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This research addresses the challenge of selecting diverse subsets from large pools by optimizing fairness across multiple incompatible views, such as textual descriptions and visual logos in trademark curation. The authors propose a novel mathematical framework that relaxes the problem to the Stiefel manifold and solves a gauge-invariant nonlinear eigenvalue problem using an adaptive self-consistent-field solver. This approach ensures robust coverage of all data dimensions without relying on a single kernel that might fail in specific views, advancing multi-view machine learning techniques.
Fair Multi-View Determinantal Coresets via Adaptive NEPv
arXiv:2608.18181v1 Announce Type: cross Abstract: Selecting a small, diverse subset from a large candidate pool often means balancing several incompatible notions of diversity. In trademark curation, for instance, a subset should cover both the language used to describe marks and the visual space of their logos. A single determinantal point process (\DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation by an ordinary single-kernel spectral problem. We formulate \emph{fair multi-view determinant selection}: maximize the weakest per-view log determinant of a size-$k$ subset. We smooth this nonsmooth objective and relax it to the Stiefel manifold. The relaxation embeds every discrete subset exactly, but unlike its single-view counterpart it has no closed-form spectral solution in general. Its stationarity condition is a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights. We derive an adaptive self-consistent-field (\SCF) solver with damping and level shifting, and round the resulting subspace by leverage-score screening followed by fair local refinement. The solver needs only feature-map products for each view. We report conflicting-view synthetic experiments and specify a multimodal USPTO protocol; the real-data multimodal results require aligned logo embeddings and are not claimed in this version.
Abstract:Selecting a small, diverse subset from a large candidate pool often means balancing several incompatible notions of diversity. In trademark curation, for instance, a subset should cover both the language used to describe marks and the visual space of their logos. A single determinantal point process (\DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation by an ordinary single-kernel spectral problem. We formulate \emph{fair multi-view determinant selection}: maximize the weakest per-view log determinant of a size-$k$ subset. We smooth this nonsmooth objective and relax it to the Stiefel manifold. The relaxation embeds every discrete subset exactly, but unlike its single-view counterpart it has no closed-form spectral solution in general. Its stationarity condition is a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights. We derive an adaptive self-consistent-field (\SCF) solver with damping and level shifting, and round the resulting subspace by leverage-score screening followed by fair local refinement. The solver needs only feature-map products for each view. We report conflicting-view synthetic experiments and specify a multimodal USPTO protocol; the real-data multimodal results require aligned logo embeddings and are not claimed in this version.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2608.18181 [stat.ML]
(or arXiv:2608.18181v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.18181 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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