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

Source-linked AI summary

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:2608.25019v1Aug 25, 2026astro-ph.SRastro-ph.GAastro-ph.IMcs.LG

TL;DR

Dating late-F-to-M main-sequence stars is difficult, especially where existing stellar-age indicators are limited. This paper develops EncoTESS to encode TESS light curves, finding that its latent representation correlates significantly with age while rotation-period correlation is relatively minor.

Problem
Ages of late-F-to-M main-sequence stars are difficult to constrain because isochrone fitting, asteroseismology, and lithium depletion have limited applicability.
Method
The authors develop EncoTESS, a self-supervised Time Series Foundation Model that encodes TESS light curves into a latent parameter space.
Results
EncoTESS’s first principal component correlates significantly with age, while its rotation-period correlation is relatively minor and approximately as strong as its flare-equivalent-duration correlation.
Takeaways & Limitations
EncoTESS’s encodings support age inference and could also be applied to variability classification and identifying distinct stellar populations.
Takeaways & Limitations
Very young EncoTESS-inferred ages should be treated with caution because some older stars are estimated to be extremely young.

Abstract

from arXiv · show

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 addresses the difficulty of aging late-F–M main-sequence stars by encoding raw TESS light curves rather than relying on correlated, measurement-dependent summary statistics. It is designed for TESS’s noisy, irregular, heteroskedastic, gapped observations while remaining efficient enough for consumer hardware.

Motivation: Late-F–M main-sequence stars are difficult to age because isochrone fitting and asteroseismology are limited, while gyrochronology is less accurate for young and reddest stars.Rotation-period, flaring, magnetic-activity, and variability-amplitude indicators provide complementary information, but flaring is stochastic and gyrochronology has intrinsic scatter and M-dwarf spindown multimodality.
Contribution: EncoTESS is introduced as a self-supervised Time Series Foundation Model that encodes TESS light curves into generalized representations for characterizing their underlying variability processes.The approach is motivated by the difficulty of jointly optimizing correlated, measurement-dependent summary statistics computed from millions of light-curve data points.
Motivation: TESS is especially valuable for this problem because its all-sky coverage includes many more M dwarfs than Kepler, despite noisier photometry and shorter sector baselines.These properties expand access to stars that are particularly difficult to date using rotation periods.
Design requirements: The model is designed to handle irregular sampling, heteroskedastic measurements, variable temporal resolution and sequence length, and approximately one-day TESS data gaps.These capabilities support extension across cadences and accommodate observational features that many existing models do not explicitly address.
Architecture: An RNN-based architecture enables EncoTESS to process long light curves efficiently on consumer hardware, avoiding the computational scaling challenges of transformer-based TSFMs.This architecture is selected specifically for efficient operation on long light-curve sequences.
Related work: Unlike StarCLR, which uses fixed 8192-point inputs and preselects light curves with prior periodic-variability evidence, EncoTESS is intended to consider all variability types without relying on periodicity.StarCLR does incorporate observational timestamps and is gap aware, but its periodicity-based training filter is a restriction for this broader goal.

2. DATA

The study assembles a 2-minute-cadence TESS light-curve dataset from exoplanet hosts, thick-disk stars, and FGKM main-sequence calibrators, then standardizes the observations and augments them with stellar and instrumental metadata. The final catalog contains 69,345 light curves from 21,507 unique stars across sectors 1–101, with a bimodal Gaia color distribution.

