arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2606. 29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks.
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2606. 14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers.
In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, while there has been a number of very recent results that establish ever-tighter lower bounds for the problem under linear and ReLU activation functions, less progress has been made towards the identification of novel polynomial-time tractable network architectures.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2607. 20811v1 Announce Type: new Abstract: In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions.
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.