The Tensor Track VII: From Quantum Gravity to Artificial Intelligence

2022/04/30 by Mohamed Ouerfelli, Ouerfelli, Mohamed, Vincent Rivasseau +3
Computer Science · Physics and Astronomy · #81T32 #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2205.10326

openalex publication_date 2022/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects
• Intriguing properties of neural networks
• FitNets: Hints for Thin Deep Nets
• Tensorizing Neural Networks
• Distilling the Knowledge in a Neural Network
• Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations
• A planar diagram theory for strong interactions
• ImageNet classification with deep convolutional neural networks
• Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations
• Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications
• Power Iteration for Tensor PCA
• Statistical-Computational Trade-offs in Tensor PCA and Related Problems via Communication Complexity
• The Computational Limits of Deep Learning
• Generative Adversarial Nets

Related

• The Tensor Track, IV
• Quantum Gravity and Random Tensors
• Report on "Geometry and representation theory of tensors for computer science, statistics and other areas."
• Random Tensor models: Combinatorics, Geometry, Quantum Gravity and Integrability
• From probabilistic graphical models to generalized tensor networks for\n supervised learning