# Fair Multi-View Determinantal Coresets via Adaptive NEPv

arXiv: https://arxiv.org/abs/2608.18181 · HTML: https://mlsanity.com/paper/2608.18181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes](https://mlsanity.com/paper/1602.05242/) (2016)
- [Faster Greedy MAP Inference for Determinantal Point Processes](https://mlsanity.com/paper/1703.03389/) (2017)
- [Randomized Rounding for the Largest Simplex Problem](https://mlsanity.com/paper/1412.0036/) (2014)
- [Approximation Algorithms for D-optimal Design](https://mlsanity.com/paper/1802.08372/) (2018)

## Abstract (arXiv)

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 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.