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.
The paper proves two universality theorems for single‑neuron neural networks. First, it establishes a strong form of the Bovdi–Geche universality conjecture for neurons over finite fields, employing a modified discrete logarithm activation function and the Weil bound on multiplicative character sums. Second, it generalises Aizenberg’s universality theorem to complex binary neurons with a weight vector independent of the target function, using an equidistribution theorem for dilates of maps into tori.
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.
The paper introduces a deep neural-operator framework for a broad class of probabilistic models, proving a universal approximation theorem under global Lipschitz conditions and explicit network-size bounds. It requires only integrability and general tail-probability conditions on the underlying stochastic processes, which are verified for European and American option-pricing problems within the forward-backward SDE framework. A numerical example with a basket of American options demonstrates that the learned model can generate optimal stopping boundaries for new strike prices without retraining.
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:2610.02253v1 Announce Type: new Abstract: The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realizatio...
arXiv:2611.05626v1 Announce Type: cross Abstract: We show exact signal recovery in generative compressed sensing for feedforward neural networks with piecewise-linear activations and a final sigmoid...