Dense Morphological Network: An Universal Function Approximator
Artificial neural networks are built on the basic operation of linear combination and non-linear activation function. Theoretically this structure can approximate any continuous function with three layer architecture. But in practice learning the parameters of such network can be hard. Also the choice of activation function can greatly impact the performance of the network. In this paper we are proposing to replace the basic linear combination operation with non-linear operations that do away with the need of additional non-linear activation function. To this end we are proposing the use of elementary morphological operations (dilation and erosion) as the basic operation in neurons. We show that these networks (Denoted as Morph-Net) with morphological operations can approximate any smooth function requiring less number of parameters than what is necessary for normal neural networks. The results show that our network perform favorably when compared with similar structured network. We have carried out our experiments on MNIST, Fashion-MNIST, CIFAR10 and CIFAR100.
 The authors introduce Morph-Net, a single layer neural network where the mapping is performed using morphological dilation and erosion. I was expecting something applied to convolutional networks as such operators are very popular in image processing, so the naming is a bit misleading. It is shown that the proposed network can approximate any smooth function, assuming a sufficiently large number of hidden neurons, that is a nice result. Clarity should be improved, for example it is mentioned that the structuring element is learned but never clearly explained how and what difficulties it poses. In the main text it is written that alpha is {-1, 1}, which would result in a combinatorial search, but never explained how it is learned in practice. This is shown only in the appendix but it is not clear to me that using a binarization with the weights is not prone to degenerate solutions and/or to learn at all if proper initialization is not used. Did the authors experiment with smooth versions or other form of binarization with straight-through estimator or sampling? In the proof for theorem 1 it is not clear if the convergence of the proposed network is faster or slower than that of a classic single layer network. The main result of the paper is that the structuring element can be learned, but there is no discussion on what it is learned. Also, there is no comparison on related approaches that try to learn the structuring element in an end-to-end fashion such as [1]. Experiments lack a more thorough comparison with state-of-the-art and at least an ablation study to show that the proposed approach is effective and has merit. For example, what is the relative contribution of using dilation and erosion jointly versus either one of them. What is the comparison with a winner-take-all unit over groups of neurons such as max-pooling? It seems that extending the work to multiple layers should be trivial but it is not reported and is left to future investigations. This hints at issues with the optimization and should be discussed, is it related to the binarization mentioned above? Overall the idea is interesting but the way the structuring element is learned should be discussed in more details and exemplified visually. Experiments need to be improved and overall applicability is uncertain at this stage. ======= [1] Masci et al., A Learning Framework for Morphological Operators Using Counter--Harmonic Mean.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Dense Morphological Network: An Universal Function Approximator
Artificial neural networks are built on the basic operation of linear combination and non-linear activation function. Theoretically this structure can approximate any continuous function with three layer architecture. But in practice learning the parameters of such network can be hard. Also the choice of activation function can greatly impact the performance of the network. In this paper we are proposing to replace the basic linear combination operation with non-linear operations that do away with the need of additional non-linear activation function. To this end we are proposing the use of elementary morphological operations (dilation and erosion) as the basic operation in neurons. We show that these networks (Denoted as Morph-Net) with morphological operations can approximate any smooth function requiring less number of parameters than what is necessary for normal neural networks. The results show that our network perform favorably when compared with similar structured network. We have carried out our experiments on MNIST, Fashion-MNIST, CIFAR10 and CIFAR100.
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 authors introduce Morph-Net, a single layer neural network where the mapping is performed using morphological dilation and erosion. I was expecting something applied to convolutional networks as such operators are very popular in image processing, so the naming is a bit misleading. It is shown that the proposed network can approximate any smooth function, assuming a sufficiently large number of hidden neurons, that is a nice result. Clarity should be improved, for example it is mentioned that the structuring element is learned but never clearly explained how and what difficulties it poses. In the main text it is written that alpha is {-1, 1}, which would result in a combinatorial search, but never explained how it is learned in practice. This is shown only in the appendix but it is not clear to me that using a binarization with the weights is not prone to degenerate solutions and/or to learn at all if proper initialization is not used. Did the authors experiment with smooth versions or other form of binarization with straight-through estimator or sampling? In the proof for theorem 1 it is not clear if the convergence of the proposed network is faster or slower than that of a classic single layer network. The main result of the paper is that the structuring element can be learned, but there is no discussion on what it is learned. Also, there is no comparison on related approaches that try to learn the structuring element in an end-to-end fashion such as [1]. Experiments lack a more thorough comparison with state-of-the-art and at least an ablation study to show that the proposed approach is effective and has merit. For example, what is the relative contribution of using dilation and erosion jointly versus either one of them. What is the comparison with a winner-take-all unit over groups of neurons such as max-pooling? It seems that extending the work to multiple layers should be trivial but it is not reported and is left to future investigations. This hints at issues with the optimization and should be discussed, is it related to the binarization mentioned above? Overall the idea is interesting but the way the structuring element is learned should be discussed in more details and exemplified visually. Experiments need to be improved and overall applicability is uncertain at this stage. ======= [1] Masci et al., A Learning Framework for Morphological Operators Using Counter--Harmonic Mean.
assistant
 The authors introduce Morph-Net, a single layer neural network where the mapping is performed using morphological dilation and erosion. I was expecting something applied to convolutional networks as such operators are very popular in image processing, so the naming is a bit misleading. It is shown that the proposed network can approximate any smooth function, assuming a sufficiently large number of hidden neurons, that is a nice result. Clarity should be improved, for example it is mentioned that the structuring element is learned but never clearly explained how and what difficulties it poses. In the main text it is written that alpha is {-1, 1}, which would result in a combinatorial search, but never explained how it is learned in practice. This is shown only in the appendix but it is not clear to me that using a binarization with the weights is not prone to degenerate solutions and/or to learn at all if proper initialization is not used. Did the authors experiment with smooth versions or other form of binarization with straight-through estimator or sampling? In the proof for theorem 1 it is not clear if the convergence of the proposed network is faster or slower than that of a classic single layer network. The main result of the paper is that the structuring element can be learned, but there is no discussion on what it is learned. Also, there is no comparison on related approaches that try to learn the structuring element in an end-to-end fashion such as [1]. Experiments lack a more thorough comparison with state-of-the-art and at least an ablation study to show that the proposed approach is effective and has merit. For example, what is the relative contribution of using dilation and erosion jointly versus either one of them. What is the comparison with a winner-take-all unit over groups of neurons such as max-pooling? It seems that extending the work to multiple layers should be trivial but it is not reported and is left to future investigations. This hints at issues with the optimization and should be discussed, is it related to the binarization mentioned above? Overall the idea is interesting but the way the structuring element is learned should be discussed in more details and exemplified visually. Experiments need to be improved and overall applicability is uncertain at this stage. ======= [1] Masci et al., A Learning Framework for Morphological Operators Using Counter--Harmonic Mean.