arXiv Machine Learning
Jun 9
Learning Dynamics Reveal a Hierarchy of Weight-Induced Layerwise Gram Metrics
arXiv:2606. 09744v1 Announce Type: new Abstract: We study feed-forward ReLU networks with fixed readout and quadratic loss.
Derivation of effective gradient flow equations and dynamical truncation of training data in Deep Learning
arXiv:2501. 07400v2 Announce Type: replace-cross Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations.
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arXiv Machine Learning
Jul 7
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
arXiv:2607. 03613v1 Announce Type: new Abstract: We study the implicit bias of noisy stochastic gradient descent in training wide two-layer ReLU networks for multivariate regression.
arXiv Machine Learning
Jul 3
From Approximation to Emergence: A Theory of Deep Learning
arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.
arXiv Machine Learning
Jun 9
Bulk-boundary decomposition of neural networks
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.
arXiv Machine Learning
Jul 9
Network Dynamics-Based Framework for Understanding Deep Neural Networks
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
arXiv Machine Learning
Jun 5
Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.
arXiv Machine Learning
Jun 17
A Dynamical Systems Perspective on the Analysis of Neural Networks
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv Machine Learning
Aug 11
Weak Correlations as the Underlying Principle for Linearization of Gradient-Based Learning Systems
arXiv:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
arXiv AI
Jun 8
Generalization in Deep Neural Networks: Minimax Rates for Gradient Methods
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
arXiv Machine Learning
Jun 5
A prism hierarchy of learning regimes in large linear autoencoders
arXiv:2606. 05335v1 Announce Type: new Abstract: Theoretical studies of machine learning models commonly consider different limiting regimes in which the learning dynamics of gradient descent becomes theoretically tractable.
arXiv AI
Jun 2
The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold
arXiv:2511. 01938v3 Announce Type: replace-cross Abstract: Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data.
arXiv Machine Learning
Jul 30
Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.