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EncoTESS: Age-Sensitive Encodings from Raw TESS Light Curves

Phil R. Van-Lane, Joshua S. Speagle, Ryan Cloutier, Christopher A. Theissen, Gwendolyn M. Eadie, Ilay Kamai

arXiv:2608.25019v1astro-ph.SRastro-ph.GAastro-ph.IMcs.LG

TL;DR

Ages of late-F-to-M main-sequence stars are difficult to estimate, motivating investigation of photometric variability as an age diagnostic. EncoTESS learns representations of TESS light curves through self-supervised training. Its encodings correlate most strongly with variability amplitude, while its first principal component correlates significantly with age despite not being designed as an age diagnostic.

  • Problem

    Ages of late-F-to-M main-sequence stars are difficult to estimate using other methods, motivating investigation of photometric variability as an age diagnostic.

    Source: §1 · p. 2

  • Method

    EncoTESS encodes TESS light curves using a self-supervised time-series foundation model trained to learn generalized time-series patterns.

    Source: §1 · p. 2

  • Results

    Variability amplitude correlates most strongly with EncoTESS encodings, while the first principal component correlates significantly with age despite not being designed as an age diagnostic.

    Source: §6.2 · p. 16

  • Takeaways & Limitations

    The encodings could support variability classification and searches for candidate members of known distinct stellar populations.

    Source: §9.2 · p. 25

    ≈0.4 dex is the typical width of EncoTESS age posteriors, and the authors recommend adding 0.08 dex of systematic error to reported ages.

    Source: §9.1 · p. 25

Abstract

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Main sequence stars of spectral types late F through M exhibit systematic variability in photometric light curves, particularly when they are young. Rotational modulation of starspots manifests as quasi-sinusoidal variability, which enables the measurement of rotation periods. Variability can also be stochastic, as in stellar flaring. However, since measurements of stochastic processes depend on the time of observation, they are typically noisier. Considering that different manifestations of variability have unique observational nuances, models that naturally unify these are incredibly useful for stellar characterization. Towards this goal, we have developed EncoTESS: a Time Series Foundation Model (TSFM) trained on a subset of TESS 2-min light curves. EncoTESS is specifically designed to handle the observational noise, heteroskedastic measurements, irregular sampling, and large data gaps common to TESS data. It is also ~1% of the size of a typical literature TSFM, so can be run easily on a modern laptop. EncoTESS encodes light curves into a fixed-size latent parameter space, which can be used to infer physical stellar properties and recovers light curve summary statistics well. EncoTESS outperforms rotation period and variability amplitude as age indicators for stars that have not converged onto the slow rotator sequence yet; broadly these include K and M stars less than ~100 Myr, and M stars less than ~1 Gyr. We focus on age inference as an application of EncoTESS in this work, but other downstream tasks such as stellar classification could also be explored. The architecture of EncoTESS enables its future extension to TESS light curves of all cadences, and additional surveys such as Kepler and the upcoming PLATO mission. The core EncoTESS framework and library of encodings produced for the stars used in this work are publicly available at https://github.com/philvanlane/encotess.

1. INTRODUCTION

EncoTESS encodes TESS light curves using a self-supervised time-series foundation model designed for noisy, irregular observations and efficient consumer-hardware execution. The introduction reports improved age inference over models using only rotation period and/or variability amplitude.

1. INTRODUCTION

  • Magnetically driven brightness variability offers age information for late-F–M main-sequence stars, whose ages are difficult to constrain using conventional methods.Minimal main-sequence color–magnitude evolution complicates isochrone fitting, and weaker oscillation amplitudes hinder asteroseismology toward cooler stars. Lithium depletion becomes less reliable for stars ≳1 Gyr.Source: §1 · p. 2
  • Gyrochronology performs reasonably well for converged FGK slow rotators, but young-star scatter and multimodal M-dwarf spindown motivate additional light-curve age indicators.Empirical gyrochronology models estimate ages probabilistically from Prot and mass or a mass proxy; the youngest, reddest stars remain particularly challenging.Source: §1 · p. 2
  • Flaring and photometric activity provide additional age information, but stochastic flares require impractically long observing baselines to constrain individual-star rates.S. Mathur et al. (2023) found that the photometric magnetic activity index Sph correlates with age. S. Messina (2021) showed that variability amplitude adds age information among stars with similar colors and Prot.Source: §1 · p. 2
  • Correlated, measurement-dependent summary statistics discard light-curve information, motivating a holistic, data-driven approach instead of analytically combining handpicked features.Different rotation-period estimators introduce their own uncertainties, while reducing an entire light curve to any single statistic inherently loses information.Source: §1 · p. 2
  • ≈10× noisier photometry and ≈27-day sector viewing periods motivate training directly on TESS rather than transferring Kepler-trained models.TESS’s all-sky coverage provides many more M dwarfs, which are especially difficult to date using Prot, whereas Kepler sampled a small sky region.Source: §1 · p. 3
  • EncoTESS adopts an RNN-based approach for efficient consumer-hardware execution while targeting irregular, heteroskedastic observations, variable sequence lengths, and different temporal resolutions.Sampling flexibility is needed to accommodate approximately one-day downlink gaps in each TESS sector and support extension to other cadences.Source: §1 · p. 3
  • Existing TESS models restrict temporal context or variability selection and omit flux measurement uncertainties, motivating a new model.D. Poznanski (2026) segments light curves into 4096-point, approximately six-day intervals, ignores small gaps, and detrends away potentially informative slow variability. J. Ding et al. (2026)’s gap-aware, multicadence StarCLR fixes sequences at 8192 points and pretrains only on light curves with prior periodogram evidence of periodicity.Source: §1 · p. 3
  • EncoTESS outperforms age-inference models using only Prot and/or variability amplitude, learning generalized light-curve patterns through self-supervision.The paper also investigates light-curve reconstruction, correlations between encodings and physical properties, recovery of traditional summary statistics, and field-star age prediction.Source: §1 · pp. 2–3

