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.
Principles and Practice of Deep Representation Learning: or a Mathematical Theory of Memory
arXiv:2606. 06624v1 Announce Type: new Abstract: In the current era of deep learning and especially generative models, there is significant investment in training very large generative models.
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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
Sep 25
Pointwise Generalization in Deep Neural Networks
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
arXiv Machine Learning
Jul 1
Explaining Machine Learning and Memorization with Statistical Mechanics
arXiv:2606. 31110v1 Announce Type: new Abstract: Artificial neural networks (NNs) and machine learning (ML) algorithms are poorly understood from a theoretical perspective, which makes it difficult to fully realize their potential and overcome their weaknesses.
arXiv AI
Sep 15
Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks
The paper discusses tensorizing neural networks by reshaping dense weight matrices into higher-order tensors and approximating them with low-rank tensor network decompositions. This approach offers promising model compression and introduces bond indices that create new latent spaces, potentially enhancing interpretability. Despite encouraging empirical results, tensorized neural networks remain underused, and the authors call for more research to address practical scaling and adoption challenges.
arXiv Machine Learning
Sep 10
The Rules-and-Facts Model for Simultaneous Generalization and Memorization in Neural Networks
arXiv:2603.25579v2 Announce Type: replace-cross Abstract: A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptio...
Hugging Face Trending Papers
Jun 22
Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
arXiv Machine Learning
Aug 10
Mathematical Principles and Experimental Discoveries of the Emergence of Symbolic Patterns in Artificial Neural Networks
arXiv:2608. 06839v1 Announce Type: new Abstract: Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning.
arXiv Machine Learning
Jul 24
Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation
arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
arXiv Machine Learning
Aug 18
On the Principles Behind Neural Network Optimizers
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv Machine Learning
Jun 15
Uncertainty Estimation and Generalization Bounds for Modern Deep Learning
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
arXiv AI
Jun 29
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.