The Tensor Track VII: From Quantum Gravity to Artificial Intelligence

Abstract

Assuming some familiarity with quantum field theory and with the tensor track approach that one of us presented in the previous series Tensor Track I to VI, we provide, as usual, the developments in quantum gravity of the last two years. Next we present in some detail two algorithms inspired by Random Tensor Theory which has been developed in the quantum gravity context. One is devoted to the detection and recovery of a signal in a random tensor, that can be associated to the noise, with new theoretical guarantees for more general cases such as tensors with different dimensions. The other, SMPI, is more ambitious but maybe less rigorous. It is devoted to significantly and fundamentally improve the performance of algorithms for Tensor principal component analysis but without complete theoretical guarantees yet. Then we sketch all sorts of application relevant to information theory and artificial intelligence and provide their corresponding bibliography.

arXiv comment23 pages, 7 figures, 1 table

References in corpus (21)

• Distilling the Knowledge in a Neural Network
• Intriguing properties of neural networks
• FitNets: Hints for Thin Deep Nets
• Comments on the Sachdev-Ye-Kitaev model
• Quantum Field Theory on Noncommutative Spaces
• Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations
• Critical behavior of colored tensor models in the large N limit
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• The Computational Limits of Deep Learning
• TensorLy: Tensor Learning in Python
• Tensor Methods in Computer Vision and Deep Learning
• Melons are branched polymers
• Double Scaling in Tensor Models with a Quartic Interaction
• Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms
• The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Operator Norm Inequalities between Tensor Unfoldings on the Partition Lattice
• From scalar fields on quantum spaces to blobbed topological recursion
• Power Iteration for Tensor PCA
• Statistical-Computational Trade-offs in Tensor PCA and Related Problems via Communication Complexity

Cited by in corpus (2)

• Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small $N$
• The Tensor Track VIII: Stochastic Analysis