2. DATA

EncoTESS uses literature-selected, 2-minute TESS light curves from exoplanet hosts, thick-disk stars, and variable or age-calibrated FGKM main-sequence stars. Its inputs combine normalized photometry, observational metadata, and Gaia-based stellar measurements.

2. DATA

  • 69,345 light curves from TESS sectors 1–101 represent 21,507 unique stars in the final dataset.Overlapping literature sources were de-duplicated. The analysis uses 2-minute TESS PDCSAP flux measurements, although the architecture supports future use of other cadences without redesign.Source: §2 · pp. 3–4, Table 1 · p. 4
  • The dataset’s color distribution is bimodal, with exoplanet hosts and thick-disk stars peaking near (BP −RP)0 ≈1 and other FGKM calibrators near ≈3.The first peak is sharp, whereas the second is broader.Source: Figure 1 · p. 4, §2 · p. 4
  • Target selection combines exoplanet hosts, thick-disk stars, and FGKM main-sequence stars exhibiting variability or having independently calibrated ages.Thick-disk targets bolster field-age training coverage; FGKM calibrators include cluster and association members, active or rotating nearby M dwarfs, and M dwarfs in wide binaries. Exoplanet records require the default flag, a TIC ID with 2-minute light curves, and a populated Gaia DR3 ID.Source: §2 · pp. 3–4

2.1. Light Curve Preprocessing

  • Preprocessing filters unreliable measurements, retains flux, uncertainty, and time, and normalizes each light curve to median zero and half-interquartile range one.Lightkurve applies the default quality bitmask; missing uncertainties receive the light curve’s median uncertainty, and times start at zero. Median-based normalization avoids the sensitivity of mean-and-standard-deviation normalization to extreme sector-edge outliers.Source: §2.1 · p. 4

2.2. TESS and Light Curve Metadata

  • Seven metadata inputs capture target brightness, observing configuration, flux normalization, and cadence to help distinguish astrophysical variability from noise and instrumental effects.Inputs are TESS magnitude, sector, camera, CCD, fmed, fH, and cadence; fmed and fH track activity while also correlating with noise and systematics. Cadence is uniformly 120 seconds here but is retained for future extensions.Source: §2.2 · p. 5

2.3. Gaia Crossmatch

  • Gaia crossmatching excludes stars lacking parallax or G, BP, or RP measurements and supplies de-reddened magnitude, color, parallax, and their uncertainties.Parallaxes receive zeropoint corrections following L. Lindegren et al. (2021); de-reddening uses G. Edenhofer et al. (2024), supplemented by G. M. Green et al. (2019) outside its coverage. Distance sampling uses C. A. L. Bailer-Jones et al. (2021) where possible and parallax otherwise, differing from P. R. Van-Lane et al. (2025).Source: §2.3 · p. 5

3. MODEL ARCHITECTURE

EncoTESS is a compact recurrent foundation model trained through self-supervised flux reconstruction to learn task-independent stellar representations. It processes timestamps explicitly, combines forward and backward context, and produces fixed-size encodings for downstream analysis.

