arXiv subjects

Austin Hoag

Publications and source records attributed to Austin Hoag.

At least 19 recordsLinked to original sources

arXiv2026

Yes, But Not Always. Generative AI Needs Nuanced Opt-in

This paper argues that a one-size-fits-all approach to specifying consent for the use of creative works in generative AI is insufficient. Real-world ownership and rights holder structures, the imitation of artistic styles and likeness, and the limitless contexts of use of AI outputs make the status quo of binary consent with opt-in by default untenable. To move beyond the current impasse, we consider levers of control in generative AI workflows at training, inference, and dissemination. Based on these insights, we position inference-time opt-in as an overlooked opportunity for nuanced consent verification. We conceptualize nuanced consent conditions for opt-in and propose an agent-based inference-time opt-in architecture to verify if user intent requests meet conditional consent granted by rights holders. In a case study for music, we demonstrate that nuanced opt-in at inference can account for established rights and re-establish a balance of power between rights holders and AI developers.

cs.CY↗

arXiv2025

Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference

Representation learning is increasingly applied to generate representations that generalize well across multiple downstream tasks. Ensuring fairness guarantees in representation learning is crucial to prevent unfairness toward specific demographic groups in downstream tasks. In this work, we formally introduce the task of learning representations that achieve high-confidence fairness. We aim to guarantee that demographic disparity in every downstream prediction remains bounded by a *user-defined* error threshold $\epsilon$, with *controllable* high probability. To this end, we propose the ***F**air **R**epresentation learning with high-confidence **G**uarantees (FRG)* framework, which provides these high-confidence fairness guarantees by leveraging an optimized adversarial model. We empirically evaluate FRG on three real-world datasets, comparing its performance to six state-of-the-art fair representation learning methods. Our results demonstrate that FRG consistently bounds unfairness across a range of downstream models and tasks.

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arXiv2025

Reinforcement Learning from Human Feedback with High-Confidence Safety Constraints

Existing approaches to language model alignment often treat safety as a tradeoff against helpfulness, which can lead to unacceptable responses in sensitive domains. To ensure reliable performance in such settings, we propose High-Confidence Safe Reinforcement Learning from Human Feedback (HC-RLHF), a method that provides high-confidence safety guarantees while maximizing helpfulness. Similar to previous methods, HC-RLHF explicitly decouples human preferences into helpfulness and harmlessness (safety), which are learned by training a reward model and a cost model, respectively. It then employs a two-step process to find safe solutions. In the first step, it optimizes the reward function under an intentionally pessimistic version of the cost constraint. In the second step, the trained model undergoes a safety test to verify whether its performance stays within an upper-confidence bound of the actual cost constraint. We provide a theoretical analysis of HC-RLHF, including proof that it will not return an unsafe solution with a probability greater than a user-specified threshold. For our empirical analysis, we apply HC-RLHF to align three different language models (Qwen2-1.5B, Qwen2.5-3B, and LLaMa3.2-3B) with human preferences. Our results demonstrate that HC-RLHF produces safe models with high probability and can improve harmlessness and helpfulness compared to previous methods.

cs.LG↗

arXiv2023

Learning Fair Representations with High-Confidence Guarantees

Representation learning is increasingly employed to generate representations that are predictive across multiple downstream tasks. The development of representation learning algorithms that provide strong fairness guarantees is thus important because it can prevent unfairness towards disadvantaged groups for all downstream prediction tasks. To prevent unfairness towards disadvantaged groups in all downstream tasks, it is crucial to provide representation learning algorithms that provide fairness guarantees. In this paper, we formally define the problem of learning representations that are fair with high confidence. We then introduce the Fair Representation learning with high-confidence Guarantees (FRG) framework, which provides high-confidence guarantees for limiting unfairness across all downstream models and tasks, with user-defined upper bounds. After proving that FRG ensures fairness for all downstream models and tasks with high probability, we present empirical evaluations that demonstrate FRG's effectiveness at upper bounding unfairness for multiple downstream models and tasks.

