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At least 73 records · Page 4

Different higher order kinematics between star-forming and quiescent galaxies based on the SAMI, MAGPI, and LEGA-C surveys

We present the first statistical study of spatially integrated non-Gaussian stellar kinematics spanning 7 Gyr in cosmic time. We use deep, rest-frame optical spectroscopy of massive galaxies (stellar mass $M_\star \gt 10^{10.5} \, \mathrm{M_\odot }$) at redshifts z = 0.05, 0.3, and 0.8 from the SAMI, MAGPI, and LEGA-C surveys, to measure the excess kurtosis h 4 of the stellar velocity distribution, the latter parametrized as a Gauss–Hermite series. We find that at all redshifts where we have large enough samples, h 4 anticorrelates with the ratio between rotation and dispersion, highlighting the physical connection between these two kinematic observables. In addition, and independently from the anticorrelation with rotation-to-dispersion ratio, we also find a correlation between h 4 and M ⋆ , potentially connected to the assembly history of galaxies. In contrast, after controlling for mass, we find no evidence of independent correlation between h 4 and aperture velocity dispersion or galaxy size. These results hold for both star-forming and quiescent galaxies. For quiescent galaxies, h 4 also correlates with projected shape, even after controlling for the rotation-to-dispersion ratio. At any given redshift, star-forming galaxies have lower h 4 compared to quiescent galaxies, highlighting the link between kinematic structure and star-forming activity.

79 ASTRONOMY AND ASTROPHYSICS↗

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗

Kaon Femtoscopy with Lévy-Stable Sources from $\sqrt{s_{NN}}$ = 200 GeV Au+Au Collisions at RHIC

Femtoscopy has the capacity to probe the space-time geometry of the particle-emitting source in heavy-ion collisions. In particular, femtoscopy of like-sign kaon pairs may shed light on the origin of non-Gaussianity of the spatial emission probability density. The momentum correlations between like-sign kaon pairs are measured in data recorded by the STAR experiment, from $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at RHIC, BNL. Preliminary results hint at the possible existence of non-Gaussian, Lévy-stable sources, with the likely presence of an anomalous diffusion process in the signal for the identically charged kaon pairs so produced. More statistically significant studies at lower centre-of-mass energies may contribute to the search for the critical end point of QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Assembly bias and local Primordial non-Gaussianity from DESI DR1 quasars

The analysis of the large-scale clustering of quasars (QSO) observed by the Dark Energy Spectroscopic Instrument (DESI) represents a promising avenue for constraining local Primordial non-Gaussianity (PNG), parameterized by f NL . The signal to be constrained is the scale-dependent bias induced in the 2-point clustering of the considered tracer sample. The resulting constraints on f NL , however, are fully degenerate with the local PNG bias parameter b ϕ , dependent on the assembly bias parameter p. Using IllustrisTNG hydrodynamical simulations, we select a QSO sample reflecting the selection criteria and properties of DESI QSOs, and provide a robust prior for p, and thus for b ϕ , building on the findings of Fondi et al. 2024. We find a distribution with mean p̅ ≃ 1.4 with weak redshift dependence, stable to selection noise and consistent with the expected recent merger history typical of quasar-hosting halos. By comparing with the CAMELS simulations we demonstrate that this prior is robust to astrophysical assumptions and cosmic variance. Finally, applying this prior to the DESI DR1 dataset, we derive updated constraints on local PNG, obtaining f NL = -3.3±9.2.

cosmological parameters from LSS↗

Cosmological constraints from the Subaru Hyper Suprime-Cam year 1 shear catalogue lensing convergence probability distribution function

Here we utilize the probability distribution function (PDF) of normalized convergence maps reconstructed from the Subaru Hyper Suprime-Cam (HSC) year 1 shear catalogue, in combination with the power spectrum, to measure the matter clustering amplitude S 8 = σ 8 $\sqrt {Ω_{m}/0.3}$. The large-scale structure’s statistical properties are incompletely described by the traditional two-point statistics, motivating our investigation of the PDF—a complementary higher-order statistic. By defining the PDF over the standard-deviation-normalized convergence map, we are able to isolate the non-Gaussian information. We use tailored simulations to compress the data vector and construct a likelihood approximation. We mitigate the impact of survey and astrophysical systematics with cuts on smoothing scales, redshift bins, and data vectors. We find S 8 = $0.860^{+0.066}_{–0.109}$ from the PDF alone and S 8 = 0.798$^{+0.029}_{–0.042}$ from the combination of the PDF and power spectrum (68% confidential level (CL)). The PDF improves the power-spectrum-only constraint by about 10%.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on compact objects from the Dark Energy Survey 5-yr supernova sample

