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The intrinsic alignments (IA) of galaxies, a key contaminant in weak lensing analyses, arise from correlations in galaxy shapes driven by tidal interactions and galaxy formation processes. Accurate IA modeling is essential for robust cosmological inference, but current approaches rely on perturbative methods that break down on nonlinear scales or on expensive simulations. We introduce IAEmu, a neural network-based emulator that predicts the galaxy position-position ( $\xi$), position-orientation ( $\omega$), and orientation-orientation ( $\eta$) correlation functions and their uncertainties using mock catalogs based on the halo occupation distribution (HOD) framework. Compared to simulations, IAEmu achieves ~3% average error for $\xi$and ~5% for $\omega$, while capturing the stochasticity of $\eta$without overfitting. The emulator provides both aleatoric and epistemic uncertainties, helping identify regions where predictions may be less reliable. We also demonstrate generalization to non-HOD alignment signals by fitting to IllustrisTNG hydrodynamical simulation data. As a fully differentiable neural network, IAEmu enables $ $10,000$$ speed-ups in mapping HOD parameters to correlation functions on GPUs, compared to CPU-based simulations. This acceleration facilitates inverse modeling via gradient-based sampling, making IAEmu a powerful surrogate model for galaxy bias and IA studies with direct applications to Stage IV weak lensing surveys. 

We investigate the problem of designing differentially private (DP), revenue- maximizing single item auction. Specifically, we consider broadly applicable settings in mechanism design where agents’ valuation distributions are indepen- dent, non-identical, and can be either bounded or unbounded. Our goal is to design such auctions with pure, i.e., (ω, 0) privacy in polynomial time.