Deep Complex Networks
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. 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 TIMIT. We achieve state-of-the-art performance on these audio-related tasks.
 The paper presents an extensive framework for complex-valued neural networks. Related literature suggests a variety of motivations for complex valued neural networks: biological evidence, richer representation capacity, easier optimization, faster learning, noise-robust memory retrieval mechanisms and more. The contribution of the current work does not lie in presenting significantly superior results, compared to the traditional real-valued neural networks, but rather in developing an extensive framework for applying and conducting research with complex-valued neural networks. Indeed, the most standard work nowadays with real-valued neural networks depends on a variety of already well-established techniques for weight initialization, regularization, activation function, convolutions, etc. In this work, the complex equivalent of many of these basics tools are developed, such as a number of complex activation functions, complex batch normalization, complex convolution, discussion of complex differentiability, strategies for complex weight initialization, complex equivalent of a residual neural network. Empirical results show that the new complex-flavored neural networks achieve generally comparable performance to their real-valued counterparts, on a variety of different tasks. Then again, the major contribution of this work is not advancing the state-of-the-art on many benchmark tasks, but constructing a solid framework that will enable stable and solid application and research of these well-motivated models.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Deep Complex Networks
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. 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 TIMIT. We achieve state-of-the-art performance on these audio-related tasks.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper presents an extensive framework for complex-valued neural networks. Related literature suggests a variety of motivations for complex valued neural networks: biological evidence, richer representation capacity, easier optimization, faster learning, noise-robust memory retrieval mechanisms and more. The contribution of the current work does not lie in presenting significantly superior results, compared to the traditional real-valued neural networks, but rather in developing an extensive framework for applying and conducting research with complex-valued neural networks. Indeed, the most standard work nowadays with real-valued neural networks depends on a variety of already well-established techniques for weight initialization, regularization, activation function, convolutions, etc. In this work, the complex equivalent of many of these basics tools are developed, such as a number of complex activation functions, complex batch normalization, complex convolution, discussion of complex differentiability, strategies for complex weight initialization, complex equivalent of a residual neural network. Empirical results show that the new complex-flavored neural networks achieve generally comparable performance to their real-valued counterparts, on a variety of different tasks. Then again, the major contribution of this work is not advancing the state-of-the-art on many benchmark tasks, but constructing a solid framework that will enable stable and solid application and research of these well-motivated models.
assistant
 The paper presents an extensive framework for complex-valued neural networks. Related literature suggests a variety of motivations for complex valued neural networks: biological evidence, richer representation capacity, easier optimization, faster learning, noise-robust memory retrieval mechanisms and more. The contribution of the current work does not lie in presenting significantly superior results, compared to the traditional real-valued neural networks, but rather in developing an extensive framework for applying and conducting research with complex-valued neural networks. Indeed, the most standard work nowadays with real-valued neural networks depends on a variety of already well-established techniques for weight initialization, regularization, activation function, convolutions, etc. In this work, the complex equivalent of many of these basics tools are developed, such as a number of complex activation functions, complex batch normalization, complex convolution, discussion of complex differentiability, strategies for complex weight initialization, complex equivalent of a residual neural network. Empirical results show that the new complex-flavored neural networks achieve generally comparable performance to their real-valued counterparts, on a variety of different tasks. Then again, the major contribution of this work is not advancing the state-of-the-art on many benchmark tasks, but constructing a solid framework that will enable stable and solid application and research of these well-motivated models.