Interaction Decompositions for Tensor Network Regression
This work addresses inefficiencies in tensor network models for machine learning practitioners, offering a method to improve performance with reduced computational resources, though it is incremental as it builds on existing tensor network frameworks.
The paper tackled the problem of inefficient utilization of the exponential feature space in tensor network regression models by analyzing interaction degrees, finding that up to 75% contribute meaningfully, and introduced a new model trained on a subset that matches or outperforms full models using only a fraction of the space.
It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the interaction decomposition as a tool that can assess the relative importance of different regressors as a function of their polynomial degree. We apply this decomposition to tensor ring and tree tensor network models trained on the MNIST and Fashion MNIST datasets, and find that up to 75% of interaction degrees are contributing meaningfully to these models. We also introduce a new type of tensor network model that is explicitly trained on only a small subset of interaction degrees, and find that these models are able to match or even outperform the full models using only a fraction of the exponential feature space. This suggests that standard tensor network models utilize their polynomial regressors in an inefficient manner, with the lower degree terms being vastly under-utilized.