Differentiable Optimization

Developed modular convex optimization layer that enables differentiation for any forward solver with seamless integration into neural networks and bi-level optimization tasks, addressing limitation in existing methods that rely on specific forward solvers.

AI-driven Protein Structure Reconstruction

Leading development of PyTorch-based open-source cryo-EM reconstruction software from scratch. Integrating the software to AI foundation models for downstream biology tasks, enabling enhanced protein structure prediction.

Statistical Model of Crystallographic Disorder

Developed statistical parametric model for analyzing positional and substitutional disorder in crystallography.

Coupling Structural and Functional Brain Connectome

Developed model for jointly analyzing brain structure connectome (DT-MRI) and the temporal dynamics of individual brain regions (fMRI)

Differentiation Through Black-Box Quadratic Programming Solvers

Connor W. Magoon*, Fengyu Yang*, Noam Aigerman, Shahar Z. Kovalsky (* equal contribution)

NeurIPS 2025

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices. To address this limitation, we introduce dQP, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver. A key insight we leverage to achieve modularity is that, once the active set of inequality constraints is known, both the solution and its derivative can be expressed using simplified linear systems that share the same matrix. This formulation fully decouples the computation of the QP solution from its differentiation. Building on this result, we provide a minimal-overhead, open-source implementation that seamlessly integrates with over 15 state-of-the-art solvers. Comprehensive benchmark experiments demonstrate dQP’s robustness and scalability, particularly highlighting its advantages in large-scale sparse problems.

[Code] [Paper]

dOPT: Differentiating Conic Optimization via Geometric Reduction

Fengyu Yang, Connor W. Magoon, Tyler Watts, Shahar Z. Kovalsky

arXiv preprint 2026

dOPT provides a solver-independent approach to differentiating conic optimization problems. At a computed solution, it constructs a smaller equality-constrained quadratic problem that retains the original solution's first-order sensitivity. Gradients are obtained through one symmetric linear solve, with reductions for convex nonlinear, quadratic, second-order cone, and semidefinite programs. Experiments demonstrate accurate gradients and improved backward-pass scalability.

[Paper]

A Generative Foundation Model for Cryo-EM Densities

Yilai Li, Jing Yuan, Yi Zhou, Zhenghua Wang, Suyi Chen, Fengyu Yang, Haibin Ling, Shahar Z. Kovalsky, Xiaoqing Zheng, Quanquan Gu

bioRxiv preprint 2025

cryoFM learns a generative prior from high-quality cryo-EM density maps using flow matching. A Bayesian framework combines this prior with experimental constraints to restore and refine maps affected by noise, uneven sampling, and reconstruction artifacts. The model supports posterior sampling and conditional post-processing, improving map interpretability across varied experimental settings.

[Paper]