Complex-Valued Neural Networks

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Overview

Complex-valued neural networks represent activations and weights as complex numbers, letting magnitude and phase interact directly rather than treating real and imaginary parts as unrelated features. Common approaches include complex convolutional and recurrent networks, unitary or phase-coherent Transformers, state-space models, and holomorphic or physics-informed networks, trained with tools such as Wirtinger derivatives. They are used for phase-rich tasks including RF and OFDM analysis, PolSAR classification, audio and EEG processing, quantum-state modeling, and prediction of physical dynamics and PDEs. Gains are most evident when phase, symmetry, or known physical structure matters, but advantages over compute- and tuning-matched real networks are not universal; robustness to phase perturbations and reliable optimization remain challenges.

Latest papers

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43 papers3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

  1. Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions

    Oct 27, 2026Kehan WangComplex-Valued Neural NetworksStochastic Differential Equations

    School of Data Science, The Chinese University of Hong Kong, Shenzhen, China

  2. Proofs of strong forms of the Bovdi--Geche universality conjecture and a complex analogue

    Oct 26, 2026Victor Bovdi, Ambrus PalUniversal ApproximationNeural Network Approximation Theory

  3. Enriched Holomorphic Neural Networks for 2D and 3D Laplace Problems

    Oct 8, 2026Kalp Shah, Andrei Vlad Nicula, Mihnea Andrei Bârsan +4Neural PDE SolversPDE Solving

    University of Amsterdam · Technical University of Denmark

  4. CNet: A Complex-Valued Deep Learning Framework with Wirtinger Autodifferentiation and FFT--Hadamard Convolution

    Oct 6, 2026Marcel CrasmaruComplex-Valued Neural NetworksAutoregressive Language Modeling

  5. Reinforcement Learning with Complex (valued) Memories

    Sep 29, 2026Sathya Kamesh Bhethanabhotla, Efstratios Gavves, André BiedenkappPartially Observable RLRecurrent Neural Networks

    University of Freiburg

  6. AURA: Angular Update Rate Adaptation for training complex-valued neural networks

    Sep 22, 2026Enrico Ballini, Allan Peter Engsig-Karup, Tito AndriolloNeural Network OptimizationComplex-Valued Neural Networks

    Aarhus University, Aarhus, Denmark. · Technical University of Denmark, Kongens Lyngby, Denmark.

  7. Complex-valued Phase-Coherent Transformers

    Sep 18, 2026Leona HiokiTransformerComplex-Valued Neural Networks

  8. CRFCAN: A Complex-Valued Cross-Domain Residual Network for Joint Channel and Phase Noise Estimation in Sub-THz OFDM Systems

    Sep 10, 2026Ruilin Wang, Xiaodai DongComplex-Valued Neural NetworksWireless Communications

    Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8P 5C2, Canada

  9. ECA-BLS: An Efficient Complex-Augmented Broad Learning System

    Aug 30, 2026A. Rahaman, A. Quadir, M. Sajid +2Complex-Valued Neural Networks

    Department of Mathematics Indian Institute of Technology Indore Indore, India

  10. Kähler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold

    Aug 20, 2026Andrew GracykRiemannian OptimizationGradient Descent

    Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

  11. Ghost Features and Spooky Transfer Learning for Hypercomplex-Valued Neural Networks

    Aug 7, 2026Guilherme Vieira Neto, Marcos Eduardo ValleComplex-Valued Neural NetworksTransfer Learning

    Universidade Estadual de Campinas (UNICAMP), Brazil

  12. IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data

    Jul 24, 2026Masashi Sode, Gianmarco PintonSelf-Supervised Pre-TrainingJoint-Embedding Predictive Architecture

    Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill and North Carolina State University, Chapel Hill, NC 27599 USA

  13. Physics-Aware Complex-Valued State Space Model with Scattering-Prior Feature Modulation for PolSAR Image Classification

    Jul 22, 2026Fangyan Zhang, Fan Zhang, Shiqi Zhou +3Complex-Valued Neural NetworksVisual SSMs

    The College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, China · The School of Information Science and Engineering, Yunnan University, Kunming, China · The Department of Signal Theory and Communications, Polytechnic University of Catalonia, Barcelona, Spain

  14. PolarBM: Complex-valued Boltzmann Machine for Modeling Audio Signals in Polar and Log-polar Coordinates

    Jul 14, 2026Toru Nakashika, Kohei YatabeUnsupervised Representation LearningComplex-Valued Neural Networks

    Graduate School of Informatics and Engineering, the University of Electro-Communications, Tokyo 182-8585, Japan · Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan

  15. Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics

    Jul 5, 2026Muhammad Idrees Khan, Hua-Dong YaoComplex-Valued Neural NetworksOperator Learning