3.1. Input Data

  • 13 metadata features accompany timestamp, flux, and uncertainty channels, with time treated explicitly to distinguish gaps from abrupt flux changes and support different cadences.The normalized time-series matrix has shape 3 x L. Adding power spectra and autocorrelation functions as input channels did not improve benchmark performance.Source: §3.1 · pp. 5, 7, Figure 2 · p. 6

3.2. Recurrent Neural Network Architecture

  • O(L) computational scaling, variable-length inputs, and fewer parameters motivate choosing RNNs over transformers for long, densely sampled light curves.State-space models (e.g., A. Gu & T. Dao 2023) offer similar computational costs and more hardware-efficient training. EncoTESS nevertheless uses the simpler RNN approach, leaving an SSM implementation for possible future work.Source: §3.2 · p. 7
  • ≈64,000 parameters make EncoTESS substantially smaller than typical time-series foundation models, which have at least O(10^6) parameters.It implements the parallel-processing minGRU architecture developed by L. Feng et al. (2024). Its task-independent design could support spectral classification and other stellar-property inference beyond age estimation.Source: §3 · p. 5, §3.2 · p. 7

3.3. Training Procedure

  • 2-minute to 4-day prediction horizons train EncoTESS through unlabeled flux reconstruction, while light-curve and metadata masking encourages robustness to missing data.A Conditional Normalizing Flow estimates full probabilistic flux likelihoods rather than a point estimate with Gaussian uncertainty.Source: §3.3 · p. 7

3.4. Model Output

  • 1536-dimensional light-curve encodings aggregate bidirectional hidden states through 12 pooling operations, converting variable-length representations into fixed-size downstream inputs.Each observation combines 64-dimensional forward and backward states into a 128-dimensional representation of surrounding light-curve context and metadata. Encoding uses all observations and metadata, without the masking applied during training.Source: §3.1 · p. 6, §3.2 · p. 7, §3.4 · p. 8
  • 44% of encoding variance lies in PC1; PCA concentrates variance in early components, while supervised PLS concentrates age-relevant information in three components.TwoNN (E. Facco et al. 2017) estimates an intrinsic dimensionality of 13, indicating substantial redundancy. PCA (H. Hotelling 1932) commonly retains 4, 8, or 16 components; UMAP (L. McInnes et al. 2018b) provides two-dimensional visualization without quantitative analysis; PLS maximizes covariance with age.Source: §3.4 · p. 8

4. FLUX RECONSTRUCTION

EncoTESS reconstructs unobserved light-curve flux with better likelihood-based performance than windowed averaging and an MLP, despite median accuracy comparable to the MLP’s. Longer prediction horizons and larger measurement errors reduce prediction confidence.

4.1. Context Effects

  • 0.5-hour predictions track variability more confidently than 17-hour predictions, which drift toward the light curve’s long-term median.Prediction horizons separate the target time from the available observations and are applied in both forward and backward directions.Source: §4.1 · p. 8, Figure 3 · p. 9
  • Prediction uncertainty has a learned noise floor; above it, larger measurement errors widen predictive distributions and shift their medians toward the overall light-curve median.Tests scaled the real measurement uncertainty from 0.3× to 3× in the CNF prediction head; uncertainty increased overall, though not symmetrically at every point.Source: §4.1 · pp. 8–9, Figure 4 · p. 9

4.2. Performance Compared to Baselines

  • EncoTESS achieves the best NLL among context-based models, while its MAE is comparable to the MLP’s; windowed averaging deteriorates at longer horizons.NLL evaluates the predictive distribution’s shape and width, whereas MAE measures the accuracy of its median. At short horizons, all three context-based models have comparable MAE.Source: Figure 5 · p. 10, §4.2 · p. 10
  • ≈100-hour prediction horizons bring EncoTESS and MLP performance close to the metadata-only baseline, indicating little remaining value from light-curve context.The metadata-only model’s performance is invariant with horizon because it has no light-curve context; at long horizons, the other models rely heavily on stellar properties.Source: §4.2 · p. 10
  • EncoTESS’s CNF prediction head improves likelihood modeling, while its RNN captures trends over hours to days.The larger advantage over the MLP in NLL than MAE supports the CNF head’s value. Despite being only slightly larger than the MLP, EncoTESS also exposes the light-curve state at any time through Ht.Source: §4.2 · pp. 10–11

5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS

EncoTESS encodings organize light curves by stellar properties and variability characteristics, and outperform simpler inputs overall when recovering variability statistics. Recovery advantages are particularly clear for skewness and kurtosis, although long-period rotation and residual observational artifacts remain limitations.

5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS

  • Independently encoded light curves cluster by star, with the example flaring M dwarf more dispersed in UMAP space than the eclipsing binary.These examples occupy opposite ends of a color–magnitude diagram. The M dwarf’s light curve is noisier and exhibits flares absent from the eclipsing binary’s example.Source: §5 · p. 11
  • Within-star encoding scatter reflects light-curve differences and can depend on sample count, sector noise, stochastic flare occurrence, and residual sector-specific systematics.Flares need not occur in every observed light curve, and noisier light curves are more susceptible to sector-specific artifacts despite mitigation.Source: §5 · pp. 11–12
  • Most eclipsing-binary light curves lie near the example binary in UMAP space, suggesting potential for automated variability classification.Proposed applications include identifying flaring, rotation, eclipsing binaries, exoplanet transits, and asteroseismic pulsations; this section does not report a classification benchmark.Source: §5 · p. 12