ABSTRACT Gravitational lensing magnification of Type Ia supernovae (SNe Ia) allows information to be obtained about the distribution of matter on small scales. In this paper, we derive limits on the fraction $\alpha$ of the total matter density in compact objects (which comprise stars, stellar remnants, small stellar groupings, and primordial black holes) of mass M > 0.03 ${\rm M}_{\odot }$ over cosmological distances. Using 1532 SNe Ia from the Dark Energy Survey Year 5 sample (DES-SN5YR) combined with a Bayesian prior for the absolute magnitude M, we obtain α < 0.12 at the 95 per cent confidence level after marginalization over cosmological parameters, lensing due to large-scale structure, and intrinsic non-Gaussianity. Similar results are obtained using priors from the cosmic microwave background, baryon acoustic oscillations, and galaxy weak lensing, indicating our results do not depend on the background cosmology. We argue our constraints are likely to be conservative (in the sense of the values we quote being higher than the truth), but discuss scenarios in which they could be weakened by systematics of the order of $\Delta \alpha \sim 0.04$.

79 ASTRONOMY AND ASTROPHYSICS↗

Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey. II. Anisotropic Large-scale Coherence in Hot Gas, Galaxies, and Dark Matter

Statistics that capture the directional dependence of the baryon distribution in the cosmic web enable unique tests of cosmology and astrophysical feedback. We use constrained oriented stacking of thermal Sunyaev–Zel’dovich (tSZ) maps to measure the anisotropic distribution of hot gas 2.5–40 Mpc away from galaxy clusters embedded in massive filaments and superclusters. The cluster selection and orientation (at a scale of ∼15 Mpc) use Dark Energy Survey (DES) Year 3 data, while expanded tSZ maps from the Atacama Cosmology Telescope Data Release 6 enable a ∼3× more significant measurement of the extended gas compared to the technique’s proof-of-concept. Decomposing stacks into cosine multipoles of order m , we detect a dipole ( m = 1) and quadrupole ( m = 2) at 8σ–10σ, as well as evidence for m = 4 signal at up to 6σ, indicating sensitivity to late-time non-Gaussianity. We compare to Cardinal simulations with spherical gas models pasted onto dark matter halos. The fiducial tSZ data can discriminate between two models that deplete pressure differently in low-mass halos (mimicking astrophysical feedback), preferring higher average pressure in extended structures. However, uncertainty in the amount of cosmic infrared background contamination reduces the constraining power. Additionally, we apply the technique to DES galaxy density and weak lensing to study for the first time their oriented relationships with tSZ. In the tSZ-to-lensing relation, averaged on 7.5 Mpc (transverse) scales, we observe dependence on redshift but not shape or radial distance. Thus, on large scales, the superclustering of gas pressure, galaxies, and total matter is coherent in shape and extent.

79 ASTRONOMY AND ASTROPHYSICS↗

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Abstract Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes,f X NL , with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via theUlagamsuite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs toσ(f NL eq ) ≈ 110,σ(f NL or, lss ) ≈ 120,σ(f NL loc ) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release theUlagamsuite to enable more survey-focused analyses.

Astronomy & Astrophysics↗

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗

Exploring the non-Gaussianity of the cosmic infrared background and its weak gravitational lensing

