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This thesis explores how deep learning models learn over time, using ideas inspired by force analysis. Specifically, we zoom in on the model's training procedure to see how one training example affects another during learning, like…

Machine Learning · Computer Science 2025-09-25 Yi Ren

Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states which produce inconsistent predictions of the same test…

Dynamical Systems · Mathematics 2021-06-16 Mohammed Eslami , Hamed Eramian , Marcio Gameiro , William Kalies , Konstantin Mischaikow

Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many…

Machine Learning · Computer Science 2024-05-16 Jinyeop Song , Ziming Liu , Max Tegmark , Jeff Gore

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

Machine Learning · Statistics 2024-06-25 Blake Bordelon , Alexander Atanasov , Cengiz Pehlevan

Motor adaptation displays a structure-learning effect: adaptation to a new perturbation occurs more quickly when the subject has prior exposure to perturbations with related structure. Although this `learning-to-learn' effect is well…

Artificial Intelligence · Computer Science 2017-07-14 Ari Weinstein , Matthew M. Botvinick

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…

We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto…

Machine Learning · Computer Science 2026-03-17 Vitaly Vanchurin

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

Machine Learning · Computer Science 2024-07-04 Francesco Cagnetta , Leonardo Petrini , Umberto M. Tomasini , Alessandro Favero , Matthieu Wyart

We investigate how neural networks (NNs) understand physics using 1D quantum mechanics. After training an NN to accurately predict energy eigenvalues from potentials, we used it to confirm the NN's understanding of physics from four…

Computational Physics · Physics 2022-11-09 Kenzo Ogure

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Machine Learning · Computer Science 2018-06-01 Na Lei , Zhongxuan Luo , Shing-Tung Yau , David Xianfeng Gu

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Machine Learning · Computer Science 2025-12-02 Hanlin Yu , Berfin Inal , Georgios Arvanitidis , Soren Hauberg , Francesco Locatello , Marco Fumero

Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance. To examine the structure of when and where memorization occurs in a deep network, we use a recently developed…

Machine Learning · Computer Science 2021-06-01 Cory Stephenson , Suchismita Padhy , Abhinav Ganesh , Yue Hui , Hanlin Tang , SueYeon Chung

Model-based reinforcement learning (RL) is a sample-efficient way of learning complex behaviors by leveraging a learned single-step dynamics model to plan actions in imagination. However, planning every action for long-horizon tasks is not…

Machine Learning · Computer Science 2022-12-13 Lucy Xiaoyang Shi , Joseph J. Lim , Youngwoon Lee

Lifelong learning occurs on timescales ranging from minutes to decades. People can lose themselves in a new skill, practicing for hours until exhausted. And they can pursue mastery over days or decades, perhaps abandoning old skills…

Physics and Society · Physics 2022-06-09 Mingzhen Lu , Tyler Marghetis , Vicky Chuqiao Yang

Larger models learn tasks smaller models do not. What drives this phenomenon? We develop a simple phenomenological argument that power-law scaling already suggests that a larger model will be able to learn a part of the data distribution…

Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…

Machine Learning · Computer Science 2024-07-08 Loek van Rossem , Andrew M. Saxe

Physics-based manipulation in clutter involves complex interaction between multiple objects. In this paper, we consider the problem of learning, from interaction in a physics simulator, manipulation skills to solve this multi-step…

Robotics · Computer Science 2019-07-29 Wissam Bejjani , Mehmet R. Dogar , Matteo Leonetti

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…

Machine Learning · Statistics 2024-10-14 Roman Worschech , Bernd Rosenow

Predicting material properties is crucial for designing better batteries, semiconductors, and medical devices. Deep learning helps scientists quickly find promising materials by predicting their energy, forces, and stresses. Companies scale…

Machine Learning · Computer Science 2025-09-29 Akshay Trikha , Kyle Chu , Advait Gosai , Parker Szachta , Eric Weiner

Designing effective rehabilitation strategies for upper extremities, particularly hands and fingers, warrants the need for a computational model of human motor learning. The presence of large degrees of freedom (DoFs) available in these…

Systems and Control · Electrical Eng. & Systems 2022-09-13 Ankur Kamboj , Rajiv Ranganathan , Xiaobo Tan , Vaibhav Srivastava
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