    Department of Mechanical Engineering, Chalmers University of Technology Gothenburg 41296, Sweden

  16. Dualformer: Efficient Feature Extractor for Complex-valued Blind Communication Signal Analysis

    Jun 30, 2026Yurui Zhao, Xiang Wang, Jingreng Lei +3TransformerAutomatic Modulation Classification

    College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China. · Department of Electrical and Computer Engineering, The University of Hong Kong

  17. Unified Complex-valued Neural Network: A Magnitude-Phase Computational Model for Event-Driven Neuromorphic Learning

    Jun 27, 2026Reza Ahmadvand, Sarah Safura Sharif, Yaser Mike BanadComplex-Valued Neural NetworksSpiking Neural Networks

    Department of Electrical and Computer Engineering, University of Oklahoma, Oklahoma, United States

  18. QC-GAN: A Parameter-Efficient Quaternion Conformer GAN for High-Fidelity Speech Enhancement

    Jun 17, 2026Shogo Yamauchi, Hideaki Tamori, Makoto Sakai +2TransformerComplex-Valued Neural Networks

    The Asahi Shimbun Company, Japan · Tokyo Woman’s Christian University, Japan

  19. Why SWAVE May Not Be All You Need:A Concept-Evolution Retrospective on Complex-Valued Recurrent Language Models

    Jun 16, 2026Ramprasath Ganesaraja, Swathika N, Sahil Dilip PanseRecurrent Neural NetworksComplex-Valued Neural Networks

    EdgeVerve Systems Limited

  20. On the Entropy Formula for Real, Complex, and Quaternionic Deep Linear Networks

    Jun 15, 2026Luis Contreras, Marco Nahas, Tejas KotwalComplex-Valued Neural NetworksDeep Linear Networks

  21. Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum states

    Jun 11, 2026Yi-Ran Xue, Rui Wang, Baigeng Wang +1Neural Quantum StatesVariational Monte Carlo

    *National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China. · Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA. · Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China. +3

  22. C-MambaPose: Phase-Preserving Complex Mamba for Cross-Environment Wi-Fi Human Pose Estimation

    Jun 5, 2026Phuc H. Nguyen, Van-Dinh NguyenDomain GeneralizationComplex-Valued Neural Networks

    VinUniversity, Hanoi, Vietnam

  23. Product units in gated recurrent units improve nuclear-mass prediction

    Jun 5, 2026Ziyuan Li, Paulo S. A. Freitas, John W. Clark +1Recurrent Neural NetworksComplex-Valued Neural Networks

    Department of Mathematics, Informatics and Technology, University of Applied Sciences Koblenz, Joseph-Rovan-Allee 2, 53424 Remagen, Germany · Technical University of Munich, Munich, Germany · Department of Mathematics, University of Madeira, Campus Universitário da Penteada, Funchal, 9020-105, Portugal +1

  24. Data Efficient Complex Feature Fusion Network For Hyperspectral Image Classification

    Jun 3, 2026Maitreya Shelare, Atharva Satam, Poonam Sonar +1Efficient Neural Network InferenceComplex-Valued Neural Networks

    Department of Electronics and Telecommunication, Rajiv Gandhi Institute of Technology, University of Mumbai, India

  25. Shortcomings and capacities of real-constrained neural networks in complex spaces

    Jun 3, 2026Andrew GracykComplex-Valued Neural NetworksStatistical Learning Theory

    Department of Mathematics Purdue University West Lafayette, IN 47907, United States

  26. PolSAR Image Classification using a Hybrid Complex-Valued Network (HybridCVNet)

    May 29, 2026Mohammed Q. AlkhatibHybrid CNN-Transformer ArchitecturesComplex-Valued Neural Networks

  27. When do complex-valued neural networks help? A study of representation, geometry, and optimization

    May 26, 2026Ashutosh KumarNeural Network OptimizationComplex-Valued Neural Networks

    Owl Autonomous Imaging, Inc.

  28. Model discovery for dynamical systems with complex-valued product units

    May 26, 2026Martin Brückmann, Babette Dellen, Uwe JaekelNonlinear System IdentificationComplex-Valued Neural Networks

    Department of Mathematics, Informatics, and Technology, RheinAhrCampus Remagen University of Applied Sciences Koblenz Joseph-Rovan-Allee 2, 53424 Remagen, Germany

  29. Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

    May 21, 2026Bhaskar Ranjan Karn, Dinesh KumarODE DiscoveryComplex-Valued Neural Networks

  30. Complex-Valued Phase-Coherent Transformer

    May 11, 2026Leona HiokiSoftmax AttentionComplex-Valued Neural Networks