Dataset composition: The Gaia DR3 dereddened color distribution is bimodal, with a sharp peak near (BP −RP)0 ≈1 from exoplanet hosts and thick-disk stars and a broader peak near ≈3 from FGKM calibrators.The source categories therefore occupy distinct regions of the color distribution.
Dataset composition: The dataset combines exoplanet hosts, thick-disk stars, and variable or independently aged FGKM main-sequence stars selected from literature catalogs.Thick-disk stars bolster the field-age light-curve sample, while the FGKM calibrators include open-cluster, association, and magnetically active or rotating nearby-star samples.
Dataset composition: 69,345 light curves from sectors 1–101 represent 21,507 unique stars in the final EncoTESS dataset.Because some targets occur in multiple literature sources, totals are lower than the sum across source-specific counts.
Light-curve processing: Each light curve retains PDCSAP flux, flux uncertainty, and observation time after default-quality filtering, missing uncertainties are replaced by the curve’s median uncertainty, and times are reset to t0 = 0.The work uses SPOC 2-minute TESS light curves and stores the three per-observation channels after these quality-control steps.
Light-curve processing: Fluxes are normalized to median flux fmed = 0 and half-interquartile range fH = 1 to reduce sensitivity to extreme outliers.The normalization parameters are also retained because they track activity and variability while correlating with noise and instrumental systematics.
Metadata: For each light curve, metadata includes TESS magnitude, sector, camera, CCD, normalization parameters, and cadence, while each star additionally has six Gaia-derived parameters including dereddened G0, color, parallax, and uncertainties.Gaia DR3 crossmatching, parallax zeropoint correction, and dereddening provide the stellar metadata used alongside the light-curve inputs.

3. MODEL ARCHITECTURE

EncoTESS is a compact RNN-based time-series foundation model that processes raw light curves, metadata, and observable timestamps without interpolation. It learns representations through masked self-supervised probabilistic reconstruction and compresses each light curve into a fixed-size latent vector for downstream use.

Input representation: Each light curve is input as a 3 × L normalized time-series matrix alongside a 13-dimensional metadata vector, with timestamps retained as observable inputs.Observable time lets the model distinguish abrupt flux changes from gradual changes across measurement gaps and supports future integration of different cadences.
Latent representation: Pooling 128-dimensional hidden states in 12 ways converts variable-length light curves into fixed 1536-dimensional encodings for downstream applications.The hidden state combines 64-dimensional forward and backward representations, and PCA further concentrates encoding variance in early principal components; PC1 alone explains 44%.
Input ablation: Adding frequency power spectra and autocorrelation functions as input channels did not improve EncoTESS performance.These alternatives were benchmarked as additional views of each light curve, with details reported in Appendix A.
RNN architecture: ≈64,000 parameters make EncoTESS far smaller than typical TSFMs, which are at least O(10^6) parameters, while its minGRU RNN supports efficient long-sequence processing.RNN computation scales as O(L), avoids fixed sequence-length requirements, and minGRU enables parallel processing; EncoTESS uses the simpler RNN approach rather than an SSM.
Training: Self-supervised training predicts flux at variable horizons from 2 minutes to 4 days, uses masking for robustness to missing data, and applies a Conditional Normalizing Flow for probabilistic likelihood estimation.Forward and backward hidden states represent light-curve context using observational and metadata channels.

4. FLUX RECONSTRUCTION

EncoTESS reconstructs unobserved light-curve flux for interpolation, gap filling, and future prediction, with confidence depending on prediction horizon and measurement uncertainty. Compared with baselines, its CNF head and recurrent architecture improve likelihood-based reconstruction, especially across hour-to-day horizons.

Measurement uncertainty: Increasing observational uncertainty broadens p(ˆf) above a learned noise floor, while the predictive median regresses toward the light curve’s overall median.The tested uncertainty scalings range from 0.3× to 3× the measured uncertainty.
Prediction horizons: Flux-prediction confidence depends strongly on the prediction horizon, with Figure 3 contrasting forward predictions at 0.5-hour and 17-hour horizons.The figure shows 1σ confidence intervals around predictions and measured normalized fluxes.
Baseline comparisons: EncoTESS achieves the best NLL across prediction horizons, while MAE is comparable at short horizons and the windowed mean degrades at long horizons.Figure 5 compares EncoTESS with windowed-mean, metadata-only, and MLP baselines; lower NLL and MAE indicate better fits.
Baseline comparisons: At approximately 100-hour horizons, EncoTESS and the MLP approach metadata-only performance, indicating that stellar properties dominate when light-curve context becomes uninformative.The metadata model is horizon-invariant because it lacks light-curve context.
Architecture interpretation: EncoTESS’s CNF head improves likelihood modeling, while its RNN captures trends over hours to days and provides light-curve state extraction through H_t.Its advantage over the MLP is larger in NLL than MAE, and the model remains only slightly larger than the MLP.

