# Deep Learning and LLM-based Methods Applied to Stellar Lightcurve
Classification

Yu-Yang Li  Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing 100101, People’s Republic of China  College of Astronomy and Space
Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal
University, Beijing 102206, China  Yu Bai  Key Laboratory of Optical
Astronomy, National Astronomical Observatories, Chinese Academy of Sciences,
20A Datun Road, Chaoyang District, Beijing 100101, People’s Republic of China
College of Astronomy and Space Sciences, University of Chinese Academy of
Sciences, Beijing 100049, China  Institute for Frontiers in Astronomy and
Astrophysics, Beijing Normal University, Beijing 102206, China  Cunshi Wang
Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing
100101, People’s Republic of China  College of Astronomy and Space Sciences,
University of Chinese Academy of Sciences, Beijing 100049, China  Mengwei Qu
State Key Laboratory of Isotope Geochemistry, Guangzhou Institute of
Geochemistry, Chinese Academy of Sciences, Guangzhou 510640,China  College of
Earth and Planetary Sciences, University of Chinese Academy of Sciences,
Beijing 100049, China  Ziteng Lu  School of Foreign Studies,
TonglingUniversity, Tongling, Anhui, 244061, People’s Republic of China
Roberto Soria  College of Astronomy and Space Sciences, University of Chinese
Academy of Sciences, Beijing 100049, China  INAF—Osservatorio Astrofisico di
Torino, Strada Osservatorio 20, I-10025 Pino Torinese, Italy  Sydney Institute
for Astronomy, School of Physics A28, The University of Sydney, Sydney, NSW
2006, Australia  Jifeng Liu  Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road,
Chaoyang District, Beijing 100101, People’s Republic of China  College of
Astronomy and Space Sciences, University of Chinese Academy of Sciences,
Beijing 100049, China  Institute for Frontiers in Astronomy and Astrophysics,
Beijing Normal University, Beijing 102206, China  New Cornerstone Science
Laboratory, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, People’s Republic of China

###### Abstract

Light curves serve as a valuable source of information on stellar formation
and evolution. With the rapid advancement of machine learning techniques, it
can be effectively processed to extract astronomical patterns and information.
In this study, we present a comprehensive evaluation of deep-learning and
large language model (LLM) based models for the automatic classification of
variable star light curves, based on large datasets from the Kepler and K2
missions. Special emphasis is placed on Cepheids, RR Lyrae, and eclipsing
binaries, examining the influence of observational cadence and phase
distribution on classification precision. Employing AutoDL optimization, we
achieve striking performance with the 1D-Convolution+BiLSTM architecture and
the Swin Transformer, hitting accuracies of 94% and 99% correspondingly, with
the latter demonstrating a notable 83% accuracy in discerning the elusive Type
II Cepheids—comprising merely 0.02% of the total dataset. We unveil
StarWhisper LightCurve (LC), an innovative Series comprising three LLM-based
models: LLM, multimodal large language model (MLLM), and Large Audio Language
Model (LALM). Each model is fine-tuned with strategic prompt engineering and
customized training methods to explore the emergent abilities of these models
for astronomical data. Remarkably, StarWhisper LC Series exhibit high
accuracies around 90%, significantly reducing the need for explicit feature
engineering, thereby paving the way for streamlined parallel data processing
and the progression of multifaceted multimodal models in astronomical
applications. The study furnishes two detailed catalogs illustrating the
impacts of phase and sampling intervals on deep learning classification
accuracy, showing that a substantial decrease of up to 14% in observation
duration and 21% in sampling points can be realized without compromising
accuracy by more than 10%.

##  1 Introduction

The phenomenon of light variation is a crucial aspect of astrophysics and has
long been studied in the field of time-domain astronomy. Cepheid variables, a
special kind of variable star, serve a critical role as a universal standard
candle, enabling us to measure the distance to clusters and galaxies with
their period-luminosity relation. Other types of variable stars, including RR
Lyrae, $\delta$ Sct, and $\gamma$ Dor stars, are characterized by their unique
absolute magnitudes, pulsation patterns, each exhibiting diverse period-
luminosity relations. The classification of these pulsating stars has
significantly enriched our understanding of their formation and evolution.
Moreover, it has shed light on the structure and dynamics of binary, n-body
systems and our Galaxy. [1, 2, 3, 4, 5, 6, 7, 8]

Long periods of observations are crucial in order to understand the nature of
variable stars. To carry out these observations, it is important to make wise
use of telescope time that is a valuable resource [9]. One such strategy
involves the use of simulations to create plans that optimally allocate
available telescope time, considering overheads and other factors. Another
strategy employs autonomous agents to optimize the observation of time-varying
phenomena [10]. In this study, we aim to understand the importance tied to
different phases of variables and the classification accuracy provided by
varying cadences. This can help us to establish robust guidelines for future
star gazing observations [11].

