Complex- and Real-Valued Neural Network Architectures
Complex-value neural networks are not a new concept, however, the use of real-values has often been favoured over complex-values due to difficulties in training and accuracy of results. Existing literature ignores the number of parameters used. We compared complex- and real-valued neural networks using five activation functions. We found that when real and complex neural networks are compared using simple classification tasks, complex neural networks perform equal to or slightly worse than real-value neural networks. However, when specialised architecture is used, complex-valued neural networks outperform real-valued neural networks. Therefore, complex–valued neural networks should be used when the input data is also complex or it can be meaningfully to the complex plane, or when the network architecture uses the structure defined by using complex numbers.
 This work re-evaluates complex-valued neural networks: complex weights, complex activation functions. The paper acknowledges that complex networks are not new, and that the findings of previous authors is that complex networks perform less well than real-valued alternatives. The paper reports a comparison of real-valued and complex-valued neural networks, controlling for storage capacity (with an interesting discussion of controlling for capacity in terms of computational inference). The paper concludes with "Overall the complex-valued neural networks do not perform as well as expected." I didn*t understand this conclusion, because previous work found complex-valued neural networks to be inferior, which is consistent with the results reported here. I did not see support in this paper for the claim in the abstract that special architectures make complex networks work better, or that they are well suited to particular data sets. The empirical results are only presented in table-of-numbers format (graphical comparisons would be easier to understand), and tables 5-8 are all zero, which doesn*t make sense for these classification tasks.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Complex- and Real-Valued Neural Network Architectures
Complex-value neural networks are not a new concept, however, the use of real-values has often been favoured over complex-values due to difficulties in training and accuracy of results. Existing literature ignores the number of parameters used. We compared complex- and real-valued neural networks using five activation functions. We found that when real and complex neural networks are compared using simple classification tasks, complex neural networks perform equal to or slightly worse than real-value neural networks. However, when specialised architecture is used, complex-valued neural networks outperform real-valued neural networks. Therefore, complex–valued neural networks should be used when the input data is also complex or it can be meaningfully to the complex plane, or when the network architecture uses the structure defined by using complex numbers.
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>



 This work re-evaluates complex-valued neural networks: complex weights, complex activation functions. The paper acknowledges that complex networks are not new, and that the findings of previous authors is that complex networks perform less well than real-valued alternatives. The paper reports a comparison of real-valued and complex-valued neural networks, controlling for storage capacity (with an interesting discussion of controlling for capacity in terms of computational inference). The paper concludes with "Overall the complex-valued neural networks do not perform as well as expected." I didn*t understand this conclusion, because previous work found complex-valued neural networks to be inferior, which is consistent with the results reported here. I did not see support in this paper for the claim in the abstract that special architectures make complex networks work better, or that they are well suited to particular data sets. The empirical results are only presented in table-of-numbers format (graphical comparisons would be easier to understand), and tables 5-8 are all zero, which doesn*t make sense for these classification tasks.
assistant
 This work re-evaluates complex-valued neural networks: complex weights, complex activation functions. The paper acknowledges that complex networks are not new, and that the findings of previous authors is that complex networks perform less well than real-valued alternatives. The paper reports a comparison of real-valued and complex-valued neural networks, controlling for storage capacity (with an interesting discussion of controlling for capacity in terms of computational inference). The paper concludes with "Overall the complex-valued neural networks do not perform as well as expected." I didn*t understand this conclusion, because previous work found complex-valued neural networks to be inferior, which is consistent with the results reported here. I did not see support in this paper for the claim in the abstract that special architectures make complex networks work better, or that they are well suited to particular data sets. The empirical results are only presented in table-of-numbers format (graphical comparisons would be easier to understand), and tables 5-8 are all zero, which doesn*t make sense for these classification tasks.