5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS

EncoTESS’s latent encodings preserve physically meaningful variability structure: light curves from the same star cluster, while noise and stochastic flaring influence their scatter. The encodings also recover multiple variability statistics, outperforming simpler controls overall, especially for skewness and kurtosis.

5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS: Independent light curves from each star cluster in latent space, while the flaring M dwarf’s encodings scatter more than the eclipsing binary’s.The differing scatter may reflect the number of light curves, sector-dependent noise, stochastic flare occurrence, and residual systematics.
5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS: EncoTESS can support automatic classification of variability types, including flaring, rotation, eclipsing binaries, exoplanet transits, and asteroseismic pulsations.Most eclipsing-binary light curves lie close to the highlighted eclipsing binary in UMAP space.
5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS: UMAP projections show clear structure for stellar color, skewness, kurtosis, rotation period, and flaring equivalent duration, indicating these quantities persist in the encodings.The trends are physically systematic: faster rotation is associated with youth, magnetic activity, and flaring, while flares increase flux skewness and kurtosis.
5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS: EncoTESS outperforms pure-noise, metadata, and MLP-derived controls in recovering four light-curve summary statistics, especially skewness and kurtosis.For Prot and EDflare, EncoTESS has comparable bias and marginally better IQR than the MLP; its advantage is clearest for higher-order flux statistics.
5. VARIABILITY CHARACTERIZATION WITH LIGHT CURVE ENCODINGS: EncoTESS’s advantage is weaker for short-duration flares and long-period rotation, where the MLP is comparable and flux predictions regress toward the mean over days.The authors suggest that a larger EncoTESS model may improve long-term rotational behavior.

6. INTERPRETABILITY

EncoTESS interpretability analyses show that its latent representations emphasize informative light-curve structure, variability amplitude, flares, eclipses, and stellar brightness. PC1 also contains age information beyond rotation period, although correlations measured only with PC1 are not an upper bound for the full latent space.

Saliency analysis: Saliency analysis shows that EncoTESS largely downweights median-flux observations but strongly weights flares, local extrema, and eclipses in its latent representation.In a high-signal-to-noise eclipsing binary, positive and negative flux values push PC1 in corresponding directions, while eclipses contribute substantially to Θ.
Saliency analysis: The forward and backward encoding channels respond differently to local fluctuations, but both contribute important information to the global structure of Θ.The forward channel reacts aggressively to local fluctuations, whereas the backward channel is more robust to them.
Variability correlations: PC1 correlates most strongly with fH, while brightness and color-magnitude features also correlate strongly; age correlation is significant, but Prot is comparatively minor and similar to EDflare.PC1 is used as an interpretable diagnostic because PCA is unsupervised, though later principal components may correlate more strongly with these features.
Age-complementary features: After removing the component of Θ fitted from rotation period, fH remains the strongest age-correlated feature, while total equivalent flare duration provides additional physical age information.The residual representation Θres is defined as the portion of Θ that Prot cannot account for; flaring therefore contributes age information complementary to rotation period.

7. AGE INFERENCE

EncoTESS encodings contain age-related information despite age not being used during training, enabling the ageET framework for stellar age inference. In leave-one-sector-out tests, ageET generally outperforms rotation- and variability-based baselines, especially for young, red stars, but extremely young estimates require caution.