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arXiv2020

Spectroscopically Confirmed Lyman-Alpha Emitters from Redshift 5 to 7 Behind Ten Galaxy Cluster Lenses

We present 36 spectroscopically confirmed intrinsically UV-faint Ly$\alpha$ emitting galaxies from follow-up observations with Keck/DEIMOS of gravitationally lensed high-redshift candidates. Candidates were selected to be between $5\lesssim z \lesssim 7$ from photometric data using \textit{HST} and \textit{Spitzer} imaging surveys. We used photometric redshift information to perform an integrated photometric redshift probability cut $>1\%$ between $5 $25{\AA} at $3\sigma$ at the fiducial depth of our survey, and only those galaxies with EW(Ly$\alpha$)$>$25{\AA} as true LAEs, and finally, only objects with $m_{AB}<26.8$, we found the LAE fraction to be flat, or modestly increase from 0.26$\pm0.04$ to 0.30$\pm0.04$. These values relative to those for lower-redshift samples are consistent with a rising LAE fraction with redshift out to $z\sim6$, but at $z\sim6.5$ there is some tension between our results and results from surveys at intrinsically brighter luminosities. We conclude intrinsically fainter galaxies have Ly$\alpha$ emission, and there is a steep drop in the LAE fraction from our high-redshift sample at $z\sim6.5$ and from similar galaxies at $z\sim7.5$. This likely indicates we are witnessing the tail end of the epoch of reionization, as such a drop is not expected due to changes of intrinsic galaxy properties between these redshifts.

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arXiv2019

Prospects for extending the Mass-Metallicity Relation to low mass at high redshift: a case study at z~1

We report J-band MOSFIRE spectroscopy of a low-mass (log$(M_*/M_\odot)=8.62^{+0.10}_{-0.06}$) star-forming galaxy at $z=0.997$ showing the detection of [NII] and [SII] alongside a strong H$\alpha$ line. We derive a gas-phase metallicity of log$(\text{O}/\text{H})=7.99^{+0.13}_{-0.23}$, placing this object in a region of $M_* - Z$ space that is sparsely populated at this redshift. Furthermore, many existing metallicity measurements in this $M_* - z$ regime are derived from only [NII]/H$\alpha$ (N2), a diagnostic widely used in high-redshift metallicity studies despite the known strong degeneracy with the ionization parameter and resulting large systematic uncertainty. We demonstrate that even in a regime where [NII] and [SII] are at the detection limit and the measurement uncertainty associated with the [NII]/[SII] ratio is high (S/N~3), the more sophisticated Dopita et al. diagnostic provides an improved constraint compared to N2 by reducing the systematic uncertainty due to the ionization parameter. This approach does not, however, dispel uncertainty associated with stochastic or systematic variations in the nitrogen-to-oxygen abundance ratio. While this approach improves upon N2, future progress in extending metallicity studies into this low-mass regime will require larger samples to allow for stochastic variations, as well as careful consideration of the global trends among dwarf galaxies in all physical parameters, not just metallicity.

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arXiv2019

Hubble Frontier Field Photometric Catalogues of Abell 370 and RXC J2248.7-4431: Multiwavelength photometry, photometric redshifts, and stellar properties

This paper presents multiwavelength photometric catalogues of the last two Hubble Frontier Fields (HFF), the massive galaxy clusters Abell 370 and RXC J2248.7-4431. The photometry ranges from imaging performed on the Hubble Space Telescope (HST) to ground based Very Large Telescope (VLT) and Spitzer/IRAC, in collaboration with the ASTRODEEP team, and using the ASTRODEEP pipeline. While the main purpose of this paper is to release the catalogues, we also perform, as a proof of concept, a brief analysis of z > 6 objects selected using drop-out method, as well as spectroscopically confirmed sources and multiple images in both clusters. While dropout methods yield a sample of high-z galaxies, the addition of longer wavelength data reveals that as expected the samples have substantial contamination at the ~30-45% level by dusty galaxies at lower redshifts. Furthermore, we show that spectroscopic redshifts are still required to unambiguously determine redshifts of multiply imaged systems. Finally, the now publicly available ASTRODEEP catalogues were combined for all HFFs and used to explore stellar properties of a large sample of 20,000 galaxies across a large photometric redshift range. The powerful magnification provided by the HFF clusters allows us an exploration of the properties of galaxies with intrinsic stellar masses as low as $M_* \gtrsim 10^7M_{\odot}$ and intrinsic star formation rates $\mbox{SFRs}\sim 0.1\mbox{-}1M_\odot/\mbox yr$ at z > 6.

