

We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct…

Machine Learning · Computer Science 2021-12-07 Huu Le , Rasmus Kjær Høier , Che-Tsung Lin , Christopher Zach

Quantum neural networks, parameterized quantum circuits optimized under a specific cost function, provide a paradigm for achieving near-term quantum advantage in quantum information processing. Understanding QNN training dynamics is crucial…

Quantum Physics · Physics 2025-08-12 Bingzhi Zhang , Junyu Liu , Liang Jiang , Quntao Zhuang

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

Applications · Statistics 2026-02-12 Jungho Kim , Sang-ri Yi , Ziqi Wang

Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of…

Machine Learning · Computer Science 2018-10-05 Christos Louizos , Matthias Reisser , Tijmen Blankevoort , Efstratios Gavves , Max Welling

We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…

Machine Learning · Computer Science 2017-12-13 Chuang Wang , Jonathan Mattingly , Yue M. Lu

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

With the rapid increase in the size of neural networks, model compression has become an important area of research. Quantization is an effective technique at decreasing the model size, memory access, and compute load of large models.…

Audio and Speech Processing · Electrical Eng. & Systems 2023-05-26 David Qiu , David Rim , Shaojin Ding , Oleg Rybakov , Yanzhang He

Integrating model-free and model-based approaches in reinforcement learning has the potential to achieve the high performance of model-free algorithms with low sample complexity. However, this is difficult because an imperfect dynamics…

Machine Learning · Computer Science 2019-06-10 Jacob Buckman , Danijar Hafner , George Tucker , Eugene Brevdo , Honglak Lee