arXiv AI
Tensor network representations of discrete maximum entropy distributions via mean polytopes
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Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography
The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
Hugging Face Trending Papers
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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
Sep 1
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
Aug 4
Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
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 Machine Learning
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Universality and Approximation Rates of Graph Neural Networks with Random Features
arXiv:2607. 26699v1 Announce Type: new Abstract: We investigate message-passing graph neural networks with random node features.
arXiv Machine Learning
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On the Rademacher Complexity of Graph Neural Networks: Unifying Expressivity and Geometry
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.