A substantial amount of labeled data is required, in order to understand the
significance of phase and cadence for different variable stars. In recent
years, astronomy has entered the era of big data. For example, the Zwicky
Transient Factory (ZTF) [12] at Palomar Observatory scans the sky every two
days with a 1.2m telescope , generating 1TB of raw data each night [13]. The
upcoming SiTian survey [14], aims to monitor over 1,000 $deg^{2}$ of sky every
30 minutes using fifty 1m class Schmidt telescopes, and is expected to produce
around 140TB of processed data each night.

As the volume of data grows, there’s a increasing requirement for efficient
and automated interpretation and analysis methods. Deep learning, a component
of machine learning, has risen as a powerful tool for image and signal
processing [15]. It can learn and extract features from data [16, 15], making
it an ideal solution for managing large, complex datasets. Specifically,
recurrent neural networks (RNNs) have shown great effectiveness in processing
time series data [17], while convolutional neural networks (CNNs) have
demonstrated their superiority in image processing tasks [16, 18]. Moreover,
the transformer architecture, with its attention mechanism [19], has shown
remarkable performance across various applications [20, 21, 22, 23]. RNNs
originally developed by [24], led to Simple RNNs, which were later enhanced by
LSTMs [25] to address long-term dependencies. These were further simplified by
GRUs [26] for computational efficiency. CNNs initially introduced for hand-
written digit recognition [27], and have evolved with architectures like
AlexNet, VGGNet, and ResNet. Recent advancements include EfficientNet [28,
29], which optimizes depth, width, and resolution for model accuracy and
efficiency.

In recent years, Transformer architecture has shown remarkable performance
across a diverse range of applications.Initially introduced to address
sequential data processing tasks [19]. Transformer use self-attention
mechanisms to model relationships with sequences, enabling them to capture
long-range dependencies and relationships between sequence elements. The
success of the Transformer in natural language processing has sparked interest
in their potential application in other domains, such as computer vision and
speech recognition. An example of a vision Transformer is the Swin Transformer
[30, 31], which has optimized the computation of attention mechanism and shown
promising results in various benchmark datasets.

Beyond the traditional reliance on extensive data for transfer learning, it is
imperative to investigate the potential of LLM that incorporate both
substantial datasets and large parameter counts. StarWhisper
111https://github.com/Yu-Yang-Li/StarWhisper is a LLM for astronomy, which has
strong astronomical ability and instruction following ability, and can
complete a series of functions such as knowledge question answering, calling
multi-modal tools, and docking telescope control systems. The StarWhisper LC
Series is initiated with the purpose of leveraging the experience gained from
the prior training of the StarWhisper language model. It seeks to explore and
discuss the potential harnessed from vast data to engender emergent properties
in the analysis of light curve data. LLMs, such as the Gemini 7B model, have
shown promise in adapting to new data types through fine-tuning with specific
prompt templates [32]. MLLMs, like the deepseek-vl-7b-chat, are adept at
handling tasks involving image classification due to their extensive training
on datasets containing chart data [33]. LALMs, such as Qwen-audio,trained on
audio datasets, exhibits exceptional performance in audio classification.
[34].

In this study, we perform a comprehensive evaluation of deep-learning and LLM-
based models for the classification of variable star light curves, using the
data from Kepler and K2 observations. The types of variable stars and the data
pre-processing are presented in Section 2. In Section 3, we utilize various
classification models, including the LSTM, the GRU, the Transformer, the
LightGBM, the EfficientNet, the Swin Transformer and StarWhisper LC serires.
Training methods are introduced in Section 4. We also present model
performance and catalogs of the phase importance and sampling intervals in
Section 5. A discussion is provided in Section 6.

##  2 Data

###  2.1 Kepler and K2

The Kepler spacecraft was launched in 2009 aiming to discover for Earth-like
planets [35]. It was equipped with an optical telescope a 95cm aperture and a
$115.6^{\circ}$ field of view. The advanced technology allowed Kepler to
precisely track light curves from 200,000 different targets. This high
precision resulted in the discovery of over 2,000 planets. For stars with V
band magnitude between 13mag to 14mag, the precision was 100 ppm (parts per
million), while for stars with V band magnitude between 9mag to 10mag, the
precision was 10 ppm. Unfortunately, after four years, half of Kepler’s four
reaction wheels failed, leading to the end of its primary mission. Yet, this
marked the beginning of the K2 mission. The K2 mission used the transit method
to detect changes in light along the ecliptic plane and created catalogs with
photometric precision closely matching that of the original Kepler mission.
The observations of K2 were controlled using the remaining reaction wheels and
thrusters, with each campaign limited to 80 days.

There are two types of light curve available, named Presearch Data
Conditioning (PDC) and Simple Aperture Photometry (SAP) light curves [36].
While SAP light curves retain long-term trends, PDC light curves were
generated by the Kepler Operation Science Center, and are free from systematic
errors. Therefore, we adopt PDC light curves for our analysis. Additionally,
we consider two types of data with different time resolutions: long-cadence
data, with a 30-minute sampling interval, and short-cadence data, with a one-
minute sampling interval. Due to the limited number of short-cadence data, we
focus on the long-cadence light curves. For each light curve, we remove the
quarter-to-quarter differences and convert the flux into relative flux,
similar to the methods used in [37, 38].