5.2. Recovery of Variability Statistics

  • Identical MLP predictors compare encodings with three control inputs, isolating representation value while recovery performance is evaluated through five-fold cross-validation.No light curves were held out from pretraining, but recovery metrics were reported from held-out folds without overlap between downstream training and test datasets.Source: §5.2 · pp. 12–13, Figure 9 · p. 13

5.1. Correlation with Physical Properties

  • Latent-space structure preserves stellar color and shows skewness, kurtosis, and flare equivalent duration generally increasing together and decreasing with rotation period.Color was supplied as metadata, whereas these variability indicators were not; a central negative-skewness region also contains a high density of transiting exoplanets. EDflare was constructed by summing individual flare equivalent durations per sector and star.Source: §5.1 · p. 12, Figure 7 · p. 12, Figure 8 · p. 13

5.2. Recovery of Variability Statistics

  • EncoTESS recovers variability statistics better overall than noise, metadata-only, and MLP inputs, with rotation-period and flare-equivalent-duration bias tied or comparable to the MLP.For rotation period (Prot) and flare equivalent duration (EDflare), EncoTESS achieves marginally better residual IQR than the MLP. Otherwise, it outperforms the controls on both median residual, indicating bias, and IQR, indicating accuracy/precision.Source: Figure 9 · p. 13, §5.2 · pp. 13–14
  • EncoTESS clearly improves skewness and kurtosis recovery, which the authors attribute to RNN memory spanning the light curve.MLP performance is comparable for EDflare because flares occupy short light-curve segments. EncoTESS predictions regress toward mean behavior over intervals of approximately days, limiting long-period rotation recovery; a larger model might improve this.Source: §5.2 · p. 14

6. INTERPRETABILITY

Saliency and correlation analyses link EncoTESS encodings to variability amplitude, flaring, eclipses, and brightness-related features. Variability amplitude and flaring provide age information complementary to rotation, although low-dimensional projections and imperfect linear residualization limit interpretation.

6.1. Saliency Analysis

  • Integrated gradients measure PC1 sensitivity, while occlusion measures changes after masking individual light-curve points; only relative contributions are interpretable.PC1 supplies a single information-rich target drawn from the encodings. Only two light curves were analyzed, although these saliency tests could be applied more broadly.Source: §6.1 · pp. 14, 16
  • Flaring and eclipses strongly influence the encodings in the two illustrated light curves, while observations near median flux generally contribute little.The median-flux pattern is stronger in the noisier M dwarf, with an exception for the eclipsing binary’s occlusion test.Source: §6.1 · pp. 14–16, Figure 10 · p. 15, Figure 11 · p. 15
  • Noisy M-dwarf extrema and moderate positive flux push PC1 oppositely, whereas high-signal eclipsing-binary contributions follow the sign of flux deviations.Both positive and negative M-dwarf extrema push PC1 negatively, while moderate positive deviations push it positively. The authors suggest this may distinguish noise from the rotational signal, rather than establish a definitive physical interpretation.Source: §6.1 · p. 15

6.1.1. Forward vs backward encoding

  • Within 5-10% depending on the metric, forward and backward channels contribute approximately equally to Θ′ despite learning different features.Forward-state integrated gradients show greater sensitivity to individual measurements and local fluctuations. The backward state is more robust to those fluctuations but particularly sensitive to eclipses; both inform the global encoding structure.Source: Figure 12 · p. 16, §6.1.1 · p. 16

6.2. Correlation with variability summary statistics

  • Variability amplitude fH correlates most strongly with PC1, with other strong correlations primarily involving target brightness and color–magnitude position.Unsupervised PC1 also correlates significantly with age, while Prot correlates only weakly, approximately as strongly as EDflare. These Pearson correlations concern only PC1; later components may correlate more strongly with the same features.Source: §6.2 · pp. 16–17, Figure 13 · p. 17

6.3. Complementary Age Information

  • Linear residualization and partial least squares isolate age-related encoding structure beyond Prot, then beyond Prot combined with color and absolute magnitude.This approximation retains nonlinear Prot information and may remove non-Prot information. Parallax, Tmag, and med(f) remain important after the combined residualization, potentially serving as absolute-magnitude proxies.Source: §6.3 · pp. 17–18
  • Nearly an order of magnitude separates two stars’ literature ages despite similar colors and rotation periods; ageET distinguishes their ages where ageP gives nearly identical estimates.Their differing rotational variability produces different mean locations in encoding space, allowing ageET estimates close to the literature ages.Source: §6.3 · p. 17, Figure 14 · p. 18
  • After linear residualization against rotation and color–magnitude information, variability amplitude fH remains the strongest age correlate, with total equivalent flare duration next among purely physical features.Flux skewness contributes little and kurtosis is unhelpful; additional age-relevant features may escape the tested summary statistics.Source: §6.3 · pp. 18–19, Figure 15 · p. 19

7. AGE INFERENCE

EncoTESS encodes age-related observables without age as a training input, and its downstream ageET framework outperforms rotation-based baselines on four of five evaluation metrics. Its advantage is strongest for young, red stars, although extremely young inferred ages require caution.

