Augmented Tensor Network approaches for multi-scale image classification

Tensor Networks (TN) methods have successfully been applied to many different machine learning (ML) tasks. Notably, Tree-Tensor Networks (TTN) have proven efficient and rapid predictors in image classification and object detection, showcasing prowess in devising high-performance algorithms.  However, these linear models exhibit limitations in encoding long-distance correlations prevalent in 2D datasets. On the other hand, Multi-scale Entanglement Renormalization Ansatz (MERA) excels in capturing correlations at different scales but is algorithmically complex to optimize within an ML framework. This study aims to harness the strength of the two architectures for building a hybrid image classification algorithm by studying the application of augmented-TTN classifier and optimizing those with state-of-the-art techniques (i.e. auto-differentiation, Riemannian optimization..). The hybrid model will be tested on standard image classification problems: Fashion-MNIST; CIFAR10; ImageNet; and benchmarked against linear TN models and CNN. Finally, we will explore how the explainability features present in TTN can be extended or reinterpreted to hybrid MERA-TTN approaches. This comprehensive analysis seeks to provide insights into the synergies between hierarchical and linear tensor network architectures, paving the way for enhanced multi-scale image classification methodologies.