###  2.2 Variable Stars

Our training samples are similar to [11], including eclipsing binaries, RR
Lyrae, $\delta$ Scuti, $\gamma$ Dor, and $\delta$ Scuti / $\gamma$ Dor
hybrids. The type II Cepheids are included, in order to make a more universal
sample. Table 1 lists our training sample and corresponding references. The
training samples are seriously biased among different variable types. This
bias often leads to decreased performance, especially in situations few-shot
or small sample scenarios [39, 40]. However, [41] suggest that certain models
may help overcome these challenges, although such cases seem to be the
exception rather than the rule. These biased training samples offer a unique
opportunity to study the algorithm’s dependence on such biases and to
understand how this dependence affects the overall performance and accuracy
when applied to astronomical data.

###  2.3 Pre-processing

A pre-processing method, as described by [11], was adopted to manage and clean
the light curves, with the aim of enhancing their features and expanding the
training data. The lightcurves were segmented into 10-day intervals. Any
segments with gaps exceeding a day were removed, while those with gaps less
than one day were interpolated with a time sequence of 30 minute intervals.

Table 1: Training Sample

Label | Input Catalog | Final Sample | References
---|---|---|---
$\delta$ Sct | 1389 | 111528 | (1), (2), (3), (4), (14), (15)
EB | 2908 | 226937 | (6), (7), (8), (9), (10), (11), (12), (13)
$\gamma$ Dor | 941 | 65786 | (14),(15)
HYB | 1552 | 33751 | (1), (2), (3), (4), (14), (15)
RR | 482 | 9306 | (5)
T2CEP | 3 | 94 | (1), (2), (3), (4), (5)
Total | 7275 | 447402 | (1)-(15)

  * Note

The input catalog column indicates the sources of data that we obtained from
several catalogs. The final sample column represents the final sample size
after applying all the pre-processing procedures. References: (1)[42],
(2)[43], (3)[44], (4)[45], (5)[46], (6)[1], (7)[2], (8)[3], (9)[4], (10)[5],
(11)[6], (12)[7], (13)[47], (14)[48], (15)[49].

Table 2: Period and Observation Time Saving

Star | Period (d) |  $\Delta_{phase}$ (%) |  $t_{phase}$ (%) |  $\Delta_{sampling}$ (%) |  $t_{sampling}$ (%)
---|---|---|---|---|---
RR_251457011 | 0.509 | 1.06 | 41 | 8.63 | 50
RR_251457012 | 0.529 | 3.48 | 71 | 0 | 0
RR_251457013 | 0.542 | 2.47 | 31 | 1.83 | 50
RR_251457014 | 0.593 | 9.99 | 29 | 9.32 | 50
RR_251457015 | 0.574 | 0.53 | 55 | 7.82 | 50
RR_251457016 | 0.510 | 1.30 | 83 | 1.38 | 50
RR_251457020 | 0.478 | 0 | 0 | 0.76 | 50
RR_251457021 | 0.546 | 0.70 | 74 | 4.48 | 80
RR_251457022 | 0.508 | 1.56 | 49 | 0 | 0
RR_251457024 | 0.553 | 0 | 0 | 0 | 0

  * Note

The table shows the period of the stars (in the unit of days) along with the
variation of accuracy and time saved (percentages), for both phase importance
and sampling research.

An alternative approach to time-series data classification involves
categorizing of images that are created from graphically represented light
curves. This is achieved using transfer learning techniques. As highlighted in
their result, the continuous wavelet transform (CWT) method has demonstrated
superior results in imaging light curves.

Figure 1: CWT images of different objects.

The Morlet wavelet was chosen as the core function for the CWT, owing to its
proven effectiveness in analyzing signals that display shifts in amplitude.
This analysis resulted in a collection of images that provide valuable
insights into the time-frequency characteristics of the signals. Importantly,
these images facilitate the identification of patterns, trends, and anomalies,
thus offering a comprehensive understanding of the signals. Figure 1 shows
some variable stars from the training sample.

###  2.4 Lomb-Scargle Periodogram

We employ the Lomb-Scargle algorithm to extract the most significant periods
complete light curves, which are used to study the phase importance of
periodic variables. The Lomb-Scargle algorithm, a variant of the Discrete
Fourier Transform (DFT) developed by [50] and [51], has been specifically
designed for unevenly sampled time-series data. It transforms a time series
into a linear combination of sinusoidal waveforms, simplifying the conversion
from time to frequency domain. We calculate the period by applying the
Lightkurve Collaboration’s LSP method [52]. Some examples are shown in Figure
2.

More specifically, we use a uniform sampling strategy in our set frequency
domain to select an array of frequency points for periodicity analysis. The
periodogram calculation is carried out by assessing the Power Spectral Density
(PSD) at each frequency. This periodogram reveals the intensity of periodic
signals across the spectrum of frequencies. Significant peaks in the
periodogram indicate strong periodic signals. We determine the exact periods
through the reciprocals of these frequencies. Our implementation also includes
considerations for normalization methods and computational strategies. We use
a specific approach to frequency sampling to ensure that the periodogram
computation is both precise and efficient. The results are shown in Table 2.

