[Paper Review] Unsupervised Learning for Stellar Spectra with Deep Normalizing Flows

Ioana Ciucă, Yuan-Sen Ting|arXiv (Cornell University)|Jul 6, 2022

Blind Source Separation Techniques4 citations

TL;DR

This paper introduces Mendis, an unsupervised deep generative model based on normalizing flows (Neural Spline Flows and GLOW) that learns the complex, high-dimensional distribution of stellar spectra without requiring labeled stellar parameters. By enabling exact likelihood evaluation and modeling of pixel-wise correlations, Mendis detects outliers—such as CEMP stars, rapidly rotating stars, and stripped stars—without prior labeling, offering a robust, interpretable method for discovering unknown atomic transitions and rare stellar objects in large spectroscopic surveys.

ABSTRACT

Stellar spectra encode detailed information about the stars. However, most machine learning approaches in stellar spectroscopy focus on supervised learning. We introduce Mendis, an unsupervised learning method, which adopts normalizing flows consisting of Neural Spline Flows and GLOW to describe the complex distribution of spectral space. A key advantage of Mendis is that we can describe the conditional distribution of spectra, conditioning on stellar parameters, to unveil the underlying structures of the spectra further. In particular, our study demonstrates that Mendis can robustly capture the pixel correlations in the spectra leading to the possibility of detecting unknown atomic transitions from stellar spectra. The probabilistic nature of Mendis also enables a rigorous determination of outliers in extensive spectroscopic surveys without the need to measure elemental abundances through existing analysis pipelines beforehand.

Motivation & Objective

• Address the limitation of supervised learning in stellar spectroscopy, which restricts discovery to known label spaces and hinders the detection of unknown outliers.
• Overcome the shortcomings of traditional unsupervised methods like PCA and VAEs, which lack exact likelihood evaluation and flexible conditional modeling.
• Develop a probabilistic, invertible model that captures complex spectral correlations and enables conditional generation of spectra given stellar parameters.
• Enable automated, label-agnostic outlier detection in massive spectroscopic surveys by evaluating the likelihood of new spectra under the learned distribution.
• Uncover hidden atomic transitions by analyzing learned pixel correlations in the spectral data, even without prior knowledge of elemental abundances.

Proposed method

• Employ normalizing flows—specifically Neural Spline Flows and GLOW—within a deep generative model to learn the invertible, bijective transformation from a simple Gaussian base distribution to the complex distribution of stellar spectra.
• Train the model on 20,000 synthetic APOGEE-like high-resolution spectra (R ≈ 22,000) generated from Kurucz atmospheric models with controlled variations in T_eff, log g, [Fe/H], and 20+ elemental abundances.
• Introduce a 25 K scatter in T_eff, 0.1 dex in log g, and 0.01 dex in [Fe/H] to simulate observational uncertainty and improve robustness.
• Use the invertibility of normalizing flows to compute exact log-likelihoods for any spectrum, enabling principled out-of-distribution detection.
• Leverage the model’s ability to generate conditional spectra by conditioning on stellar parameters, allowing exploration of the spectral distribution under different physical conditions.
• Analyze learned correlation structures between spectral pixels by computing the Jacobian of the flow, revealing which wavelength pairs are correlated due to shared elemental transitions.

Experimental results

Research questions

• RQ1 Can normalizing flows model the complex, high-dimensional distribution of stellar spectra more effectively than PCA or VAEs, especially in capturing pixel-level correlations?
• RQ2 To what extent can an unsupervised model like Mendis detect rare or extreme stellar objects (e.g., CEMP stars, rapidly rotating stars) without relying on precomputed labels?
• RQ3 Can the probabilistic framework of normalizing flows uncover unknown atomic transitions by identifying correlated features in the spectral data?
• RQ4 How robust is the likelihood-based outlier detection in Mendis when applied to spectra with unknown or extreme physical properties?
• RQ5 Can the learned spectral distribution serve as a prior for downstream tasks such as semi-supervised learning or domain adaptation in stellar spectroscopy?

Key findings

• Mendis successfully learns the distribution of synthetic stellar spectra with high fidelity, generating spectra that are visually indistinguishable from real training spectra.
• The model accurately captures pixel-wise correlations across the spectrum, revealing that correlated features correspond to transitions from the same chemical element, even when elemental abundances are unknown.
• Out of distribution detection via likelihood evaluation successfully identifies known extreme stellar types—such as CEMP stars, rapidly rotating stars, and stripped stars—as low-likelihood samples, despite their visual similarity to training spectra.
• The likelihood of outlier spectra is significantly lower than that of in-distribution spectra, demonstrating the method’s robustness in triaging rare or unusual objects without prior labeling.
• The model maintains accurate correlation structures even when trained on noisy, degraded spectra with realistic signal-to-noise ratios (SNR = 300), indicating strong generalization to observational conditions.
• The method enables discovery of unknown atomic transitions by identifying correlated pixel pairs in the spectral data, providing a data-driven alternative to ab initio quantum mechanical calculations.