Coverage Risk Minimization: A Unified Framework for Long-Tailed Deep Fine-grained Clustering

Long-tailed distributions and fine-grained semantics frequently co-occur in real-world visual data: tail classes lack sufficient data support, while semantically similar categories share highly similar visual representations, rendering reliable intra-class aggregation and inter-class separation considerably more challenging. To this end, we revisit fine-grained long-tailed clustering from the perspective of forward representation optimization and propose **D4C**, a hierarchical coverage risk optimization framework with density-aware forward control that continuously shapes clustering-conducive geometric structures across different representation levels. Theoretically, starting from the PAC upper bound of coverage risk, we isolate an optimizable average term and a geometric bottleneck governed by the worst-case covering radius, and adopt optimal transport and geometric repulsive potentials as their differentiable surrogates to coordinate sample coverage and center separation. Concurrently, we introduce a vMF mixture model at each representation level to characterize the local density structure, guiding samples to aggregate toward local density peaks. To tackle imbalanced support among long-tailed categories, we further design long-tail-aware transport marginals, and over-segmentation with Ward merging and EMA teacher freezing keep coverage-risk minimization stable. Extensive experiments on multiple long-tailed and fine-grained clustering benchmarks demonstrate that D4C achieves state-of-the-art performance.