ABSTRACT Gravitational lensing deflects the paths of photons, altering the statistics of cosmic backgrounds and distorting their information content. We take the cosmic infrared background (CIB), which provides plentiful information about galaxy formation and evolution, as an example to probe the effect of lensing on non-Gaussian statistics. Using the Websky simulations, we first quantify the non-Gaussianity of the CIB, revealing additional detail on top of its well-measured power spectrum. To achieve this, we use needlet-like multipole-band filters to calculate the variance and higher-point correlations. Using our simulations, we show the two-, three- and four-point spectra, and compare our calculated power spectra and bispectra to Planck values. We then lens the CIB, shell-by-shell with corresponding convergence maps, to capture the broad redshift extent of both the CIB and its lensing convergence. The lensing of the CIB changes the three- and four-point functions by a few tens of per cent at large scales, unlike with the power spectrum, which changes by less than two per cent. We expand our analyses to encompass the full intensity probability distribution functions (PDFs) involving all n-point correlations as a function of scale. In particular, we use the relative entropy between lensed and unlensed PDFs to create a spectrum of templates that can allow estimation of lensing. The underlying CIB model is missing the important role of star bursting, which we test by adding a stochastic lognormal term to the intensity distributions. The novel aspects of our filtering and lensing pipeline should prove useful for any radiant background, including line intensity maps.

79 ASTRONOMY AND ASTROPHYSICS↗

Globally optimal interferometry with lossy twin Fock probes

Parity or quadratic spin (e.g., J z 2 ) readouts of a Mach–Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the J z 2 readout is restricted to an o ( N ) occupation imbalance. We show that a method of moments readout of two quadratic spin observables J z 2 and J + 2 + J − 2 is globally optimal for Dicke state probes; i.e., the error saturates the QFI for all θ . In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on TF states, showing that the method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four-mode state | N 4 , N 4 , N 4 , N 4 〉 and its lossy counterparts, showing that an advantage for the estimation of any linear function of the local MZ phases θ 1 and θ 2 (compared to independent probing of the MZ phases by two copies of | N 4 , N 4 〉 ) appears when more than one particle is lost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Beyond the 3rd moment: a practical study of using lensing convergence CDFs for cosmology with DES Y3

ABSTRACT Widefield surveys probe clustered scalar fields – such as galaxy counts, lensing potential, etc. – which are sensitive to different cosmological and astrophysical processes. Constraining such processes depends on the statistics that summarize the field. We explore the cumulative distribution function (CDF) as a summary of the galaxy lensing convergence field. Using a suite of N-body light-cone simulations, we show the CDFs’ constraining power is modestly better than the second and third moments, as CDFs approximately capture information from all moments. We study the practical aspects of applying CDFs to data, using the Dark Energy Survey (DES Y3) data as an example, and compute the impact of different systematics on the CDFs. The contributions from the point spread function and reduced shear approximation are $\lesssim 1~{{\ \rm per\ cent}}$ of the total signal. Source clustering effects and baryon imprints contribute 1–10 per cent. Enforcing scale cuts to limit systematics-driven biases in parameter constraints degrade these constraints a noticeable amount, and this degradation is similar for the CDFs and the moments. We detect correlations between the observed convergence field and the shape noise field at 13σ. The non-Gaussian correlations in the noise field must be modelled accurately to use the CDFs, or other statistics sensitive to all moments, as a rigorous cosmology tool.

79 ASTRONOMY AND ASTROPHYSICS↗

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc -1 by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement of the galaxy-velocity power spectrum of DESI tracers with the kinematic Sunyaev-Zeldovich effect using DESI DR2 and ACT DR6

Joint analyses of high-resolution CMB temperature maps with galaxy surveys provide a unique way to reconstruct the radial velocity field of the underlying matter distribution via the kinematic Sunyaev-Zeldovich (kSZ) effect. Using data from the Atacama Cosmology Telescope (ACT) DR6 and the Dark Energy Spectroscopic Instrument (DESI) DR2, we present radial velocity reconstructions for luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasars (QSOs). Leveraging the spectroscopic data, we are able to reliably model the foreground contamination and report a negligible impact on our main observables. We detect the velocity-galaxy cross-correlation at $17.0σ$ for LRGs, and for the first time, at $8.3σ$ for ELGs and $6.8σ$ for QSOs. We further report the first detection of the velocity-velocity correlation using LRGs at $3.1σ$, as well as the highest cumulative detection of the kSZ effect to date at $20.8 σ$. Similarly to previous results, we find a lower amplitude of the kSZ signal compared to our fiducial halo model prediction and electron profile assuming a Battaglia profile. Combining these new observables, we obtain constraints on local-type primordial non-Gaussianity (PNG): $f_{\rm NL}^{\rm loc} = 15.9_{-34.4}^{+34.6}$ at 68% confidence, which represents the tightest constraint to date derived from the velocity field. The measurements presented here already exhibit lower noise on a per-mode basis than the galaxy auto-correlation on the largest scales, $k<0.004~\rm{Mpc^{-1}}$, highlighting the key role these observables will play in the context of future CMB experiments such as the Simons Observatory.