Age information in encodings: EncoTESS encodings show clear age structure in UMAP space, although age was not an input during training, demonstrating that they naturally encode age-related observables.The encodings therefore provide an alternative basis for stellar age inference using information learned to characterize the light curves.
AgeET framework: AgeET aggregates each star’s light-curve encodings by max pooling across 1536 dimensions and uses a PLS-derived age-informative representation within a ChronoFlow-like Bayesian framework.Mean and median pooling were tested but max pooling was most stable; an MLP representation was unstable and overfit.
Age inference performance: In 4/5 metrics, ageET outperforms agePfH and ageP, yielding more accurate, less biased estimates with fewer catastrophic failures; agePfH leads only in posterior coverage.Table 3 compares Pearson r, median absolute error, median residual, residuals >0.5 dex, and p16–p84 coverage; agePfH outperforms ageP in all metrics.
Age inference performance: AgeET residuals are narrower and closer to zero than ageP residuals, particularly for young red stars, indicating that EncoTESS provides better age calibration than rotation period.The comparison uses the median age posterior from the ageET and ageP leave-one-sector-out tests.
Age-dependent performance: AgeET outperforms ageP for stars younger and redder than the slow-rotator regime, while ageP is more reliable for converged FGKM stars; EncoTESS adds variability information complementary to Prot and fH.A small population is inferred as extremely young incorrectly, so ageET estimates ≲a few Myr should be treated cautiously.

8. APPLICATION TO FIELD STARS

For 2,430 heterogeneous-age exoplanet hosts, ageETXH recovers ages primarily from CMD indicators, with variability metadata adding information only for stars younger than 2 Gyr. Its performance is comparable to a CMD-plus-variability baseline, indicating no additional age information from the RNN architecture for these field stars.

8. APPLICATION TO FIELD STARS: The field-star test used 2,430 exoplanet hosts with heterogeneous age estimates from default NASA Exoplanet Archive records, most older than the catalog’s oldest cluster stars.These field stars are typically older and less variable than open-cluster stars, motivating a separate age-recovery test.
8. APPLICATION TO FIELD STARS: Age recovery used k-fold validation with uniform sampling across 10 age bins spanning 0–14 Gyr, while omitting leave-one-space-out tests because field hosts lack the clusters’ spatial biases.The age inference model, ageETXH, learned p(τ) directly rather than using Bayesian inference.
8. APPLICATION TO FIELD STARS: ageETXH compresses EncoTESS encodings Θ into four dimensions with a two-hidden-layer MLP, then predicts age using a six-transform CNF with two hidden layers.It was compared with Gaussian-noise, CMD-only, and CMD-plus-variability metadata baselines.
8. APPLICATION TO FIELD STARS: CMD indicators provide most of ageETXH’s predictive power, while variability metadata adds useful information only in the 0–2 Gyr bin; beyond ≈2 Gyr, CMD-based variants are statistically indistinguishable.Overall, ageETXH performs comparably to the CMD-plus-variability variant, showing that the RNN architecture contributes no additional age information for these stars.

9. DISCUSSION AND FUTURE WORK

The authors propose expanding EncoTESS across all TESS cadences and sectors, other surveys, and additional astronomical time-series products. They also identify applications beyond age inference, while noting systematic uncertainties and opportunities for contrastive learning and asteroseismic calibration.

Future survey extensions: EncoTESS could be expanded to all TESS light curves and cadences, updated as new sectors arrive, and applied to Kepler, K2, PLATO, and cluster-integrated light curves.Its time-aware architecture can accommodate these extensions, but expansion to all TESS data still requires testing; PLATO offers longer baselines and a larger field of view than TESS and Kepler (H. Rauer et al. 2025).
Future architecture: EncoTESS has potential as a stellar time-series foundation model for multi-survey, multicadence light curves, regardless of whether its core architecture is retained or revised.The authors note that rapidly advancing TSFM and SSM methods may provide components addressing scalability and heterogeneity.
Systematic uncertainties: EncoTESS age posteriors typically have widths of ≈0.4 dex, exceeding the ≈0.08 dex uncertainty from dust-map, membership, and calibration-age systematics identified for ChronoFlow.These systematics remain important when posterior age predictions are narrow, while EncoTESS uses observational metadata to help account for data-acquisition effects.
Methodological improvements: Contrastive learning could reduce observational artifacts in Θ while preserving astrophysical information, and adding asteroseismic calibrators could improve age inference and other applications.The current training is self-supervised flux reconstruction, whereas contrastive learning would align encodings from similar stars and separate dissimilar stellar types.
Additional applications: Beyond age inference, EncoTESS could support variability classification, stellar-population discovery in latent space, and inference of properties such as mass or temperature.Known stellar populations could be used to identify nearby candidates in Θ space, while the ageET architecture could be modified to predict parameters other than age.