7. AGE INFERENCE

  • Age structure appears in EncoTESS’s UMAP encodings despite age never being a training input, motivating their use for stellar age inference.The encodings offer an alternative way to leverage learned light-curve information rather than deriving an analytical prescription combining individual variability indicators.Source: §7 · p. 19, Figure 16 · p. 20

7.1. Bayesian Inference Framework

  • ageET applies a ChronoFlow (V25)-based Bayesian framework to a compact, PLS-derived age representation, separately from the core EncoTESS architecture.Each star’s 1536-dimensional encodings are max-pooled across light curves, which proved more stable than mean or median pooling. PLS compression avoids unstable high-dimensional modeling; an alternative MLP representation overfit.Source: §7.1 · pp. 19–20

7.2. Comparison to Gyrochronology

  • 2,893 stars with literature ages and rotation periods underpin comparisons using identical Bayesian frameworks, priors, and posterior grids.Exoplanet hosts were excluded because their ages were heterogeneous and typically uncertain. Evaluation used ten leave-one-sector-out folds, an 85%/15% training/validation split within training folds, and five random-seed repetitions whose posteriors were combined.Source: §7.2 · p. 20
  • Sector-disjoint testing prevents encodings and variability amplitude from exploiting correlations between sector-specific systematics and stellar ages.Any star observed in a held-out sector was excluded from training and validation, including its observations from other sectors. This guards against learning sector–age correlations caused by localized stellar clusters.Source: §7.2 · pp. 20–21
  • 4/5 metrics favor ageET over agePfH and ageP: Pearson r, median absolute error (MAE), median residual, and percentage of residuals > 0.5 dex.agePfH achieves the best p16–p84 coverage; ageET and ageP have overly conservative posteriors by 4–7%. Compared with ageP, ageET also produces narrower residuals centered closer to zero, particularly for young red stars.Source: Table 3 · p. 21, §7.2 · p. 21, Figure 17 · p. 22
  • ageET beats ageP and agePfH for younger, redder stars, revealing age information complementary to rotation and variability amplitude.This includes late K stars younger than ∼100 Myr and M stars ≲1 Gyr; ageP is more reliable for ∼F/G stars and older K/M stars. The likelihood maps use inferred ages, and the KM subset was deliberately selected where ageET performs best.Source: §7.2 · pp. 21, 23, Figure 18 · p. 22, Figure 19 · p. 22
  • ≲a few Myr ageET estimates require caution because some genuinely older stars receive extremely young inferred ages.At log τinf ≲0.75, ageP outperforms ageET even for young red stars.Source: §7.2 · p. 23

8. APPLICATION TO FIELD STARS

For field exoplanet hosts, ageETXH derives most of its predictive power from CMD information, with variability metadata helping at young ages but no additional age information from the RNN architecture. Heterogeneous reference ages make this a qualitative assessment.

8. APPLICATION TO FIELD STARS

  • 2,430 exoplanet hosts with NASA Exoplanet Archive age estimates provide a qualitative test of age information in Θ for field stars.Most hosts are older than the catalog’s oldest cluster stars. Their heterogeneous, often highly uncertain reference ages introduce systematic biases that were not analyzed.Source: §8 · p. 23
  • ageETXH directly learns p(τ) from Θ rather than using Bayesian inference, exploiting relatively uniform host ages without preliminary dimensionality reduction.K-fold validation balanced training and validation sampling across 10 age bins spanning 0–14 Gyr. LOSO tests were omitted because these hosts lack the spatial biases affecting cluster stars.Source: §8 · p. 23
  • ageETXH performs comparably to the CMD-plus-variability baseline overall, indicating no additional age information from its RNN architecture for these hosts.Baselines used same-scale Gaussian noise instead of Θ, CMD metadata alone, or CMD metadata plus the variability fields fH and med(f).Source: §8 · pp. 23–24, Figure 20 · p. 24
  • 0–2 Gyr hosts benefit from fH and med(f), while CMD-containing variants are statistically indistinguishable beyond ≈2 Gyr.Most predictive power comes from CMD indicators, and all models struggle beyond ≈6 Gyr.Source: §8 · p. 24, Figure 20 · p. 24

9. DISCUSSION AND FUTURE WORK

Future work includes expanding EncoTESS across surveys and cadences, broadening its astrophysical applications, and evaluating alternative foundation models. Age estimates should include additional systematic uncertainty, while observational metadata help distinguish artifacts from astrophysical signals.

