TGRank: Task-Guided Rank Learning for Low-Rank Tensor Representations

Low-rank tensor representations model multidimensional feature tensors through factorized structures parameterized by continuous factorization variables and discrete ranks. While the factorization variables can be optimized end to end under task supervision, the ranks are typically prescribed before training and held fixed thereafter. Learning these ranks is nontrivial because rank decrease and rank increase operate on structures with different optimization histories: the former evaluates task-trained structure, whereas the latter must assess candidate structure whose task value has not yet been established. Motivated by this asymmetry, we propose TGRank, a task-guided framework that learns ranks during task optimization through adjacent rank changes. Specifically, TGRank employs direction-specific task evidence: rank decrease is guided by the task consequence of suppressing trained structure, whereas rank increase is guided by the task utility revealed after brief adaptation of candidate structure. Extensive experiments across super-resolution, image classification, and semantic segmentation demonstrate that TGRank learns nonuniform task-adaptive ranks and consistently outperforms matched fixed-rank counterparts.