##  3 Model Construction

In order to classify variable stars from their light curves, we have explored
various deep learning models. The basic architectures of these models are
shown in Figure 3.

###  3.1 CNN and RNN

We explore several advanced LSTM architectures. For Conv1D + BiLSTM, it
combines 1-dimensional convolutional layers with bidirectional LSTM layers.
The convolutional layer is used to extract features from the data [53], while
the bidirectional LSTM layer capture contextual information from both the past
and future time steps [54]. For Conv1D + BiLSTM + Attention, the addition of
an attention mechanism enables the model to focus on specific parts of the
input data, improving performance by giving higher weights to more relevant
parts [19]. This can help improve the accuracy of classification and
facilitate further research on the importance of different phases for
classification [55].

GRU models are a variation of LSTM that are computationally more efficient as
they have fewer parameters, making them easier to train and less prone to
overfitting [26, 56]. Specifically, we use the Conv1D + BiGRU architecture.

In addition to the deep learning approaches, it is also important to consider
the performance of classic machine learning methods for comparison. One such
method is LightGBM, a gradient-boosting decision tree (GBDT) framework that
uses tree-based learning algorithms [57].

###  3.2 Transformer

Transformer are highly effective in managing data dependencies, a critical
aspect of time series analysis. This results in favorable outcomes [58, 59].
Their multiple attention mechanisms are skilled in identifying the most
relevant parts of input data [19]. By combining a 1-dimensional convolutional
layer with a transformer encoder layer, we can effectively capture both global
dependencies and local interactions in the data. This approach addresses the
transformer architecture’s limitation in detectinglocal nuances.

We have adopted the Swin Transformer for few-shot classification tasks (i.e.
T2CEP). Transformers excel in modeling long-range dependencies in computer
vision tasks [60, 61] by focusing directly on an image’s essential parts [19].
The Swin Transformer takes this a step further; it streamlines computation by
limiting attention within small windows while maintaining effectiveness [30,
31].

Table 3: Accuracy and Macro F1-Score

Input Format | Model | Accuracy(All/T2CEP) | Macro F1-Score
---|---|---|---
Time-Series | Conv1D+Transformer | 85%/17% | 0.7
| LightGBM | 87%/25% | 0.71
| BiLSTM+Attention | 93% | 0.76
| Conv1D+BiGRU | 93% | 0.76
| Conv1D+BiLSTM | 94% | 0.77
CWT Image | Efficientnet | 99% | 0.82
| Swin Transformer | 99%/83% | 0.96
Textual Time-Series | LLM-based model | 89% | 0.80
Lightcurve Image | MLLM-based model | 95% | 0.94
Transformed Audio | LALM-based model | 93% | 0.71

  * Note

The table presents the accuracy and macro F1-score for various models,
including the accuracy of some models specifically on T2CEP.

###  3.3 Efficientnet

For a more thorough comparative analysis, we have adopted an advanced CNN
known as the pretrained EfficientNet. This network exceeds its predecessors by
integrating optimization elements for depth, width, and resolution within its
framework. In comparison, previous networks only optimized one or two of these
elements [28, 29]. EfficientNet uses a diverse range of architectural
techniques including depth-wise separable convolutions, squeeze-and-excitation
blocks, and dynamic image scaling. These techniques are validated to boost
performance while reducing computational resource requirements.

###  3.4 StarWhisper LC Series

####  3.4.1 LLM

LLMs, owing to their emergent capabilities, can learn new languages (broadly
defined) through few-shot learning or fine-tuning processes, like lean3 [62].
The Gemini 7B model 222storage.googleapis.com/deepmind-
media/gemini/gemini_1_report.pdf, pre-trained on a vast corpus of text,
exhibits emergent behavior, enabling it to perform tasks not explicitly
covered during its initial training. Therefore, we are contemplating the
integration of specific prompt template as shown in 4, to transform time
series data into a form of language in a broader sense, in order to leverage
these advanced models more effectively.

####  3.4.2 MLLM

Next, we introduce a MLLM trained on the deepseek-vl-7b-chat [63]. MLLMs
expand upon the capabilities of LLMs by incorporating the ability to process
and interpret visual information alongside text. The deepseek-vl-7b-chat
model, with its extensive training on chart data, is particularly well-suited
for tasks involving time series image classification, making it a valuable
addition to the StarWhisper LC series.

####  3.4.3 LALM

The final model in the series is based on audio processing, utilizing the
Qwen-audio [64]. This model has been specifically enhanced for audio
classification tasks, offering a novel approach to time series analysis by
converting time series data into audio signals. A sampling frequency of 500Hz
is used to transform the normalized time-series data into audio signals, which
possess distinct characteristics that aid in classification.

Table 4: Prompt and Output Template

Instruction
---
Given the normalized flux data at 0.02 day intervals (delimited by the triple
backticks), classify the TYPE of light curve. Return the answer in an
Assignment Statement, containing ONE variable: TYPE. Only return the
classification, not the Python code.

