Fair Multi-View Determinantal Coresets via Adaptive NEPv

• URL: http://arxiv.org/abs/2608.18181v1
• Date: Tue, 18 Aug 2026 02:32:32 GMT
• Title: Fair Multi-View Determinantal Coresets via Adaptive NEPv
• Abstract summary: In trademark curation, a subset should cover both the language used to describe marks and the visual space of their logos.<n>A single determinantal point process (DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation.<n>We formulate emphfair multi-view selection: maximize the weakest per-view log of a size-$k$ subset.
• Score: 6.555429729518591
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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