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Related papers: Emergent Low-Rank Training Dynamics in MLPs with S…

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A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights' stable ranks. Intuitively, the latter are indicators of the…

Machine Learning · Computer Science 2021-10-07 Bogdan Georgiev , Lukas Franken , Mayukh Mukherjee , Georgios Arvanitidis

A core component present in many successful neural network architectures, is an MLP block of two fully connected layers with a non-linear activation in between. An intriguing phenomenon observed empirically, including in transformer…

Machine Learning · Computer Science 2024-06-27 Pranjal Awasthi , Nishanth Dikkala , Pritish Kamath , Raghu Meka

Whether deep neural networks can exhibit emergent behaviour is not only relevant for understanding how deep learning works, it is also pivotal for estimating potential security risks of increasingly capable artificial intelligence systems.…

Machine Learning · Computer Science 2025-04-11 Pascal de Jong , Felix Meigel , Steffen Rulands

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Machine Learning · Computer Science 2016-05-03 Ewout van den Berg

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…

Machine Learning · Computer Science 2025-03-25 Raphaël Berthier , Andrea Montanari , Kangjie Zhou

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the…

Machine Learning · Computer Science 2018-12-13 Guy Gur-Ari , Daniel A. Roberts , Ethan Dyer

Peer-to-peer learning is an increasingly popular framework that enables beyond-5G distributed edge devices to collaboratively train deep neural networks in a privacy-preserving manner without the aid of a central server. Neural network…

Machine Learning · Computer Science 2025-04-23 Shreyas Chaudhari , Srinivasa Pranav , Emile Anand , José M. F. Moura

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

Disordered Systems and Neural Networks · Physics 2026-01-01 Davide Badalotti , Carlo Baldassi , Marc Mézard , Mattia Scardecchia , Riccardo Zecchina

We rigorously study the relation between the training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class…

Machine Learning · Computer Science 2025-05-19 Gerard Ben Arous , Reza Gheissari , Jiaoyang Huang , Aukosh Jagannath

Understanding the training dynamics of deep neural networks (DNNs), particularly how they evolve low-dimensional features from high-dimensional data, remains a central challenge in deep learning theory. In this work, we introduce the…

Machine Learning · Computer Science 2025-07-21 Jiang Yang , Yuxiang Zhao , Quanhui Zhu

Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples. In this work we focus on two-layer neural networks trained using data which lie on a low…

Machine Learning · Computer Science 2023-11-17 Odelia Melamed , Gilad Yehudai , Gal Vardi

Interpreting the learning dynamics of neural networks can provide useful insights into how networks learn and the development of better training and design approaches. We present an approach to interpret learning in neural networks by…

Machine Learning · Computer Science 2022-03-29 Ayush Manish Agrawal , Atharva Tendle , Harshvardhan Sikka , Sahib Singh

Small neural networks with a constrained number of trainable parameters, can be suitable resource-efficient candidates for many simple tasks, where now excessively large models are used. However, such models face several problems during the…

Machine Learning · Computer Science 2021-09-21 Alexander Kovalenko , Pavel Kordík , Magda Friedjungová

Modern deep neural networks are highly over-parameterized compared to the data on which they are trained, yet they often generalize remarkably well. A flurry of recent work has asked: why do deep networks not overfit to their training data?…

Machine Learning · Computer Science 2023-03-24 Minyoung Huh , Hossein Mobahi , Richard Zhang , Brian Cheung , Pulkit Agrawal , Phillip Isola

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

Machine Learning · Computer Science 2026-05-22 Alexander Tyurin

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Machine Learning · Computer Science 2025-08-14 Johannes Hertrich , Sebastian Neumayer

Although transformer-based models have shown exceptional empirical performance, the fundamental principles governing their training dynamics are inadequately characterized beyond configuration-specific studies. Inspired by empirical…

Machine Learning · Computer Science 2025-10-09 Zheng-An Chen , Tao Luo

We show that deep neural networks trained across diverse tasks exhibit remarkably similar low-dimensional parametric subspaces. We provide the first large-scale empirical evidence that demonstrates that neural networks systematically…

Machine Learning · Computer Science 2025-12-09 Prakhar Kaushik , Shravan Chaudhari , Ankit Vaidya , Rama Chellappa , Alan Yuille

Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this…

Machine Learning · Computer Science 2019-02-11 Phan-Minh Nguyen

The multi-stage phenomenon in the training loss curves of neural networks has been widely observed, reflecting the non-linearity and complexity inherent in the training process. In this work, we investigate the training dynamics of neural…

Machine Learning · Computer Science 2024-11-07 Zheng-An Chen , Tao Luo , GuiHong Wang