AutoClassMK: A public neural network for automatic 2D MK classification of normal stars in basic Python

Technical Summary of AutoClassMK

Problem Statement
The paper addresses the need for transparent, automated classification of normal stellar spectra within the Morgan-Keenan (MK) system. While neural networks (NNs) have become increasingly important in astronomy, their "opaque" nature often obscures the underlying mechanics. The authors aim to demystify the basic methodology of simple NNs, specifically back-propagation, by providing a fully functional, transparent implementation for 2D MK classification (Spectral Class and Luminosity Class) that relies entirely on basic Python and NumPy, avoiding specialized deep learning libraries for the core logic.

Methodology
The authors developed AutoClassMK, a five-layer, fully-connected (dense), double-headed neural network.

• Data Augmentation and Training Sets:

  • The training set was constructed by augmenting the libr18 MK atlas (Gray & Corbally 2014). To ensure every combination of Spectral Class (SC) and Luminosity Class (LC) was represented, the authors simplified the LC scheme: LC II and IV were re-labeled as III and V, respectively, and LC Ia/Ib as I.
  • Each of the 122 primary spectra in the libr18 atlas was augmented into 300 noisy variations (totaling 36,600 training samples). These variations simulated realistic observational errors, including:
    • Random zeroth- and first-order horizontal registration errors (wavelength/pixel alignment).
    • Random Doppler shifts.
    • Errors in continuum rectification (zeroth, first, and second-order polynomial fitting).
    • Variations in spectral broadening (simulating macroturbulence and rotation via Gaussian convolution kernels).
    • Poisson noise (signal-to-noise ratio ~70, deliberately underestimated to train the network on noisier data).
  • An independent test set of 2,910 spectra was generated from the libr18 27 atlas using similar augmentation (30 variations per spectrum).

• Network Architecture:

  • Input: 1,600 neurons, corresponding to normalized flux values across 1,600 pixels (representing the 3800–4600 Å range).
  • Hidden Layers: Three fully-connected layers with 768, 256, and 64 neurons, respectively.
  • Activation: The network utilizes either Rectified Linear Units (RELU) or Gaussian Error Linear Units (GELU).
  • Output (Double-Headed): The final layer bifurcates into two parallel linear transformations:
    • SC Head: 31 neurons (for 31 spectral classes).
    • LC Head: 3 neurons (for the simplified luminosity classes I, III, and V).
  • Loss and Optimization: The network employs Softmax activation at the output heads to generate probability distributions. Training minimizes Cross-Entropy (CE) loss using Mini-batch Stochastic Gradient Descent (SGD). The gradient calculation relies on the derivative of the loss with respect to the logits ($\vec{p} - \vec{l}$).

• Implementation:

  • The core algorithm is written in basic Python and NumPy, explicitly detailing matrix multiplications, bias updates, and back-propagation steps.
  • A secondary implementation in PyTorch was created to enable CUDA GPU execution and provide further insight, utilizing the same architecture.

Key Results

• Convergence: The network converged within approximately 100 iterations. The Cross-Entropy loss asymptotically approached ~0.018 for SC and ~0.002 for LC.
• Performance on Test Set (2,910 samples):
  • Luminosity Classification (LC): Achieved high precision (0.97), recall (0.87), and an F1 score of 0.97. The network correctly classified all 87 LC V stars and 78 of 81 LC I stars in the specific libr18 225 test subset.
  • Spectral Classification (SC): Achieved an average F1 score of 0.86, with precision and recall around 0.88 and 0.87, respectively.
• Generalization: When tested on augmented spectra from the libr18 225 atlas (85 spectra, 255 total variations), the predicted spectral class was generally within one sub-class of the true class. The network struggled most with distinguishing LC III from LC V, misclassifying 13 of 87 LC III stars as LC V.

Significance and Claims
The primary significance of AutoClassMK, as claimed by the authors, is its transparency and educational value. By avoiding specialized libraries for the core network operations, the code serves as a "de-mystified" starting point for students to understand the mechanics of back-propagation and neural network training. The authors position the work not as a state-of-the-art solution surpassing complex Convolutional Neural Networks (CNNs), but as a robust, simple, and fully inspectable baseline for 2D MK classification. The paper emphasizes that the network successfully learns to recognize noisy, mis-calibrated spectra, demonstrating the utility of simple NNs for this specific empirical classification task. All code, training sets, and test sets are made publicly available via the OpenStars website.