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arXiv2019

Stellar Properties of z ~ 8 Galaxies in the Reionization Lensing Cluster Survey

Measurements of stellar properties of galaxies when the universe was less than one billion years old yield some of the only observational constraints of the onset of star formation. We present here the inclusion of \textit{Spitzer}/IRAC imaging in the spectral energy distribution fitting of the seven highest-redshift galaxy candidates selected from the \emph{Hubble Space Telescope} imaging of the Reionization Lensing Cluster Survey (RELICS). We find that for 6/8 \textit{HST}-selected $z\gtrsim8$ sources, the $z\gtrsim8$ solutions are still strongly preferred over $z\sim$1-2 solutions after the inclusion of \textit{Spitzer} fluxes, and two prefer a $z\sim 7$ solution, which we defer to a later analysis. We find a wide range of intrinsic stellar masses ($5\times10^6 M_{\odot}$ -- $4\times10^9$ $M_{\odot}$), star formation rates (0.2-14 $M_{\odot}\rm yr^{-1}$), and ages (30-600 Myr) among our sample. Of particular interest is Abell1763-1434, which shows evidence of an evolved stellar population at $z\sim8$, implying its first generation of star formation occurred just $< 100$ Myr after the Big Bang. SPT0615-JD, a spatially resolved $z\sim10$ candidate, remains at its high redshift, supported by deep \textit{Spitzer}/IRAC data, and also shows some evidence for an evolved stellar population. Even with the lensed, bright apparent magnitudes of these $z \gtrsim 8$ candidates (H = 26.1-27.8 AB mag), only the \textit{James Webb Space Telescope} will be able further confirm the presence of evolved stellar populations early in the universe.

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arXiv2019

Inferences on the Timeline of Reionization at z~8 From the KMOS Lens-Amplified Spectroscopic Survey

Detections and non-detections of Lyman alpha (Ly$\alpha$) emission from $z>6$ galaxies ($<1$ Gyr after the Big Bang) can be used to measure the timeline of cosmic reionization. Of key interest to measuring reionization's mid-stages, but also increasing observational challenge, are observations at z > 7, where Ly$\alpha$ redshifts to near infra-red wavelengths. Here we present a search for z > 7.2 Ly$\alpha$ emission in 53 intrinsically faint Lyman Break Galaxy candidates, gravitationally lensed by massive galaxy clusters, in the KMOS Lens-Amplified Spectroscopic Survey (KLASS). With integration times of ~7-10 hours, we detect no Ly$\alpha$ emission with S/N>5 in our sample. We determine our observations to be 80% complete for 5$\sigma$ spatially and spectrally unresolved emission lines with integrated line flux $>5.7\times10^{-18}$ erg s$^{-1}$ cm$^{-2}$. We define a photometrically selected sub-sample of 29 targets at $z=7.9\pm0.6$, with a median 5$\sigma$ Ly$\alpha$ EW limit of 58A. We perform a Bayesian inference of the average intergalactic medium (IGM) neutral hydrogen fraction using their spectra. Our inference accounts for the wavelength sensitivity and incomplete redshift coverage of our observations, and the photometric redshift probability distribution of each target. These observations, combined with samples from the literature, enable us to place a lower limit on the average IGM neutral hydrogen fraction of $> 0.76 \; (68\%), \; > 0.46 \; (95\%)$ at z ~ 8, providing further evidence of rapid reionization at z~6-8. We show that this is consistent with reionization history models extending the galaxy luminosity function to $M_\textrm{UV} \lesssim -12$, with low ionizing photon escape fractions, $f_\textrm{esc} \lesssim 15\%$.

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arXiv2019

Constraining the neutral fraction of hydrogen in the IGM at redshift 7.5

We present a large spectroscopic campaign with Keck/MOSFIRE targeting Lyman-alpha emission (Ly$\alpha$) from intrinsically faint Lyman-break Galaxies (LBGs) behind 12 efficient galaxy cluster lenses. Gravitational lensing allows us to probe the more abundant faint galaxy population to sensitive Ly$\alpha$ equivalent width limits. During the campaign we targeted 70 LBG candidates with MOSFIRE Y-band, selected photometrically to cover Ly$\alpha$ over the range $7 5$ emission lines in 2 of these galaxies and find that they are likely Ly$\alpha$ at $z=7.148\pm0.001$ and $z=7.161\pm0.001$. We present new lens models for 4 of the galaxy clusters, using our previously published lens models for the remaining clusters to determine the magnification factors for the source galaxies. Using a Bayesian framework that employs large scale reionization simulations of the intergalactic medium (IGM) as well as realistic properties of the interstellar medium and circumgalactic medium, we infer the volume-averaged neutral hydrogen fraction, $\overline{x}_{\mathrm{HI}}$, in the IGM during reionization to be $\overline{x}_{\mathrm{HI}}=0.88^{+0.05}_{-0.10}$ at $z=7.6\pm0.6$. Our result is consistent with a late and rapid reionization scenario inferred by Planck.