    ‘‘‘{flux}‘‘‘

Output
TYPE = ’Label’

  * •

For other LLM-based models, replace “Python code” with “description,” and
“flux” with “image path or audio path.”

##  4 Training

###  4.1 Auto deep learning methods

Auto deep learning methods are a set of techniques that aim to automate the
process of designing, training, and evaluating neural network models. These
methods typically use techniques such as Bayesian optimization [65],
reinforcement learning [66], or evolutionary algorithms [67] to optimize the
model architecture and hyperparameters for the best possible performance.

Bayesian optimization is a powerful approach for hyperparameter tuning and
exploration[68]. It utilizes Gaussian Processes Regression (GPR) or Tree-
structured Parzen Estimators (TPE) to model the probability distribution of
historical data and employs the Sequential Model-Based Optimization (SMBO)
framework for iterative hyperparameter selection.

The SMBO process is an iterative method for hyperparameter optimization that
consists of four main steps [69]. First, a probability distribution model is
built based on the existing tuning history. Next, an acquisition function,
such as Expected Improvement (EI), is employed to select the next
hyperparameter. Following this, the new observation is incorporated into the
existing tuning history. The process is then repeated until the predefined
maximum number of iterations is reached.

In this study, we used Auto deep learning to automate the process of training
and evaluating deep learning models. Specifically, 80% of the data was
allocated for training and the remaining 20% was used as a validation set.
Bayesian optimization allow us to efficiently find the best set of
hyperparameters[70].

###  4.2 LLM-based models training

For LLM, the light curve data was prepared to fit within the model’s context
length limitations and underwent a normalization process. The fine-tuning
process involves all layers of the model using the Qlora technique [71] a
highly efficient fine-tuning method that achieves near-full fine-tuning
performance with significantly reduced memory requirements.

The MLLM’s training involved a comprehensive fine-tuning process that adjusted
both the textual and visual processing components of the model. This approach
is necessary to effectively handle the multimodal nature of the task,
leveraging the model’s pre-trained knowledge of visual patterns for time
series image classification.

For the LALM, the success of the training phase hinge on the conversion of
time series data into audio signals. This innovative approach allow the model
to classify light curves transformed into audio signals, demonstrating the
potential of audio-based analysis in scientific research.

Figure 2: The images of different variable types processed using the Lomb-
Scargle method, with a selected frequency range from 0 to Nyquist frequency.
The final frequency is also indicated in each figure.  Figure 3: Deep learning
models structures for different input formats. It should be noted that not all
branch combination models are adopted due to varying degrees of effectiveness.

##  5 Result

###  5.1 Performance

The confusion matrices (Appendix) serve as the basis for computing numerous
performance. $\rm F_{1}-$score, a balance indicator derived from precision and
recall, is calculated as their harmonic mean. We here calculate the Macro$-\rm
F_{1}-$score [72] to evaluate the model’s overall performance, which averages
the F1 scores across all classes, making it a vital measure when working with
imbalanced data.

For transfer learning, both models achieved an accuracy of 99$\%$. The Swin
Transformer achieved the highest Macro$-\rm F_{1}-$score of 0.96,
demonstrating high effectiveness even with a small sample size. It achieved an
83$\%$ accuracy rate on T2CEP, a class comprising only 94 out of 447,402
samples. For the non-pretrained models, RNN-based models showed efficiency
while maintaining high accuracy levels. The Conv1D+BiLSTM model showed the
best performance with an accuracy of 94$\%$. It achieved a Macro-F1 score of
0.77, comparable to that of the pre-trained Efficientnet. This proves its
ability to manage imbalanced data.

Transfer learning’s good performances are due to preprocessing via the CWT, a
technique that simplifies the process of initial feature extraction. Its
efficiency is further supported by its prior training on a numerous of images,
enhancing its feature extraction capability. However, the HYB category
performs short relative to others, when evaluating classification accuracy for
variable stars. This underperformance could be due to the intrinsic complexity
of the HYB category, resulting in an overlap of features and subsequently
complicating the classification process [73, 11].

The StarWhisper LC series also yielded impressive results in the
classification of light curves, showcasing the robust capabilities of LLM-
based models in scientific data analysis. The LLM, despite the significant
data reduction achieved by trimming the time-series data to input samples of
0.2d and normalizing the data’s precision to one part in a hundred thousand,
attained an accuracy rate of approximately 89%. This demonstrates the model’s
ability to efficiently process and analyze condensed time-series data without
substantial loss of information. The MLLM, which did not utilize CWT
remarkably achieved a 95% accuracy rate, underscoring its inherent strength in
handling multimodal data, including chart data akin to time series image
classification. Furthermore, it exhibits excellent classification performance
on small samples like T2CEP, with an $\rm F_{1}-$score of 0.94, which further
validates the sensitivity of image-based models to small sample sizes. The
LALM’s innovative approach of converting time-series data into audio signals
for classification led to a commendable accuracy rate of 93%, highlighting the
potential of audio-based analysis in scientific research. These results
collectively emphasize the effectiveness and versatility of the StarWhisper LC
series in leveraging transfer learning and LLM-based model for high-accuracy
classification tasks in the realm of astrophysics.