10. CONCLUSION · APPENDIX

EncoTESS is a compact RNN-based foundation model that robustly encodes raw TESS light curves and captures multiple forms of stellar variability. It improves age inference for younger, redder stars where gyrochronology is less precise, while offering a foundation for broader survey applications.

10. CONCLUSION: EncoTESS was trained on 69,345 2-minute TESS light curves from 21,507 ∼FGKM main-sequence stars using an RNN architecture.The model was designed to handle high noise, measurement uncertainty, irregular sampling, and large data gaps.
10. CONCLUSION: The RNN architecture and probabilistic prediction head outperform naive models for flux prediction and recovering light-curve summary statistics.Forward and backward training components encode different light-curve features: the forward model is more sensitive to local flux variations, while both contribute equally to the encoding.
10. CONCLUSION: EncoTESS characterizes stars from raw light curves by encoding rotation, flaring, and higher-order flux-distribution moments into a latent representation.The representation tracks multiple variability types rather than relying on a single summary statistic.
10. CONCLUSION: EncoTESS outperforms Prot and variability amplitude as age indicators for younger, redder stars that have not converged onto the slowly-rotating sequence.This indicates that EncoTESS extracts age-dependent variability signatures complementary to Prot, supporting age inference where gyrochronology is less precise.
10. CONCLUSION: Extending EncoTESS to multicadence TESS data and Kepler, K2, and PLATO light curves could advance stellar-variability characterization, age inference, and downstream science.The architecture also supports training the model as light curves are observed and maintaining an encoding library updated with new data.
10. CONCLUSION: Overall, EncoTESS provides a conceptual foundation for data-driven stellar-variability characterization and useful data products for downstream science.The conclusions frame the model as a promising basis for future applications beyond the demonstrated age-inference task.

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

EncoTESS gains no meaningful performance from adding power-spectrum and autocorrelation channels, while its 1536-dimensional encodings support UMAP, PCA, and age-focused PLS representations. PCA captures variance unsupervised, whereas the top three PLS dimensions concentrate age information while limiting overfitting.

A. MODEL PERFORMANCE WITH ADDITIONAL INPUT CHANNELS: The added channels represent the light curve in complementary frequency and time-offset domains: the power spectrum and autocorrelation function.The power spectrum highlights frequency-specific periodicity, while autocorrelation coefficients become large at time offsets corresponding to strong periodic signals.
A. MODEL PERFORMANCE WITH ADDITIONAL INPUT CHANNELS: Power-spectrum and autocorrelation encodings were reconstructed with UNet-style CNN autoencoders and concatenated into each RNN hidden-state input.Power spectra were resampled to 16,000 frequency bins up to 360 cycles/day and combined with f-statistics.
A. MODEL PERFORMANCE WITH ADDITIONAL INPUT CHANNELS: All tests showed comparable performance with or without power-spectrum and autocorrelation channels, making their added model complexity unnecessary.Tests covered reconstruction loss, rotation-period recovery, age inference, and reconstruction of both auxiliary representations; power-spectrum reconstruction improved only marginally.
B.1. UMAP Representation: UMAP projects the 1536-dimensional encoding Θ into two dimensions optimized to preserve clustering structure, making relative light-curve positions useful for visualization.The numerical UMAP coordinates themselves are not meaningful.
B.2. PCA Representation: PCA reorients Θ along orthogonal directions of decreasing variance; PC1 explains 44%, PCs 2–4 add 28%, and PCs 5–1536 explain the remaining 28%.PCA is therefore used for most quantitative analyses as an intuitive and flexible low-dimensional representation.
B.2. PCA Representation: The useful number of PCA components need not equal intrinsic dimensionality because PCA is linear, whereas TwoNN captures nonlinear dimensionality.More than 13 PCs may be needed to represent a nonlinear 13-dimensional space.
B.3. PLS Representation: PLS maximizes covariance with stellar age τ rather than encoding variance, concentrating age information in the top three dimensions while avoiding higher-dimensional overfitting.Correlations with fabricated ages rose significantly beyond three dimensions, indicating that added signal was primarily noise.