9. DISCUSSION AND FUTURE WORK

  • EncoTESS’s time-aware architecture could accommodate all TESS sectors and cadences, but this expansion requires testing.Future versions could fine-tune on newly available sectors and update a public encoding library. Encodings are already provided for all light curves processed by the current version.Source: §9 · p. 24
  • EncoTESS could transfer to Kepler, K2, and PLATO, with possible extensions to cluster-integrated light curves (e.g., T. M. Wainer et al. 2023).PLATO (H. Rauer et al. 2025) offers 2 years per hemisphere versus TESS’s 27 days per sector, and ≈2100 deg2 versus Kepler’s ≈115 deg2. Its characteristics provide an opportunity to test longer-term variability encoding.Source: §9 · p. 24
  • Fine-tuning general TSFMs may become more efficient than astronomy-specific pretraining; off-the-shelf tabular models also merit testing for downstream tasks.General TSFMs (e.g., A. Das et al. 2023; X. Liu et al. 2024) achieve forecasting performance comparable to fully supervised task-specific models, although most literature TSFMs still omit measurement uncertainty. Whether retaining EncoTESS or adopting proven components, the authors see substantial potential in multi-survey, multicadence stellar TSFMs.Source: §9 · p. 24

9.1. Systematics

  • ≈0.08 dex of additional systematic uncertainty should accompany EncoTESS age estimates, although its typical ≈0.4 dex posterior width dominates.P. R. Van-Lane et al. (2025) identify dust-map choice, cluster membership criteria, and calibration ages as sources of this uncertainty in ChronoFlow.Source: §9.1 · p. 25
  • Observational metadata help separate instrumental artifacts from astrophysical signals; contrastive learning could further reduce artifacts in the encodings.Inputs include sector, camera, CCD, fH, med(f), and Tmag. Unlike current self-supervised flux reconstruction, contrastive learning could align encodings of identical or similar stars and separate dissimilar stars, following J. Ding et al. (2026).Source: §9.1 · p. 25

9.2. Downstream Astrophysics

  • Encodings could support variability classification and identify candidates for known stellar populations through proximity in latent space.D. Poznanski (2026) and J. Ding et al. (2026) presented variability classification as an application of their frameworks.Source: §9.2 · p. 25
  • The ageET architecture could predict mass or temperature instead of age, while adding asteroseismic calibrators could benefit age inference and other applications.Expanding the training sample to include asteroseismic calibrators is considered attainable in the near future.Source: §9.2 · p. 25

10. CONCLUSION · APPENDIX

EncoTESS encodes raw TESS light curves into fixed-dimensional representations and outperforms rotation period and variability amplitude as age indicators for younger, redder stars not yet on the slowly-rotating sequence.

10. CONCLUSION

  • 69,345 2-minute TESS light curves from 21,507 ∼FGKM main-sequence stars trained EncoTESS to handle noise, measurement uncertainty, irregular sampling, and large gaps.Inputs combine raw light curves, stellar properties, and acquisition parameters to distinguish astrophysical effects from observational systematics. Fixed-dimensional encodings support downstream classification or age inference.Source: §10 · p. 25
  • The RNN architecture and probabilistic prediction head enable EncoTESS to outperform more naive models in flux prediction and summary-statistic recovery.Forward and backward training encode different light-curve features: the forward model is more sensitive to local flux variations, but both contribute equally to the encoding.Source: §10 · p. 25
  • ≈64,000 parameters make EncoTESS at least two orders of magnitude smaller than typical literature TSFMs and runnable on most modern laptops.Source: §10 · p. 25
  • EncoTESS encodings track rotation, flaring, and higher-order moments of the flux distribution, capturing multiple forms of stellar variability.These representations provide data products for downstream stellar characterization.Source: §10 · pp. 25–26
  • EncoTESS outperforms Prot and variability amplitude as age indicators for younger, redder stars not yet on the slowly-rotating sequence.Its age-dependent variability signatures complement Prot, supporting age inference where gyrochronology is less precise.Source: §10 · p. 25
  • Currently trained on TESS 2-minute light curves, EncoTESS could extend to multicadence data and Kepler, K2, and PLATO observations.These proposed extensions could support stellar-variability characterization and age inference.Source: §10 · p. 25
  • The architecture could support live training as light curves arrive, maintaining a library of encodings updated with newly acquired data.Source: §10 · pp. 25–26

A. MODEL PERFORMANCE WITH ADDITIONAL INPUT CHANNELS … B.3. PLS Representation

Adding power-spectrum and autocorrelation channels did not improve EncoTESS enough to justify their complexity and computational expense. Lower-dimensional encodings support visualization with UMAP, quantitative analysis with PCA, and age inference with PLS.