###  5.2 Catalogs

####  5.2.1 Phase Importance

Using the Conv1D + BiLSTM model, we assess the impact on accuracy by obscuring
observation points in a specific phase. We set the zero phase to correspond to
the peak of the light curve. The resulting decrease in the model’s confidence
level for accurate classification helped us measure the importance of each
phase. Table 5 lists the importance with an interval of 0.1 phase. Figure 5,
Figure 6 and Figure 7 reveal that the key features for GDOR, DSCT, and HYB,
are primarily located in the phase interval following the peak flux. For EB
and RR shown in the Figure 8 and Figure 9, the main concentration is detected
in the phase interval during which the flux returns to its peak. According to
the heatmap distribution, significant or dark intervals predominantly occur in
the first half of the EB and RR. In contrast, DSCT and HYB show two distinct
phase intervals localized within them. We discuss the time saving associated
with this and present a catalog in Section 6.

####  5.2.2 Sampling

The observation schedule is significantly influenced by sampling, which itself
is limited by the telescope’s clear aperture, the CCD’s read-out speed, the
scientific object of the survey. We calculated the sampling-importance
relations for the variables with a single prime frequency. We adjusted the
sampling rate by changing the number of points per period. The effect on
classification accuracy is shown in Figure 10.

We found that for EB, accuracy can remain above 75$\%$ even if sampling points
are decreased to one-tenth. For RR and DSCT stars, halving the sampling rate
still maintains an accuracy of around 80$\%$. This can be explained by the
phase importance: except for EB, the key features are located in only a few
specific phases. It is probably that there is a significant decrease in the
prediction model’s accuracy beyond a certain sampling rate. This is likely due
to an increase in the sampling interval, leading to the model’s failure to
capture former phase features. The observed correlation between sampling and
phase importance further substantiates the reliability of the method we
employed.

We also found that at a specific lower sampling interval, some variables
exhibit a decline in accuracy with increasing sampling. We suggest that within
this sampling interval, the specific instrumental noise may have led to a
decline in accuracy, given that accuracy generally increases with higher
sampling rates beyond this range. This suggests a critical sampling threshold
where feature capture is optimized before noise becomes predominant. Table 6
list the accuracies corresponding to different sampling rates.

##  6 Discussion

###  6.1 Observation time Saving

By correlating classification accuracy across variables with phase importance,
we sequentially eliminate multiple phase intervals in ascending order of
significance. This process help us estimate the maximum observational time
that can be saved for each star type. It is suggest that, on average, a 14$\%$
reduction in observation time can be achieved across different variables,
provided the accuracy variation remains within 10$\%$ over a given observation
period. Specifically, RR and EB stars can save an average of 44$\%$ and 29$\%$
of observation time, respectively.

In addition, we link classification accuracy with the number of sampling
points within each period to assess the potential decrease in observation time
by reducing the sampling rate. Given that the accuracy variation within a
single observation period remains under 10$\%$, our findings indicate an
average potential reduction of 21$\%$ in the number of sampling points for
observations. Among these, EB stars can benefit from an average reduction of
54$\%$ in the number of sampling points required for observations. The results
are presented in Table 2.

Our proposed RNN-based models show substantial performance without the need
for image preprocessing. Furthermore, using automated deep learning enables us
to more efficiently identify suitable hyperparameters. Additionally, we take
into consideration the impact of masked points or unobserved points within the
complete phase on classification accuracy. For EB stars with sampling points
reduced to just 10$\%$, and DSCT stars with sampling halved, the accuracy
consistently hovers around 0.75. And RR stars maintain an accuracy of over
0.85 even when its sampling is reduced by half. As a result, our method is apt
for more efficient, and potentially real-time, astronomical time-series
recognition scenarios, such as exoplanets [55] and transients [74].

###  6.2 Learning form imbalanced data

Imbalanced samples are a common occurrence in astronomical data. In this
study, for the first time, we have applied transfer learning models that were
previously trained on a significant volume of image data to augment the
recognition capabilities for these less prevalent variable stars. Notably, the
Swin Transformer and MLLM yield particularly fairly good results.

Additionally, we find that the self-attention mechanism can significantly
enhance the recognition ability to recognize small samples. We will further
consider applying data augmentation, resampling, pre-training, and other
methods in self-attention-based deep learning models, in order to improve
their performance on tasks involving imbalanced data, such as the TESS
variable star.

###  6.3 Time serises as Language

Our research highlights the potential of leveraging the emergent capabilities
of LLM-based models for the processing of light curves, a task that requires
rapid convergence as shown in 4, resistance to overfitting, and minimal
susceptibility to data quality variations [14]. By integrating these models
with additional capability modules, such as visual and audio encoding, we aim
to enhance their performance and applicability in the domain of astronomy.
This approach not only introduces a novel analytical method for astronomical
data but also explore the development of multimodal models that can process a
variety of astronomical inputs.

