Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction

We perform field-level likelihood-free inference of the matter density parameter $Ω_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $Ω_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $σ_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $Ω_m$ with mean relative errors of about $10\%$ in-distribution and $10$--$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $Ω_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.

Understanding galaxy morphology evolution across cosmic time requires models that can generate realistic galaxy populations conditioned on redshift. In this work, we study efficient redshift-conditioned generative modeling for astrophysical image synthesis using diffusion models and pixel-MeanFlow. We first review the connections between score-based diffusion models, Flow Matching, one-step generative models, and modern diffusion samplers. We then evaluate DDPM, DDIM, DEIS-AB2, DPM++2M, and one-step pixel-MeanFlow on the GalaxiesML-64 dataset using morphology-based metrics, including ellipticity, semi-major axis, Sérsic index, and isophotal area. Our results show a clear accuracy-efficiency trade-off: standard DDPM sampling achieves the best distributional fidelity but requires high computational cost, while second-order samplers substantially improve efficiency over DDIM. Pixel-MeanFlow enables single-step generation and achieves competitive performance on several morphology statistics, though it remains weaker than many-step DDPM for fine-grained structure. Our results demonstrate that one-step generative models can recover key galaxy morphology statistics at orders-of-magnitude lower computational cost, opening a path toward efficient conditional simulators for large cosmological surveys and simulation-based scientific inference.

Existing astronomy foundation models provide strong galaxy representations, but adapting them to new survey conditions and survey-specific morphology recognition tasks still requires substantial human supervision. We show that VLM-based VQA systems contain meaningful visual-semantic priors that can serve as weak supervision for downstream morphology classifiers and improve morphology classification under limited human-label budgets. We first introduce a survey-oriented VQA benchmark spanning two representative imaging regimes and evaluate state-of-the-art VLMs on galaxy morphology questions. The results show that these models capture useful morphology signals and informative uncertainty, but are not sufficiently reliable to replace human annotators. Motivated by this finding, we use a general-purpose VLM as a morphology teacher for Zoobot, an astronomy foundation model pretrained on large-scale Galaxy Zoo annotations. Across two survey domains and multiple annotation budgets, the VLM teacher consistently improves Zoobot's downstream morphology classification. These results demonstrate that a general-purpose VLM provides knowledge complementary to an astronomy foundation model and can teach it to better recognize galaxy morphology under limited human supervision. The resulting pipeline is designed for label-efficient adaptation to forthcoming large-scale surveys, including the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and the Nancy Grace Roman Space Telescope. The benchmark and code are publicly available at https://github.com/fw-ic/VLM-morphology-teacher.