Dimension d = O(m^{-2} log n) nearly achieves the optimal margin m^rd(+∞, A) for retrieval embeddings, with matching lower bounds showing d = O(k log(n/k)) suffices and is necessary for m = Θ(k^{-1/2}) on k-sparse query matrices.
On the Restricted Isometry Property of Centered Self Khatri-Rao Products
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this work we establish the Restricted Isometry Property (RIP) of the centered column-wise self Khatri-Rao (KR) products of $n\times N$ matrix with iid columns drawn either uniformly from a sphere or with iid sub-Gaussian entries. The self KR product is an $n^2\times N$-matrix which contains as columns the vectorized (self) outer products of the columns of the original $n\times N$-matrix. Based on a result of Adamczak et al. we show that such a centered self KR product with independent heavy tailed columns has small RIP constants of order $s$ with probability at least $1-C\exp(-cn)$ provided that $s\lesssim n^2/\log^2(eN/n^2)$. Our result is applicable in various works on covariance matching like in activity detection and MIMO gain-estimation.
years
2026 4verdicts
UNVERDICTED 4representative citing papers
JWST MIRI observations of 634 galaxies at 0.2<z<2 yield IR luminosity functions with faint-end slope α≈0.147, implying lower dust-obscured SFRD than previous ALMA/Herschel/Spitzer studies.
Nereid is proposed as Neptune's sole surviving regular satellite rather than a captured irregular satellite, based on new spectroscopic data and dynamical modeling.
Bayesian photometric cosmic chronometer analysis on VIPERS PDR2 data yields H(z=0.65)=93.68±28.27(stat)±10.67(syst) km/s/Mpc, consistent with spectroscopic CC results and Planck ΛCDM, as a proof of concept for photometric surveys.
citing papers explorer
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Is Dimensionality a Barrier for Retrieval Models?
Dimension d = O(m^{-2} log n) nearly achieves the optimal margin m^rd(+∞, A) for retrieval embeddings, with matching lower bounds showing d = O(k log(n/k)) suffices and is necessary for m = Θ(k^{-1/2}) on k-sparse query matrices.
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MEGA and SMILES Find Fewer Dusty Galaxies than Expected at Cosmic Noon
JWST MIRI observations of 634 galaxies at 0.2<z<2 yield IR luminosity functions with faint-end slope α≈0.147, implying lower dust-obscured SFRD than previous ALMA/Herschel/Spitzer studies.
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Nereid as a Regular Satellite of Neptune
Nereid is proposed as Neptune's sole surviving regular satellite rather than a captured irregular satellite, based on new spectroscopic data and dynamical modeling.
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Towards Bayesian Photometric Cosmic Chronometers: Application to VIPERS
Bayesian photometric cosmic chronometer analysis on VIPERS PDR2 data yields H(z=0.65)=93.68±28.27(stat)±10.67(syst) km/s/Mpc, consistent with spectroscopic CC results and Planck ΛCDM, as a proof of concept for photometric surveys.