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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

How large language models (LLMs) align with the neural representation and computation of human language is a central question in cognitive science. Using representational geometry as a mechanistic lens, we addressed this by tracking…

Neurons and Cognition · Quantitative Biology 2026-02-10 Yixuan Liu , Zhiyuan Ma , Likai Tang , Runmin Gan , Xinche Zhang , Jinhao Li , Chao Xie , Sen Song

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

Machine Learning · Computer Science 2021-05-04 Michael M. Bronstein , Joan Bruna , Taco Cohen , Petar Veličković

Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system,…

Robotics · Computer Science 2022-10-17 Jee-eun Lee , Jaemin Lee , Tirthankar Bandyopadhyay , Luis Sentis

Humans possess a remarkable capacity to recognize and manipulate abstract structure, which is especially apparent in the domain of geometry. Recent research in cognitive science suggests neural networks do not share this capacity,…

Artificial Intelligence · Computer Science 2024-02-07 Declan Campbell , Sreejan Kumar , Tyler Giallanza , Thomas L. Griffiths , Jonathan D. Cohen

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

Machine Learning · Computer Science 2022-06-07 Satrajit Chatterjee , Piotr Zielinski

We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking…

Machine Learning · Computer Science 2024-05-28 Yeachan Park , Minseok Kim , Yeoneung Kim

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of…

Machine Learning · Computer Science 2023-06-06 Akhilan Boopathy , Kevin Liu , Jaedong Hwang , Shu Ge , Asaad Mohammedsaleh , Ila Fiete

Training Neural Networks (NNs) without overfitting is difficult; detecting that overfitting is difficult as well. We present a novel Random Matrix Theory method that detects the onset of overfitting in deep learning models without access to…

Machine Learning · Computer Science 2026-05-15 Hari K. Prakash , Charles H Martin

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Machine Learning · Computer Science 2022-11-03 Kosio Beshkov , Jonas Verhellen , Mikkel Elle Lepperød

Intrinsically motivated goal exploration algorithms enable machines to discover repertoires of policies that produce a diversity of effects in complex environments. These exploration algorithms have been shown to allow real world robots to…

Machine Learning · Computer Science 2018-10-11 Alexandre Péré , Sébastien Forestier , Olivier Sigaud , Pierre-Yves Oudeyer

Imitation learning holds the promise of equipping robots with versatile skills by learning from expert demonstrations. However, policies trained on finite datasets often struggle to generalize beyond the training distribution. In this work,…

Machine Learning · Computer Science 2025-04-28 Yixiao Wang

Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap…

Machine Learning · Computer Science 2026-05-21 Lucky Verma

As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light…

A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We…

Machine Learning · Computer Science 2020-01-01 Daniel Gissin , Shai Shalev-Shwartz , Amit Daniely

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

Large-scale transformers achieve impressive results on program synthesis benchmarks, yet their true generalization capabilities remain obscured by data contamination and opaque training corpora. To rigorously assess whether models are truly…

Machine Learning · Computer Science 2026-05-01 Henrik Voigt , Michael Habeck , Joachim Giesen

Generative models have recently been explored for synthesizing neural network weights. These approaches take neural network checkpoints as training data and aim to generate high-performing weights during inference. In this work, we examine…

Machine Learning · Computer Science 2025-10-06 Boya Zeng , Yida Yin , Zhiqiu Xu , Zhuang Liu

Dexterous manipulation of arbitrary objects, a fundamental daily task for humans, has been a grand challenge for autonomous robotic systems. Although data-driven approaches using reinforcement learning can develop specialist policies that…

Robotics · Computer Science 2021-11-05 Wenlong Huang , Igor Mordatch , Pieter Abbeel , Deepak Pathak

Deep learning has enabled remarkable improvements in grasp synthesis for previously unseen objects from partial object views. However, existing approaches lack the ability to explicitly reason about the full 3D geometry of the object when…

Robotics · Computer Science 2020-03-19 Mark Van der Merwe , Qingkai Lu , Balakumar Sundaralingam , Martin Matak , Tucker Hermans
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