astro-ph.GA↗

arXiv2018

The OSIRIS Lens-Amplified Survey (OLAS) I: Dynamical Effects of Stellar Feedback in Low Mass Galaxies at z ~ 2

We introduce the OSIRIS Lens-Amplified Survey (OLAS), a kinematic survey of gravitationally lensed galaxies at cosmic noon taken with Keck adaptive optics. In this paper we present spatially resolved spectroscopy and nebular emission kinematic maps for 17 star forming galaxies with stellar masses 8 < log($M_*$/$M_{\odot}$) < 9.8 and redshifts 1.2 < z < 2.3. OLAS is designed to probe the stellar mass ($M_*$) and specific star formation rate (sSFR) range where simulations suggest that stellar feedback is most effective at driving gaseous outflows that create galaxy-wide potential fluctuations which can generate dark matter cores. We compare our kinematic data with the trend between sSFR, $M_*$ and H$\alpha$ velocity dispersion, $\sigma$, from the Feedback In Realistic Environments (FIRE) simulations. Our observations reveal a correlation between sSFR and sigma at fixed $M_*$ that is similar to the trend predicted by simulations: feedback from star formation drives star-forming gas and newly formed stars into more dispersion dominated orbits. The observed magnitude of this effect is in good agreement with the FIRE simulations, in which feedback alters the central density profiles of low mass galaxies, converting dark matter cusps into cores over time. Our data support the scenario that stellar feedback drives gaseous outflows and potential fluctuations, which in turn drive dark matter core formation in dwarf galaxies.

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arXiv2018

Mass Modeling of Frontier Fields Cluster MACS J1149.5+2223 Using Strong and Weak Lensing

We present a gravitational lensing model of MACS J1149.5+2223 using ultra-deep Hubble Frontier Fields imaging data and spectroscopic redshifts from HST grism and VLT/MUSE spectroscopic data. We create total mass maps using 38 multiple images (13 sources) and 608 weak lensing galaxies, as well as 100 multiple images of 31 star-forming regions in the galaxy that hosts Supernova Refsdal. We find good agreement with a range of recent models within the HST field of view. We present a map of the ratio of projected stellar mass to total mass ($f_{\star}$), and find that the stellar mass fraction for this cluster peaks on the primary BCG. Averaging within a radius of 0.3 Mpc, we obtain a value of $\langle f_{\star} \rangle = 0.012^{+0.004}_{-0.003}$, consistent with other recent results for this ratio in cluster environments, though with a large global error (up to $\delta f_{\star} = 0.005$) primarily due to the choice of an IMF. We compare values of $f_{\star}$ and measures of star formation efficiency for this cluster to other Hubble Frontier Fields clusters studied in the literature, finding that MACS1149 has a higher stellar mass fraction than these other clusters, but a star formation efficiency typical of massive clusters.

astro-ph.GA↗

arXiv2018

Mass and Light of Abell 370: A Strong and Weak Lensing Analysis

We present a new gravitational lens model of the Hubble Frontier Fields cluster Abell 370 ($z = 0.375$) using imaging and spectroscopy from Hubble Space Telescope and ground-based spectroscopy. We combine constraints from a catalog of 1344 weakly lensed galaxies and 39 multiply-imaged sources comprised of 114 multiple images, including a system of multiply-imaged candidates at $z=7.93 \pm 0.02$, to obtain a best-fit mass distribution using the cluster lens modeling code Strong and Weak Lensing United. As the only analysis of A370 using strong and weak lensing constraints from Hubble Frontier Fields data, our method provides an independent check on assumptions in other methods on the mass distribution. Convergence, shear, and magnification maps are made publicly available through the HFF website. We find that the model we produce is similar to models produced by other groups, with some exceptions due to the differences in lensing code methodology. In an effort to study how our total projected mass distribution traces light, we measure the stellar mass density distribution using Spitzer/Infrared Array Camera imaging. Comparing our total mass density to our stellar mass density in a radius of 0.3 Mpc, we find a mean projected stellar to total mass ratio of $\langle f* \rangle = 0.011 \pm 0.003$ (stat.) using the diet Salpeter initial mass function. This value is in general agreement with independent measurements of $\langle f* \rangle$ in clusters of similar total mass and redshift.