A. MODEL PERFORMANCE WITH ADDITIONAL INPUT CHANNELS

  • Power-spectrum and autocorrelation channels expose frequency-domain and time-offset structure, potentially helping RNNs learn patterns separated by long offsets.Power spectra were resampled to 16,000 bins up to 360 cycles/day, combining power values with periodicity f-statistics. Autocorrelation coefficients were computed by applying scipy.fft.ifft to the resampled power spectra.Source: A. MODEL PERFORMANCE WITH ADDITIONAL… · p. 30
  • UNet-style (O. Ronneberger et al. 2015) CNN autoencoders most successfully reconstructed the extra channels; their encodings entered each RNN hidden-state computation through concatenation.The authors trained EncoTESS versions with and without these additional encodings.Source: A. MODEL PERFORMANCE WITH ADDITIONAL… · p. 30
  • Adding power-spectrum and autocorrelation channels yielded comparable reconstruction and inference performance, so EncoTESS excludes their extra complexity and computational expense.Tests assessed reconstruction loss, rotation-period recovery, age recovery, and reconstruction of both additional channels. The example power-spectrum reconstruction showed marginal feature improvements but a similar overall shape.Source: Figure 21 · p. 30, Figure 22 · p. 31, A. MODEL PERFORMANCE WITH ADDITIONAL… · p. 31

B. LOW-DIMENSIONAL ENCODING REPRESENTATIONS

  • Three dimensionality-reduction methods provide lower-dimensional representations of EncoTESS’s 1536-dimensional light-curve encodings.These representations are derived from the encoding space Θ.Source: B. LOW-DIMENSIONAL ENCODING… · p. 31

B.1. UMAP Representation

  • UMAP preserves clustering structure for visualization, but its two-dimensional projections are not used quantitatively because they poorly capture the encodings’ intrinsic dimensionality.Relative light-curve positions reveal trends; individual UMAP coordinate values are not meaningful and are omitted from plots.Source: §B.1 · p. 31

B.2. PCA Representation

  • 44% of encoding variance is explained by PC1, another 28% by PCs 2–4, and the remaining 28% by PCs 5–1536.PCA selects orthogonal directions of greatest variance; most quantitative analyses use 4, 8, or 16 components according to downstream needs. Its linear component count need not match intrinsic dimensionality: capturing the nonlinear 13-dimensional structure identified by TwoNN requires more than 13 PCs.Source: §B.2 · pp. 31–32

B.3. PLS Representation

  • 3 PLS dimensions are used for age inference because correlations with fabricated ages increased significantly beyond three dimensions, indicating overfitting.PLS maximizes covariance with stellar age rather than encoding variance, concentrating age information in its leading components. By contrast, unsupervised PCA may place more age information in lower components.Source: §B.3 · p. 32

C. DETAILED MODEL ARCHITECTURE … C.1.2. Light Curve Masking

EncoTESS combines learned input encodings, an RNN, self-supervised flux prediction, and aggregation into fixed-size representations. Training masks metadata and light-curve segments to discourage metadata reliance and improve robustness to gaps; downstream age encodings use unmasked inputs.

C. DETAILED MODEL ARCHITECTURE

  • EncoTESS’s implementation comprises learned input encodings, a core RNN, a Conditional Normalizing Flow (CNF) flux-prediction head, and aggregation into fixed-size representations.The appendix documents these components with the goal of complete reproducibility.Source: C. DETAILED MODEL ARCHITECTURE · p. 32

C.1. Input Encoding

  • 88-parameter timestamp encoding produces eight-dimensional vectors, combined with normalized flux and uncertainty into 10-dimensional inputs per observation.The jointly trained MLP has an eight-dimensional ReLU hidden layer and an eight-dimensional linear output layer. Its encoding supports periodic and quasi-periodic learning by bringing temporally separated but phase-near timestamps closer.Source: §C.1 · p. 32
  • 41,376 parameters in the metadata MLP transform 13 fields and their binary masks into a 32-dimensional vector.Its 26-dimensional input passes through three 128-dimensional hidden layers with layer normalization, GELU activation, and 10% dropout, followed by a linear output without activation.Source: §C.1 · p. 32

C.1.1. Metadata Masking

  • 15% of light curves have all metadata masked; remaining cases receive field-level masking while retaining at least one field.Masked fields and their corresponding mask-channel entries are set to zero; unmasked fields retain their true values and receive mask-channel entries of one.Source: §C.1.1 · p. 33
  • Resampling metadata masks every batch and epoch discourages reliance on systematic metadata signatures.Metadata masking is disabled when computing representations for downstream age inference to retain maximal information.Source: §C.1.1 · p. 33