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

EncoTESS uses encoded time series and metadata inputs, an RNN-based representation framework, self-supervised flux prediction, and aggregation into a fixed-size latent representation Θ. Training masks metadata and light-curve segments to reduce reliance on systematic signatures, improve robustness to gaps, and preserve information-rich unmasked inputs for downstream inference.

C. DETAILED MODEL ARCHITECTURE: The implementation comprises encoding layers, a core RNN framework, a Conditional Normalizing Flow head for self-supervised flux prediction, and aggregation into fixed-size latent representations Θ.These components mirror the paper’s high-level architecture and are documented for reproducibility.
C.1. Input Encoding: Timestamps are mapped to 8-dimensional learned encodings with an 88-parameter MLP to improve learning of periodic and quasi-periodic temporal trends.The timestamp encoder is trained jointly with the rest of EncoTESS.
C.1. Input Encoding: Metadata are processed into a 32-dimensional vector by a 41,376-parameter MLP with three 128-dimensional hidden layers, normalization, GELU activation, and 10% dropout.The first hidden layer receives 26 inputs: 13 metadata fields and their 13-dimensional binary mask channel.
C.1.1. Metadata Masking: Metadata masking combines a 15% probability of masking all fields with field-level masking, retaining at least one field when the block mask is not applied.Masked fields are set to zero with mask indicators set to zero; unmasked fields retain their values with indicators set to one, and masks are recomputed each batch and epoch to reduce over-reliance on systematic metadata signatures.
C.1.2. Light Curve Masking: Light-curve masking improves robustness to data gaps and reduces overfitting by exposing EncoTESS to different portions of each light curve during training.The segment-length distribution emphasizes short-term variability while retaining sensitivity to offsets approximately as large as the largest TESS gaps.
C.1.2. Light Curve Masking: Iterative masking targets 50% of each light curve, but overlapping segments typically leave approximately 40% masked.The final segment is truncated so the masked total does not exceed 50%.
C.1.2. Light Curve Masking: Masked light-curve points are excluded from hidden-state computations but retained as prediction targets, providing additional training across data gaps.When computing Θ for downstream age inference, neither metadata nor light-curve masking is applied so the representation retains maximal information.

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

EncoTESS uses recurrent hidden states to summarize light-curve variability with metadata, while minGRU refactoring enables parallel computation instead of sequential processing. Bidirectional minGRU cells additionally capture asymmetric variability using context from both preceding and following observations.