Chaussidon, Edmond [LBL, Berkeley] (ORCID:00000001↗

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗

Primordial non-Gaussianity with angular correlation function: integral constraint and validation for DES

ABSTRACT Local primordial non-Gaussianity (PNG) is a promising observable of the underlying physics of inflation, characterized by $f_{\rm NL}^{\rm loc}$. We present the methodology to measure $f_{\rm NL}^{\rm loc}$ from the Dark Energy Survey (DES) data using the two-point angular correlation function (ACF) with scale-dependent bias. One of the focuses of the work is the integral constraint (IC). This condition appears when estimating the mean number density of galaxies from the data and is key in obtaining unbiased $f_{\rm NL}^{\rm loc}$ constraints. The methods are analysed for two types of simulations: ∼246 goliat-png N-body small area simulations with fNL equal to −100 and 100, and 1952 Gaussian ice-cola mocks with fNL = 0 that follow the DES angular and redshift distribution. We use the ensemble of goliat-png mocks to show the importance of the IC when measuring PNG, where we recover the fiducial values of fNL within the 1σ when including the IC. In contrast, we found a bias of ΔfNL ∼ 100 when not including it. For a DES-like scenario, we forecast a bias of ΔfNL ∼ 23, equivalent to 1.8σ, when not using the IC for a fiducial value of fNL = 100. We use the ice-cola mocks to validate our analysis in a realistic DES-like set-up finding it robust to different analysis choices: best-fitting estimator, the effect of IC, BAO damping, covariance, and scale choices. We forecast a measurement of fNL within σ(fNL) = 31 when using the DES-Y3 BAO sample, with the ACF in the 1 deg < θ < 20 deg range.

79 ASTRONOMY AND ASTROPHYSICS↗

Signal-preserving CMB component separation with machine learning

Analysis of microwave sky signals, such as the cosmic microwave background, often requires component separation using multifrequency methods, whereby different signals are isolated according to their different frequency behaviors. Many so-called blind methods, such as the internal linear combination (ILC), make minimal assumptions about the spatial distribution of the signal or contaminants, and only assume knowledge of the frequency dependence of the signal. The ILC produces a minimum-variance linear combination of the measured frequency maps. In the case of Gaussian, statistically isotropic fields, this is the optimal linear combination, as the variance is the only statistic of interest. However, in many cases the signal we wish to isolate, or the foregrounds we wish to remove, are non-Gaussian and/or statistically anisotropic (in particular for the case of Galactic foregrounds). In such cases, it is possible that machine learning (ML) techniques can be used to exploit the non-Gaussian features of the foregrounds and thereby improve component separation. However, many ML techniques require the use of complex, difficult-to-interpret operations on the data. We propose a hybrid method whereby we train an ML model using only combinations of the data that , and combine the resulting ML-predicted foreground estimate with the ILC solution to reduce the error from the ILC. We demonstrate our methods on simulations of extragalactic temperature and Galactic polarization foregrounds and show that our ML model can exploit non-Gaussian features, such as point sources and spatially varying spectral indices, to produce lower-variance maps than ILC—e.g., reducing the variance of the B-mode residual by factors of up to 5—while preserving the signal of interest in an unbiased manner. Moreover, we often find improved performance even when applying our ML technique to foreground models on which it was not trained. Published by the American Physical Society 2025

McCarthy, Fiona (ORCID:0000000253893565)↗

Evaluating generative networks using Gaussian mixtures of image features

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fréchet Inception Distance (FID). However, FID assumes that images featurized using the penultimate layer of Inception follow a Gaussian distribution. This assumption allows FID to be easily computed, since FID uses the 2-Wasserstein distance of two Gaussian distributions fitted to the featurized images. However, we show that Inception features of the ImageNet dataset are not Gaussian; in particular, each marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using inception (or another classifier) to featurize the images, estimate two GMMs, and use the restricted 2-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to image perturbations. By modelling the non-Gaussian features obtained from inception as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.

machine learning, genrative adversarial networks↗