arXiv:2608.29279v1 Announce Type: new Abstract: Deep learning is often criticized for its theoretical research lagging behind practice. To make deep learning easier to understand, the entropy space t...
arXiv:2607. 23349v1 Announce Type: new Abstract: We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions.
arXiv:2605. 26477v2 Announce Type: replace Abstract: While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions.
We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically.
arXiv:2609.07184v1 Announce Type: cross Abstract: We present tensor network representations for discrete maximum entropy distributions under expectation constraints. To this end, we introduce Computa...
arXiv:2608. 15335v1 Announce Type: new Abstract: We consider for an arbitrary fixed $\rho$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $\rho$ layers, $n$ neurons in the first layer (the input layer) and only one neuron, the output neuron, in the last layer.
arXiv:2607. 26699v1 Announce Type: new Abstract: We investigate message-passing graph neural networks with random node features.
arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.
arXiv:2605. 00600v2 Announce Type: replace-cross Abstract: Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling.
arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.
In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error.
arXiv:2607. 06781v1 Announce Type: new Abstract: In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations.