RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
The Complex Gradient Operator and the CR-Calculus
9 Pith papers cite this work, alongside 382 external citations. Polarity classification is still indexing.
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Pith papers citing it
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external citations · Pith
abstract
A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-order considerations are examined in some detail filling a gap in the pedagogic literature.
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Wirtinger-based Jacobian yields explicit singularity condition extended to all bus types, with bus-wise index C_W where min C_W,i > 1 certifies nonsingularity and gives a fast stability margin.
Complex-valued networks show task-dependent gains over real baselines on phase-sensitive data like PSK but not QAM, with large benchmark gaps often caused by hyperparameter instability rather than inherent superiority.
Framework transforms complex chance-constrained problems into convex SOCPs for individual constraints and uses copulas for joint constraints under moment, support, and data-driven ambiguity sets, demonstrated on beamforming.
Unified framework for complex zero-sum games with chance constraints that converts probabilistic constraints into convex second-order cone programs under various distribution assumptions.
Preconditioned ULA with exact likelihood enables faster, higher-quality posterior sampling for Cartesian and non-Cartesian MRI reconstructions than annealed sampling or DPS.
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
CCV-QAOA is a new complex-valued continuous-variable variant of QAOA that solves real and complex multivariate optimization problems via a variational framework.
Complex SGD using Wirtinger calculus achieves convergence guarantees paralleling the real-valued setting without analyticity assumptions, and directional bias results extend to complex kernel regression.
citing papers explorer
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Robust Uniform Recovery of Structured Signals from Nonlinear Observations
RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
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A Wirtinger Power Flow Jacobian Singularity Condition for Voltage Stability in Converter-Rich Power Systems
Wirtinger-based Jacobian yields explicit singularity condition extended to all bus types, with bus-wise index C_W where min C_W,i > 1 certifies nonsingularity and gives a fast stability margin.
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When do complex-valued neural networks help? A study of representation, geometry, and optimization
Complex-valued networks show task-dependent gains over real baselines on phase-sensitive data like PSK but not QAM, with large benchmark gaps often caused by hyperparameter instability rather than inherent superiority.
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Distributionally Robust Complex Chance-Constrained Optimization
Framework transforms complex chance-constrained problems into convex SOCPs for individual constraints and uses copulas for joint constraints under moment, support, and data-driven ambiguity sets, demonstrated on beamforming.
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Robust Chance Constrained Complex Zero-Sum Games
Unified framework for complex zero-sum games with chance constraints that converts probabilistic constraints into convex second-order cone programs under various distribution assumptions.
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Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm
Preconditioned ULA with exact likelihood enables faster, higher-quality posterior sampling for Cartesian and non-Cartesian MRI reconstructions than annealed sampling or DPS.
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Complex Field Formulation of the Quantum Estimation Theory
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
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A Complex-Valued Continuous-Variable Quantum Approximation Optimization Algorithm (CCV-QAOA)
CCV-QAOA is a new complex-valued continuous-variable variant of QAOA that solves real and complex multivariate optimization problems via a variational framework.
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Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces
Complex SGD using Wirtinger calculus achieves convergence guarantees paralleling the real-valued setting without analyticity assumptions, and directional bias results extend to complex kernel regression.