arXiv AI
Deep belief networks are exact
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Understanding Deep Learning via Entropy Space Theory
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 Machine Learning
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Exploration of the generative capabilities of Boltzmann machines applied to social systems under the majority rule
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 Machine Learning
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Proofs of strong forms of the Bovdi--Geche universality conjecture and a complex analogue
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 Machine Learning
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Variational Inference for Evidential Deep Learning
arXiv:2605. 26477v2 Announce Type: replace Abstract: While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions.
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Universality and Approximation Rates of Graph Neural Networks with Random Features
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 AI
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Tensor network representations of discrete maximum entropy distributions via mean polytopes
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...