UNITS framework proves self-supervised splitting risk in MRI reconstruction is a weighted supervised risk, yielding identical Bayes-optimal predictors and relating training residuals to prediction bias.
Deep Complex Networks
10 Pith papers cite this work. Polarity classification is still indexing.
10
Pith papers citing it
abstract
At present, the vast majority of building blocks, techniques, and architectures for deep learning are based on real-valued operations and representations. However, recent work on recurrent neural networks and older fundamental theoretical analysis suggests that complex numbers could have a richer representational capacity and could also facilitate noise-robust memory retrieval mechanisms. Despite their attractive properties and potential for opening up entirely new neural architectures, complex-valued deep neural networks have been marginalized due to the absence of the building blocks required to design such models. In this work, we provide the key atomic components for complex-valued deep neural networks and apply them to convolutional feed-forward networks and convolutional LSTMs. More precisely, we rely on complex convolutions and present algorithms for complex batch-normalization, complex weight initialization strategies for complex-valued neural nets and we use them in experiments with end-to-end training schemes. We demonstrate that such complex-valued models are competitive with their real-valued counterparts. We test deep complex models on several computer vision tasks, on music transcription using the MusicNet dataset and on Speech Spectrum Prediction using the TIMIT dataset. We achieve state-of-the-art performance on these audio-related tasks.
representative citing papers
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
Proposes dropout-based BayesCVNNs with automated configuration search and FPGA accelerators that deliver 4.5x–13x speedups over GPUs while enabling uncertainty estimation for complex-valued neural networks.
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.
PMNet uses unitary phasor dynamics and hierarchical anchors to make explicit memory stable for long sequences, matching a 3x larger Mamba model on long-context robustness with a 119M parameter network.
Sigmoid gating on L2-normalised complex cosine scores, with no row normalisation, generalises across long-range, positional, phase and vision tasks, though the depth-stability theorem assumes its own substance.
FEDIN improves CTR prediction by using target-aware frequency filtering to isolate low-entropy periodic interest signals from high-entropy noise in user attention patterns.
CNNs trained on simulated data outperform conventional methods for complex signal denoising and interference mitigation in automotive radar.
Magnitude-only encoding reaches 99.57% accuracy on 3-class and 71.19% on 8-class SAR tasks in hybrid models, beating phase-inclusive alternatives, while phase boosts pure quantum models by up to 21.65 points.
citing papers explorer
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Towards a Unified Theoretical Framework for Splitting-based Self-Supervised MRI Reconstruction
UNITS framework proves self-supervised splitting risk in MRI reconstruction is a weighted supervised risk, yielding identical Bayes-optimal predictors and relating training residuals to prediction bias.
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SurReal: Fr\'echet Mean and Distance Transform for Complex-Valued Deep Learning
SurReal architecture applies weighted Fréchet mean convolution and distance-based FC layers to complex data, improving accuracy on MSTAR (94% to 98%) and RadioML with 8-10% of baseline model size.
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Algorithm and Hardware Co-Design for Efficient Complex-Valued Uncertainty Estimation
Proposes dropout-based BayesCVNNs with automated configuration search and FPGA accelerators that deliver 4.5x–13x speedups over GPUs while enabling uncertainty estimation for complex-valued neural networks.
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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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Phasor Memory Networks: Stable Backpropagation Through Time for Scalable Explicit Memory
PMNet uses unitary phasor dynamics and hierarchical anchors to make explicit memory stable for long sequences, matching a 3x larger Mamba model on long-context robustness with a 119M parameter network.
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Complex-Valued Phase-Coherent Transformer
Sigmoid gating on L2-normalised complex cosine scores, with no row normalisation, generalises across long-range, positional, phase and vision tasks, though the depth-stability theorem assumes its own substance.
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FEDIN: Frequency-Enhanced Deep Interest Network for Click-Through Rate Prediction
FEDIN improves CTR prediction by using target-aware frequency filtering to isolate low-entropy periodic interest signals from high-entropy noise in user attention patterns.
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Complex Signal Denoising and Interference Mitigation for Automotive Radar Using Convolutional Neural Networks
CNNs trained on simulated data outperform conventional methods for complex signal denoising and interference mitigation in automotive radar.
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Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data
Magnitude-only encoding reaches 99.57% accuracy on 3-class and 71.19% on 8-class SAR tasks in hybrid models, beating phase-inclusive alternatives, while phase boosts pure quantum models by up to 21.65 points.
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