  The computing cost and memory demand of deep learning pipelines have grown
fast in recent years and thus a variety of pruning techniques have been
developed to reduce model parameters. The majority of these techniques focus on
reducing inference costs by pruning the network after a pass of full training.
A smaller number of methods address the reduction of training costs, mostly
based on compressing the network via low-rank layer factorizations. Despite
their efficiency for linear layers, these methods fail to effectively handle
convolutional filters. In this work, we propose a low-parametric training
method that factorizes the convolutions into tensor Tucker format and
adaptively prunes the Tucker ranks of the convolutional kernel during training.
Leveraging fundamental results from geometric integration theory of
differential equations on tensor manifolds, we obtain a robust training
algorithm that provably approximates the full baseline performance and
guarantees loss descent. A variety of experiments against the full model and
alternative low-rank baselines are implemented, showing that the proposed
method drastically reduces the training costs, while achieving high
performance, comparable to or better than the full baseline, and consistently
outperforms competing low-rank approaches.