astro-ph.GA↗

arXiv2018

A Candidate $z\sim10$ Galaxy Strongly Lensed into a Spatially Resolved Arc

The most distant galaxies known are at z~10-11, observed 400-500 Myr after the Big Bang. The few z~10-11 candidates discovered to date have been exceptionally small- barely resolved, if at all, by the Hubble Space Telescope. Here we present the discovery of SPT0615-JD, a fortuitous z~10 (z_phot=9.9+/-0.6) galaxy candidate stretched into an arc over ~2.5" by the effects of strong gravitational lensing. Discovered in the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury program and companion S-RELICS Spitzer program, this candidate has a lensed H-band magnitude of 25.7+/-0.1 AB mag. With a magnification of \mu~4-7 estimated from our lens models, the de-lensed intrinsic magnitude is 27.6+/-0.3 AB mag, and the half-light radius is r_e<0.8 kpc, both consistent with other z>9 candidates. The inferred stellar mass (log [M* /M_Sun]=9.7^{+0.7}_{-0.5}) and star formation rate (\log [SFR/M_Sun yr^{-1}]=1.3^{+0.2}_{-0.3}) indicate that this candidate is a typical star-forming galaxy on the z>6 SFR-M* relation. We note that three independent lens models predict two counterimages, at least one of which should be of a similar magnitude to the arc, but these counterimages are not yet detected. Counterimages would not be expected if the arc were at lower redshift. However, the only spectral energy distributions capable of fitting the Hubble and Spitzer photometry well at lower redshifts require unphysical combinations of z~2 galaxy properties. The unprecedented lensed size of this z~10 candidate offers the potential for the James Webb Space Telescope to study the geometric and kinematic properties of a galaxy observed 500 Myr after the Big Bang.

astro-ph.GA↗

arXiv2017

Precise weak lensing constraints from deep high-resolution $K_\mathrm{s}$ images: VLT/HAWK-I analysis of the super-massive galaxy cluster RCS2$J$232727.7$-$020437 at $z=0.70$

We demonstrate that deep good-seeing VLT/HAWK-I $K_\mathrm{s}$ images complemented with $g$+$z$-band photometry can yield a sensitivity for weak lensing studies of massive galaxy clusters at redshifts \mbox{$0.7\lesssim z \lesssim 1.1$}, which is almost identical to the sensitivity of HST/ACS mosaics of single-orbit depth. Key reasons for this good performance are the excellent image quality frequently achievable for $K_\mathrm{s}$ imaging from the ground, a highly effective photometric selection of background galaxies, and a galaxy ellipticity dispersion that is noticeably lower than for optically observed high-redshift galaxy samples. Incorporating results from the 3D-HST and UltraVISTA surveys we also obtained a more accurate calibration of the source redshift distribution than previously achieved for similar optical weak lensing data sets. Here we studied the extremely massive galaxy cluster RCS2$J$232727.7$-$020437 (\mbox{$z=0.699$}), combining deep VLT/\mbox{HAWK-I} $K_\mathrm{s}$ images (point spread function with a 0\farcs35 full width at half maximum) with LBT/LBC photometry. The resulting weak lensing mass reconstruction suggests that the cluster consists of a single overdensity, which is detected with a peak significance of $10.1\sigma$. We constrained the cluster mass to \mbox{$M_\mathrm{200c}/(10^{15} \mathrm{M}_\odot) =2.06^{+0.28}_{-0.26}(\mathrm{stat.})\pm 0.12 (\mathrm{sys.})$} assuming a spherical Navarro, Frenk \& White model and simulation-based priors on the concentration, making it one of the most massive galaxy clusters known in the \mbox{$z\gtrsim 0.7$} Universe. We also cross-checked the HAWK-I measurements through an analysis of overlapping HST/ACS images, yielding fully consistent estimates of the lensing signal.

astro-ph.CO↗

arXiv2017

The Reionization Lensing Cluster Survey (RELICS) and the Brightest High-z Galaxies

Massive foreground galaxy clusters magnify and distort the light of objects behind them, permitting a view into both the extremely distant and intrinsically faint galaxy populations. We present here the z ~ 6 - 8 candidate high-redshift galaxies from the Reionization Lensing Cluster Survey (RELICS), a Hubble and Spitzer Space Telescope survey of 41 massive galaxy clusters spanning an area of ~200 arcmin^2. These clusters were selected to be excellent lenses and we find similar high-redshift sample sizes and magnitude distributions as CLASH. We discover 321 candidate galaxies with photometric redshifts between z ~ 6 to z ~ 8, including extremely bright objects with H-band magnitudes of m_AB ~ 23 mag. As a sample, the observed (lensed) magnitudes of these galaxies are among the brightest known at z> 6, comparable to much wider, blank-field surveys. RELICS demonstrates the efficiency of using strong gravitational lenses to produce high-redshift samples in the epoch of reionization. These brightly observed galaxies are excellent targets for follow-up study with current and future observatories, including the James Webb Space Telescope.

astro-ph.GA↗

arXiv2017

HST Grism Observations of a Gravitationally Lensed Redshift 10 Galaxy

We present deep spectroscopic observations of a Lyman-break galaxy candidate (hereafter MACS1149-JD) at $z\sim9.5$ with the $\textit{Hubble}$ Space Telescope ($\textit{HST}$) WFC3/IR grisms. The grism observations were taken at 4 distinct position angles, totaling 34 orbits with the G141 grism, although only 19 of the orbits are relatively uncontaminated along the trace of MACS1149-JD. We fit a 3-parameter ($z$, F160W mag, and Ly$\alpha$ equivalent width) Lyman-break galaxy template to the three least contaminated grism position angles using an MCMC approach. The grism data alone are best fit with a redshift of $z_{\mathrm{grism}}=9.53^{+0.39}_{-0.60}$ ($68\%$ confidence), in good agreement with our photometric estimate of $z_{\mathrm{phot}}=9.51^{+0.06}_{-0.12}$ ($68\%$ confidence). Our analysis rules out Lyman-alpha emission from MACS1149-JD above a $3\sigma$ equivalent width of 21 \AA{}, consistent with a highly neutral IGM. We explore a scenario where the red $\textit{Spitzer}$/IRAC $[3.6] - [4.5]$ color of the galaxy previously pointed out in the literature is due to strong rest-frame optical emission lines from a very young stellar population rather than a 4000 \AA{} break. We find that while this can provide an explanation for the observed IRAC color, it requires a lower redshift ($z\lesssim9.1$), which is less preferred by the $\textit{HST}$ imaging data. The grism data are consistent with both scenarios, indicating that the red IRAC color can still be explained by a 4000 \AA{} break, characteristic of a relatively evolved stellar population. In this interpretation, the photometry indicate that a $340^{+29}_{-35}$ Myr stellar population is already present in this galaxy only $\sim500~\mathrm{Myr}$ after the Big Bang.

astro-ph.GA↗

arXiv2017

Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionization

Within one billion years of the Big Bang, intergalactic hydrogen was ionized by sources emitting ultraviolet and higher energy photons. This was the final phenomenon to globally affect all the baryons (visible matter) in the Universe. It is referred to as cosmic reionization and is an integral component of cosmology. It is broadly expected that intrinsically faint galaxies were the primary ionizing sources due to their abundance in this epoch. However, at the highest redshifts ($z>7.5$; lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations to date are intrinsically bright and, therefore, not necessarily representative of the general population. Here, we report the unequivocal spectroscopic detection of a low luminosity galaxy at $z>7.5$. We detected the Lyman-$\alpha$ emission line at $\sim 10504$ {\AA} in two separate observations with MOSFIRE on the Keck I Telescope and independently with the Hubble Space Telescope's slit-less grism spectrograph, implying a source redshift of $z = 7.640 \pm 0.001$. The galaxy is gravitationally magnified by the massive galaxy cluster MACS J1423.8+2404 ($z = 0.545$), with an estimated intrinsic luminosity of $M_{AB} = -19.6 \pm 0.2$ mag and a stellar mass of $M_{\star} = 3.0^{+1.5}_{-0.8} \times 10^8$ solar masses. Both are an order of magnitude lower than the four other Lyman-$\alpha$ emitters currently known at $z > 7.5$, making it probably the most distant representative source of reionization found to date.

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