C.2. Recurrent Neural Network Framework: The recurrent framework represents sequential observations as hidden states Ht that accumulate process information from an initial state H0 through the final state HL.This hidden-state formulation underlies the light-curve encoding procedure.
C.2. Recurrent Neural Network Framework: MinGRU refactoring removes the traditional RNN bottleneck by making each hidden state depend only on inputs through the current point, enabling simultaneous computation.Traditional RNNs require sequential computation of every Ht; L. Feng et al. (2024) show how this dependency can be refactored while retaining comparable performance to transformers and standard LSTM/GRU networks.
C.2. Recurrent Neural Network Framework: The minGRU input projection transforms each 42-dim point input through a 64-dim linear layer, alongside 64-dim layers for the custom activation and sigmoid gate.The layers are denoted J, b, and a, respectively.
C.2. Recurrent Neural Network Framework: The architecture produces a 64-dim hidden state at every light-curve point, encoding preceding observations, metadata, and variability for downstream analysis.These hidden states are the core products of EncoTESS.
C.2.1. Bidirectionality: Bidirectionality models each light curve with distinct forward and backward minGRU cells to capture behavior that differs by time direction, such as stellar flares.Flares typically show an abrupt flux rise followed by a smoother decay, making directional context useful.
C.2.1. Bidirectionality: Combining forward and backward states yields a 128-dim representation at every point, describing variability in both preceding and following light-curve portions with stellar and light-curve metadata.The forward state summarizes inputs from x0 to xt, while the backward state summarizes inputs from xt to xL.
C.2.1. Bidirectionality: Each minGRU cell contains 11,072 parameters, giving the bidirectional RNN architecture a total of 22,144 parameters.The cell includes the input projection J.

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

EncoTESS is trained to reconstruct noisy light curves probabilistically from context that excludes the target observation, using hidden-state offsets to capture patterns across multiple timescales. Final light-curve encodings concatenate summary statistics of 128-dimensional hidden states into a fixed 1536-dimensional latent representation.

C.3. Model Training: EncoTESS predicts each target flux from light-curve and metadata context while excluding information from the observation being predicted.The maximum context uses the preceding forward hidden state and following backward hidden state, with arbitrary offsets available for longer-term patterns.
C.3. Model Training: A Conditional Normalizing Flow predicts a calibrated full likelihood rather than a single flux value because individual light-curve measurements are highly noisy.This prioritizes recovering general trends over accurately predicting any individual flux measurement.
C.3. Model Training: The model uses a 28,974-dimensional Neural Spline Flow with two transforms, each containing two 64-dimensional ReLU hidden layers and a 23-dimensional linear output.The output corresponds to an 8-bin spline.
C.3. Model Training: Training samples hidden-state offsets from 1 to 2880, spanning 2 minutes to approximately 4 days under constant 2-minute sampling.The offset distribution emphasizes short-term variability while retaining sensitivity to gaps roughly as large as those in TESS light curves.
C.3. Model Training: Training minimizes the average negative log-likelihood across every unmasked observation in each light-curve batch.NLL evaluates the predicted density at the observed flux and is preferred for non-Gaussian likelihoods over metrics such as χ2.
C.4. Computation of LC Encodings: After optimization, EncoTESS computes hidden states for every observation, whose characteristic information is aggregated into fixed-size stellar representations.Each hidden state is 128-dimensional, so the states are summarized rather than used directly as the encoding.
C.4. Computation of LC Encodings: Concatenating hidden-state extrema and moments, endpoint states, rate-of-change statistics, and four sequential-bin means produces a 1536-dimensional encoding Θ for each light curve.The resulting latent dimensions can be interpreted as stellar parameters, although their physical meanings are not directly explicit.

D. LATENT SPACE CORNER PLOT

The latent-space corner plot shows that PC1, and to a lesser extent PC3, carry strong age signal, while PC2 contains distinct clustered subpopulations potentially useful for classification. The top eight PCs are shown for visualization, although more than 13 linear components are needed to preserve the intrinsically approximately 13-dimensional latent space.

D. LATENT SPACE CORNER PLOT: The plot shows the top 8 PCs for visualization, although preserving all information requires > 13 linear PCs because Θ has intrinsic nonlinear dimensionality ≈13.The intrinsic dimensionality was measured using TwoNN.
D. LATENT SPACE CORNER PLOT: PC1 correlates relatively strongly with PC3 and PC5.
D. LATENT SPACE CORNER PLOT: PC2 contains distinct clustered subpopulations absent from the other PCs, potentially enabling classification.
D. LATENT SPACE CORNER PLOT: PC1 carries strong age signal, with weaker age information in PC3.The age gradient is shown across the top eight PCs of Θ′.