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Abstract We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $$K \geq 1$$, a multivariate non-linearity is applied in each AMP iteration, and the algorithm is spectrally initialized with $$K$$ super-critical sample eigenvectors. We derive the forms of the Onsager debiasing coefficients and corresponding AMP state evolution, which depend on the free cumulants of the noise spectral distribution. This extends previous results for such models with $K=1$ and an independent initialization. Applying this approach to Bayesian principal components analysis, we introduce a Bayes-OAMP algorithm that uses as its non-linearity the posterior mean conditional on all preceding AMP iterates. We describe a practical implementation of this algorithm, where all debiasing and state evolution parameters are estimated from the observed data, and we illustrate the accuracy and stability of this approach in simulations. 

Abstract Utilizing Zwicky Transient Facility (ZTF) data and existing RR Lyrae stars (RRLs) catalogs, this study achieves the first calibration of theP−ϕ₃₁−R₂₁− [Fe/H] andP−ϕ₃₁−A₂−A₁− [Fe/H] relations in the ZTF photometric system for RRab and RRc stars. We also recalibrate the period–absolute magnitude–metallicity (PMZ) and period–Wesenheit–metallicity (PWZ) relations in the ZTFgribands for RRab and RRc stars. Based on nearly 4100 stars with precise measurements ofP,ϕ₃₁,A₂, andA₁, and available spectroscopic metallicity estimates, the photometric metallicity relations exhibit strong internal consistency across different bands, supporting the use of a weighted averaging method for the final estimates. The photometric metallicity estimates of globular clusters based on RR Lyrae members also show excellent agreement with high-resolution spectroscopic measurements, with a typical scatter of 0.15 dex for RRab stars and 0.14 dex for RRc stars, respectively. Using hundreds of local RRLs with newly derived photometric metallicities and precise Gaia Data Release 3 parallaxes, we establish the PMZ and PWZ relations in multiple bands. Validation with globular cluster RR Lyrae members reveals typical distance errors of 3.1% and 3.0% for the PMZ relations, and 3.1% and 2.6% for the PWZ relations for RRab and RRc stars, respectively. Compared to PMZ relations, the PWZ relations are tighter and almost unbiased, making them the recommended choice for distance calculations. We present a catalog of 73,795 RRLs with precise photometric metallicities; over 95% of them have accurate distance measurements. Compared to Gaia DR3, approximately 25,000 RRLs have precise photometric metallicities and distances derived for the first time. 

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue distribution, and fall short of providing precise quantitative characterizations of the “spike” eigenvalues and eigenvectors that often capture the low-dimensional signal structure of the learning problem. In this work, we characterize these signal eigenvalues and eigenvectors for a nonlinear version of the spiked covariance model, including the CK as a special case. Using this general result, we give a quantitative description of how spiked eigenstructure in the input data propagates through the hidden layers of a neural network with random weights. As a second application, we study a simple regime of representation learning where the weight matrix develops a rank-one signal component over training and characterize the alignment of the target function with the spike eigenvector of the CK on test data. 

Abstract Stellar parameters for large samples of stars play a crucial role in constraining the nature of stars and stellar populations in the Galaxy. An increasing number of medium-band photometric surveys are presently used in estimating stellar parameters. In this study, we present a machine learning approach to derive estimates of stellar parameters, including [Fe/H], logg, andT_eff, based on a combination of medium-band and broadband photometric observations. Our analysis employs data primarily sourced from the Stellar Abundances and Galactic Evolution Survey (SAGES), which aims to observe much of the Northern Hemisphere. We combine theuv-band data from SAGES DR1 with photometric and astrometric data from Gaia EDR3, and apply the random forest method to estimate stellar parameters for approximately 21 million stars. We are able to obtain precisions of 0.09 dex for [Fe/H], 0.12 dex for logg, and 70 K forT_eff. Furthermore, by incorporating Two Micron All Sky Survey and Wide-field Infrared Survey Explorer infrared photometric and Galaxy Evolution Explorer ultraviolet data, we are able to achieve even higher precision estimates for over 2.2 million stars. These results are applicable to both giant and dwarf stars. Building upon this mapping, we construct a foundational data set for research on metal-poor stars, the structure of the Milky Way, and beyond. With the forthcoming release of additional bands from SAGES such DDO51 and Hα, this versatile machine learning approach is poised to play an important role in upcoming surveys featuring expanded filter sets. 

Abstract Photometric stellar surveys now cover a large fraction of the sky, probe to fainter magnitudes than large-scale spectroscopic surveys, and are relatively free from the target selection biases often associated with such studies. Photometric-metallicity estimates that include narrow/medium-band filters can achieve comparable accuracy and precision to existing low-resolution spectroscopic surveys such as Sloan Digital Sky Survey/SEGUE and LAMOST. Here we report on an effort to identify likely members of the Galactic disk system among the very metal-poor (VMP; [Fe/H] ≤ −2) and extremely metal-poor (EMP; [Fe/H] ≤ −3) stars. Our analysis is based on an initial sample of ∼11.5 million stars with full space motions selected from the SkyMapper Southern Survey (SMSS) and Stellar Abundance and Galactic Evolution Survey (SAGES). After applying a number of quality cuts to obtain the best available metallicity and dynamical estimates, we analyze a total of ∼5.86 million stars in the combined SMSS/SAGES sample. We employ two techniques that, depending on the method, identify between 876 and 1476 VMP stars (6.9%−11.7% of all VMP stars) and between 40 and 59 EMP stars (12.4%−18.3% of all EMP stars) that appear to be members of the Galactic disk system on highly prograde orbits (v_ϕ> 150 km s⁻¹). The total number of candidate VMP/EMP disklike stars is 1496, the majority of which have low orbital eccentricities, ecc ≤ 0.4; many have ecc ≤ 0.2. The large fractions of VMP/EMP stars associated with the Milky Way disk system strongly suggest the presence of an early-forming “primordial” disk.