C.1.2. Light Curve Masking

  • ≈40% of a typical light curve is masked during training to improve robustness against data gaps and reduce overfitting.Segments are added until their summed lengths reach 50%, truncating the last segment and ignoring overlaps. The segment distribution prioritizes short-term variability while retaining sensitivity to offsets approximately as large as the largest TESS gaps.Source: §C.1.2 · p. 33
  • Masked light-curve points are excluded from hidden-state computations but retained as prediction targets, providing training across data gaps.Light-curve masking is disabled when computing representations for downstream age inference to retain maximal information.Source: §C.1.2 · p. 33

C.2. Recurrent Neural Network Framework · C.2.1. Bidirectionality

EncoTESS uses parallel minGRU computations to encode light-curve observations and metadata into hidden states for downstream analysis. Separate forward and backward cells provide context from both sides of each observation.

C.2. Recurrent Neural Network Framework

  • ≈50× training speedup over sequential GRU was measured for minGRU on sequences of ≈16,000 data points.EncoTESS uses the minGRU implementation from L. Feng et al. (2024); testing minLSTM produced comparable performance.Source: §C.2 · p. 34
  • Following L. Feng et al. (2024), minGRU refactors sequential hidden-state dependencies into dependencies on preceding inputs, enabling simultaneous computation across a light curve.Traditional RNN hidden states accumulate information observation by observation, creating a sequential computational bottleneck.Source: §C.2 · pp. 33–34
  • 64-dim hidden states encode observations up to each time point and light-curve metadata, forming EncoTESS’s core products for downstream analysis.Training is intended to make these states describe variability in the context of stellar and light-curve metadata.Source: §C.2 · p. 34

C.2.1. Bidirectionality

  • Distinct, architecturally identical forward and backward minGRU cells capture direction-dependent behavior, including asymmetric flares with abrupt rises and smoother decays.The two cells are designated minGRUf and minGRUb.Source: §C.2.1 · p. 34
  • 128-dim hidden states at each light-curve point characterize preceding and following variability in the context of stellar and light-curve metadata.Each point has both a forward and a backward hidden state.Source: §C.2.1 · p. 34
  • The RNN architecture totals 22,144 parameters, with 11,072 parameters per minGRU cell including input projection J, a 64-dimensional linear layer that transforms each point’s 42-dimensional input.The 64-dimensional linear layer b uses a custom activation function defined by L. Feng et al. (2024), while the 64-dimensional linear layer a uses sigmoid activation.Source: §C.2.1 · p. 34, §C.2 · p. 34

C.3. Model Training · C.4. Computation of LC Encodings

EncoTESS trains a conditional normalizing flow to predict flux distributions without exposing the target observation. It then aggregates hidden states into fixed-size light-curve encodings.

C.3. Model Training

  • EncoTESS predicts full flux likelihoods conditioned on light-curve context, metadata, encoded prediction time, and measurement error, rather than discrete flux values.The conditional normalizing flow accommodates flexible distribution shapes, prioritizing general trends and well-calibrated likelihoods over individual predictions of noisy flux measurements.Source: §C.3 · p. 35
  • Target-observation information is withheld by using forward states before and backward states after the prediction time, with larger offsets teaching longer-term patterns.The nearest permitted context consists of the preceding forward hidden state and the following backward hidden state.Source: §C.3 · p. 35
  • 28,974-dim Neural Spline Flow (C. Durkan et al. 2019) uses two transforms, each containing two 64-dim ReLU hidden layers and a 23-dim output.Each transform's output corresponds to an 8-bin spline.Source: §C.3 · p. 35
  • 2-minute and 4-day offsets correspond to k = 1 and k = 2880, respectively, assuming constant 2-minute sampling.A different offset is drawn for each training batch, prioritizing short-term variability while retaining sensitivity to offsets approximately matching the largest TESS light-curve gaps.Source: §C.3 · p. 35
  • Training minimizes average negative log-likelihood across every unmasked observation in all light curves within a batch.The loss evaluates predicted probability density at the observed flux; the authors favor it over χ2 for assessing non-Gaussian likelihoods.Source: §C.3 · p. 35

C.4. Computation of LC Encodings

  • 1536-dim light-curve encodings concatenate hidden-state statistics, endpoint states, rate-of-change statistics, and means within four sequential equal-observation bins.Aggregation compresses per-observation 128-dim hidden states, otherwise totaling O(10^7) features per light curve. Components comprise maximum/minimum/mean/standard deviation (512-dim), first/last states (256-dim), absolute-time rate-of-change mean/standard deviation (256-dim), and four sequential-bin means (512-dim).Source: §C.4 · pp. 35–36

D. LATENT SPACE CORNER PLOT

The latent-space corner plot shows a strong age signal in PC1 and a weaker signal in PC3. PC2 reveals distinct clustered subpopulations that could potentially support classification.

D. LATENT SPACE CORNER PLOT

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