The optimization of LLMs for inferential tasks, coupled with their capacity
for parallel and rapid data processing [75], underscores their utility in
handling the vast and complex datasets encountered in astronomy field. There
is a promising prospect of training specialized astronomical encoding modules
that build upon the robust foundation of LLMs. Such modules could be tailored
to interpret and analyze astronomical phenomena with a high degree of accuracy
and efficiency.

Future, we will focus on refining the models by adjusting parameters such as
data volume, sampling points, precision, and temporal length. This will enable
us to delve deeper into the feature extraction thresholds of the models and
further enhance their capabilities for astronomy-specific tasks. Moreover, the
potential for applying this methodology to other time series tasks is
significant, offering a versatile path for developing multi-task applications
that operate on a multimodal basis.

Figure 4: Loss curves of LLM-based methods.

###  6.4 SiTian project

The SiTian prototype, introduced in [14], is scheduled to release its internal
data. The data contains information from three bands, and we aim to construct
its light curves using numerical simulations and evaluate their
classifications using deep learning techniques. Given the large volume of
data, striking a balance between prediction time and accuracy is essential.

Highly accurate models, particularly sensitive to smaller samples, can
significantly enhance SiTian’s capabilities in identifying variable stars. The
catalogs we’ve developed related to phase importance and sampling provide
insights into optimal observation intervals and sampling rates during
monitoring. This allows for a calculated tradeoff between model accuracy and
the time costs associated with training and prediction, ensuring efficient and
effective astronomical analyses.

## Acknowledgments

The research presented in this paper was generously funded by the National
Programs on Key Research and Development Project, with specific contributions
from grant numbers 2019YFA0405504 and 2019YFA0405000. Additional support came
from the National Natural Science Foundation of China (NSFC) under grants
NSFC-11988101, 11973054, and 11933004. We also received backing from the
Strategic Priority Program of the Chinese Academy of Sciences, granted under
XDB41000000. Special acknowledgment goes to the China Manned Space Project for
their science research grant, denoted by NO.CMS-CSST-2021-B07.

JFL extends gratitude for the support received from the New Cornerstone
Science Foundation, particularly via the NewCornerstone Investigator Program,
and the honor of the XPLORER PRIZE.

This research incorporates data sourced from the Kepler mission, with its
funding being attributed to the NASA Science Mission Directorate. We sourced
all data for this study from the Mikulsk Archive for Space Telescopes (MAST).
The operation of STScI is overseen by the Association of Universities for
Research in Astronomy, Inc., under the NASA contract NAS5-26555. The MAST’s
support for non-HST data comes through the NASA Office of Space Science,
notably grant NNX09AF08G, and various other grants and contracts.

## Appendix

In Figures 11 through 17, we present the confusion matrices of different
models. The main body of each matrix, represented by varying shades of blue,
illustrates the number of each crossed object in the classification model.

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Figure 5: The importance-phase diagram for GDOR is provided. The upper section
displays the flux variation of specific object, with heatmap illustrating
phase importance. The lower part of the diagram shows the importance-phase for
GDOR. The dispersion observed in the folded light curve might be associated
with the normalization process of the flux.  Figure 6: The importance-phase
diagrams for DSCT are provided. The upper section displays the flux variation
of an example, with heatmaps illustrating phase importance. The lower part of
the diagrams shows the importance-phase for the variable.  Figure 7: The
importance-phase diagrams for HYB are provided. The upper section displays the
flux variation of an example, with heatmaps illustrating phase importance. The
lower part of the diagrams shows the importance-phase for the variable.
Figure 8: The importance-phase diagrams for EB are provided. The upper section
displays the flux variation of specific objects, with heatmaps illustrating
phase importance. The lower part of the diagrams shows the importance-phase
for each variable.  Figure 9: The importance-phase diagrams for RR are
provided. The upper section displays the flux variation of specific objects,
with heatmaps illustrating phase importance. The lower part of the diagrams
shows the importance-phase for each variable.  Table 5: Phase Importance
Catalog

