The shear-to-cosmology paradigm

Context. Precise cosmological inference from next-generation weak-lensing surveys requires non-Gaussian information beyond two-point statistics, while conventional field-level analyses based on convergence reconstruction can introduce additional systematics. Aims. This work aims to develop a scalable and robust framework that directly maps shear fields to cosmological parameters, exploiting non-Gaussian information while avoiding convergence reconstruction to improve constraints from stage-IV weak-lensing surveys. Methods. We propose a hybrid machine-learning (ML) framework that combines field-level inference (FLI) with simulation-based inference (SBI). The FLI network performs field-level compression by extracting informative, non-Gaussian features directly from shear field, which are then passed to SBI to model complex posteriors. To mitigate noise from intrinsic galaxy shapes, we further developed a blind, training-free, PCA-based shear denoising method. Results. Using CSST-like mock catalogs, we show that shear-based inference achieves an approximately twofold improvement in FoM over convergence-based approaches. Furthermore, within the shear-based framework, the combination of PCA denoising and ML compression yields a 36.4% FoM improvement relative to standard two-point statistics. Conclusions. This work establishes a scalable framework for shear-based cosmological inference that unlocks field-level non-Gaussian information and significantly improves constraints for stage-IV weak-lensing surveys.