Optimizing Deep Learning Photometric Redshifts for the Roman Space Telescope with HST/CANDELS

Technical Summary: Optimizing Deep Learning Photometric Redshifts for the Roman Space Telescope with HST/CANDELS

Problem Statement
The Nancy Grace Roman Space Telescope will generate vast amounts of high-resolution, deep near-infrared imaging, necessitating accurate photometric redshift (photo-z) estimates for hundreds of millions of galaxies to study cosmology, galaxy evolution, and transients. While deep learning (DL) methods utilizing pixel-level information have demonstrated superior performance over traditional template-fitting and classical machine learning (ML) methods for low-redshift, ground-based imaging, their efficacy on faint, high-redshift ($z \sim 3$) space-based data remains untested. A critical challenge is the scarcity of spectroscopic redshift (spec-z) labels for faint sources; Roman's imaging will far outpace its spectroscopic follow-up. Consequently, there is a need to determine if DL algorithms can effectively leverage the abundance of unlabeled images alongside limited labeled data to achieve optimal photo-z precision in this regime.

Methodology
The authors utilized the Hubble Space Telescope (HST) CANDELS survey as a proxy for Roman data, selecting 99,505 sources with reliable redshift labels ($z_{ref}$) derived from spectroscopy, grism data, and multi-band photometry. The dataset was split into labeled (training, validation, test) and unlabeled subsets. The study compared four distinct approaches:

1. Classical Baselines:

   • Template Fitting: LePHARE, fitting observed photometry to spectral energy distribution (SED) templates.
   • ML Photometry: A fully-supervised Multi-Layer Perceptron (MLP) trained on integrated photometric colors and magnitudes.

2. Deep Learning Approaches:

   • Fully-Supervised CNN: A ConvNeXt architecture trained solely on labeled images to predict redshift directly from pixel data.
   • Self-Supervised CNN: A two-stage approach using contrastive learning (MoCo) to pre-train on all unlabeled images to learn latent representations, followed by fine-tuning on the labeled subset for redshift prediction.
   • Semi-Supervised CNN (PITA): A novel "Photo-z Inference with a Triple-task Algorithm" that jointly optimizes three loss functions simultaneously:
     • Contrastive Loss ($L_{contrastive}$): Learned from all images (labeled and unlabeled) to capture morphological features.
     • Color Loss ($L_{color}$): Learned from all images to ensure the latent space encodes photometric colors.
     • Redshift Loss ($L_{z}$): Learned only from labeled images to align the latent space with redshift values.

The authors employed Uniform Manifold Approximation and Projection (UMAP) to visualize the latent spaces generated by the self-supervised and semi-supervised models, analyzing how well these spaces encoded magnitude, color, morphology, and redshift.

Key Results

• Performance Metrics: The semi-supervised PITA algorithm achieved the best performance across all metrics (bias, normalized median absolute deviation $\sigma_{NMAD}$, and outlier fraction $f_{outlier}$) for both bright ($m_{F160W} < 22$) and faint ($m_{F160W} < 25$) sources. Compared to the photometry-MLP baseline, PITA reduced bias by 34%, $\sigma_{NMAD}$ by 14%, and $f_{outlier}$ by 17% for the full test set, with even greater improvements for bright sources.
• Deep Learning vs. Photometry: The fully-supervised CNN outperformed both template-fitting and photometry-only ML methods, confirming that pixel-level information contains additional redshift-relevant data beyond integrated flux, even for faint, high-redshift galaxies.
• Failure of Pure Self-Supervision: The self-supervised contrastive learning approach, while successful in previous low-redshift studies, underperformed relative to the fully-supervised CNN in this high-redshift regime. UMAP visualizations revealed that the self-supervised latent space primarily encoded magnitude and size (morphology) but failed to capture smooth gradients of color and redshift, leading to significant fluctuations in photo-z inference.
• Scalability with Label Scarcity: PITA demonstrated robust performance even when the size of the labeled training set was significantly reduced. Unlike fully-supervised models which degrade rapidly with fewer labels, PITA maintained superior accuracy by leveraging the unlabeled data to learn informative features (via contrastive and color losses) while using the sparse labels to align the latent space for regression.

Significance and Claims
The paper claims that for the Roman Space Telescope, where spectroscopic labels will be sparse for the majority of sources (especially at high redshift and faint magnitudes), semi-supervised deep learning is the optimal strategy. The authors argue that purely self-supervised methods may fail to encode the specific physical properties (color and redshift) necessary for photo-z inference in deep, space-based datasets because the dominant variance in pixel data is driven by brightness and morphology rather than color.

By introducing the PITA algorithm, the authors demonstrate that incorporating domain knowledge—specifically, the explicit prediction of photometric colors alongside redshift—guides the latent space to be physically informative. This allows for smooth interpolation between sparse training redshifts, enabling accurate photo-z estimates for both bright (label-rich) and faint (label-scarce) sources. The study concludes that future surveys should utilize semi-supervised approaches that combine unlabeled image data with domain-specific constraints (like color) to maximize the scientific return from deep imaging missions.