Star/Focused phase | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9
---|---|---|---|---|---|---|---|---|---|---
DSCT_001026294 | 0.9996 | 0.9934 | 1.0000 | 1.0000 | 0.9995 | 0.9986 | 0.9986 | 0.9692 | 0.6977 | 0.0000
DSCT_001162150 | 0.1585 | 0.1310 | 1.0000 | 0.7921 | 0.3214 | 0.1172 | 0.1245 | 0.0323 | 0.0184 | 0.0000
DSCT_001163943 | 0.3598 | 0.1016 | 1.0000 | 0.4261 | 0.0467 | 0.1701 | 0.0711 | 0.0031 | 0.0393 | 0.0188
DSCT_001294670 | 0.3018 | 0.3963 | 1.0000 | 0.6999 | 0.0631 | 0.0211 | 0.0327 | 0.0001 | 0.0034 | 0.0004
DSCT_001430590 | 0.1579 | 0.2669 | 1.0000 | 0.5738 | 0.4043 | 0.0964 | 0.0573 | 0.0266 | 0.0102 | 0.0041
DSCT_001434660 | 0.0923 | 0.1533 | 1.0000 | 0.6423 | 0.6384 | 0.1624 | 0.0591 | 0.0247 | 0.0037 | 0.0142
DSCT_001570023 | 0.0688 | 0.1608 | 1.0000 | 0.5841 | 0.4261 | 0.0822 | 0.0513 | 0.0040 | 0.0000 | 0.0027
DSCT_001571717 | 0.9996 | 0.9994 | 1.0000 | 0.9999 | 1.0000 | 0.9997 | 1.0000 | 0.9942 | 0.9730 | 0.0000
DSCT_001572768 | 0.0000 | 0.9147 | 0.9228 | 0.9773 | 0.9816 | 0.8840 | 0.8007 | 0.8885 | 0.4628 | 0.4773
DSCT_001575977 | 0.1454 | 0.6365 | 1.0000 | 0.8420 | 0.2347 | 0.3248 | 0.3394 | 0.0303 | 0.0057 | 0.0241

  * •

Phase-importance catalog illustrates the relationship between importance and
phase, with the first ten rows shown.

Table 6: Sampling Catalog

Star/Sampling Rate | 0.02d | 0.04d | 0.06d | 0.08d | 0.1d | 0.12d | 0.14d | 0.16d | 0.18d | 0.2d
---|---|---|---|---|---|---|---|---|---|---
DSCT_001026294 | 0.9288 | 0.4412 | 0.0002 | 0.0003 | 0.0000 | 0.0000 | 0.0434 | 0.0847 | 0.0998 | 0.0141
DSCT_001162150 | 0.9817 | 0.9598 | 0.1599 | 0.6392 | 0.3082 | 0.1531 | 0.4663 | 0.2866 | 0.1713 | 0.1649
DSCT_001163943 | 0.9891 | 0.7806 | 0.6678 | 0.5106 | 0.5077 | 0.6081 | 0.6654 | 0.6412 | 0.5840 | 0.4549
DSCT_001294670 | 0.9985 | 0.9980 | 0.9521 | 0.7222 | 0.3226 | 0.6149 | 0.5517 | 0.5106 | 0.5157 | 0.2001
DSCT_001430590 | 0.9935 | 0.9918 | 0.2952 | 0.6864 | 0.6574 | 0.2160 | 0.1984 | 0.5479 | 0.2953 | 0.3322
DSCT_001434660 | 0.9746 | 0.9851 | 0.8613 | 0.3703 | 0.4243 | 0.3810 | 0.5342 | 0.2130 | 0.3090 | 0.2803
DSCT_001570023 | 0.9944 | 0.9897 | 0.8082 | 0.8866 | 0.4413 | 0.2945 | 0.5183 | 0.4653 | 0.2904 | 0.1887
DSCT_001571717 | 0.9656 | 0.0958 | 0.0018 | 0.0159 | 0.0000 | 0.0001 | 0.3438 | 0.0925 | 0.0448 | 0.0198
DSCT_001572768 | 0.9253 | 0.3443 | 0.1441 | 0.1154 | 0.1095 | 0.0479 | 0.0768 | 0.0454 | 0.1152 | 0.1194
DSCT_001575977 | 0.9839 | 0.7853 | 0.6452 | 0.3186 | 0.3033 | 0.3250 | 0.2376 | 0.3029 | 0.2770 | 0.2040

  * •

Sampling catalog illustrate the relationship between accuracy and sampling
rate, with the first ten rows shown here

Figure 10: The influence of each period sampling point on model accuracy.
Figure 11: The confusion matrix of Conv1D+Transformer model are presented,
including T2CEP class. The diagonal elements represent the correct
predictions, along with the percentages of correctly classified observations
for each true class.  Figure 12: The confusion matrix of LIGHTGBM model are
presented, including T2CEP class. The diagonal elements represent the correct
predictions, along with the percentages of correctly classified observations
for each true class.  Figure 13: The confusion matrix of BiLSTM+Attention
model. The diagonal elements represent the correct predictions, along with the
percentages of correctly classified observations for each true class.  Figure
14: The confusion matrix of Conv1D+GRU model. The diagonal elements represent
the correct predictions, along with the percentages of correctly classified
observations for each true class.  Figure 15: The confusion matrix of
Conv1D+BiLSTM model. The diagonal elements represent the correct predictions,
along with the percentages of correctly classified observations for each true
class.  Figure 16: The confusion matrix of Efficientnet model. The diagonal
elements represent the correct predictions, along with the percentages of
correctly classified observations for each true class.  Figure 17: The
confusion matrix of Swin Transformer model are presented, including T2CEP
class. The diagonal elements represent the correct predictions, along with the
percentages of correctly classified observations for each true class.  Figure
18: The confusion matrix of LLM method in StarWhisper LC.  Figure 19: The
confusion matrix of MLLM method in StarWhisper LC.  Figure 20: The confusion
matrix of LALM in StarWhisper LC.