Unsupervised Deep Structure Learning by Recursive Dependency Analysis
We introduce an unsupervised structure learning algorithm for deep, feed-forward, neural networks. We propose a new interpretation for depth and inter-layer connectivity where a hierarchy of independencies in the input distribution is encoded in the network structure. This results in structures allowing neurons to connect to neurons in any deeper layer skipping intermediate layers. Moreover, neurons in deeper layers encode low-order (small condition sets) independencies and have a wide scope of the input, whereas neurons in the first layers encode higher-order (larger condition sets) independencies and have a narrower scope. Thus, the depth of the network is automatically determined---equal to the maximal order of independence in the input distribution, which is the recursion-depth of the algorithm. The proposed algorithm constructs two main graphical models: 1) a generative latent graph (a deep belief network) learned from data and 2) a deep discriminative graph constructed from the generative latent graph. We prove that conditional dependencies between the nodes in the learned generative latent graph are preserved in the class-conditional discriminative graph. Finally, a deep neural network structure is constructed based on the discriminative graph. We demonstrate on image classification benchmarks that the algorithm replaces the deepest layers (convolutional and dense layers) of common convolutional networks, achieving high classification accuracy, while constructing significantly smaller structures. The proposed structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.
 This paper tackles the important problem of structure learning by introducing an unsupervised algorithm, which encodes a hierarchy of independencies in the input distribution and allows introducing skip connections among neurons in different layers. The quality of the learnt structure is evaluated in the context of image classification, analyzing the impact of the number of parameters and layers on the performance. The presentation of the paper could be improved. Moreover, the paper largely exceeds the recommended page limit (11 pages without references). My main comments are related to the experimental section: - Section 5 highlights that experiments were repeated 5 times; however, the standard deviation of the results is only reported for some cases. It would be beneficial to include the standard deviations of all experiments in the tables summarizing the obtained results. - Are the differences among results presented in table 1 (MNIST) and table 2 (CIFAR10) statistically significant? - It is not clear how the numbers of table 4 were computed (size replaced, size total, t-size, replaced-size). Would it be possible to provide the number of parameters of the vanilla model, the pre-trained feature extractor and the learned structure separately? - In section 5.2., there is only one sentence mentioning comparisons to alternative approaches. It might be worth expanding this and including numerical comparisons. - It seems that the main focus of the experiments is to highlight the parameter reduction achieved by the proposed algorithm. There is a vast literature on model compression, which might be worth reviewing, especially given that all the experiments are performed on standard image classification tasks.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Unsupervised Deep Structure Learning by Recursive Dependency Analysis
We introduce an unsupervised structure learning algorithm for deep, feed-forward, neural networks. We propose a new interpretation for depth and inter-layer connectivity where a hierarchy of independencies in the input distribution is encoded in the network structure. This results in structures allowing neurons to connect to neurons in any deeper layer skipping intermediate layers. Moreover, neurons in deeper layers encode low-order (small condition sets) independencies and have a wide scope of the input, whereas neurons in the first layers encode higher-order (larger condition sets) independencies and have a narrower scope. Thus, the depth of the network is automatically determined---equal to the maximal order of independence in the input distribution, which is the recursion-depth of the algorithm. The proposed algorithm constructs two main graphical models: 1) a generative latent graph (a deep belief network) learned from data and 2) a deep discriminative graph constructed from the generative latent graph. We prove that conditional dependencies between the nodes in the learned generative latent graph are preserved in the class-conditional discriminative graph. Finally, a deep neural network structure is constructed based on the discriminative graph. We demonstrate on image classification benchmarks that the algorithm replaces the deepest layers (convolutional and dense layers) of common convolutional networks, achieving high classification accuracy, while constructing significantly smaller structures. The proposed structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.
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 paper tackles the important problem of structure learning by introducing an unsupervised algorithm, which encodes a hierarchy of independencies in the input distribution and allows introducing skip connections among neurons in different layers. The quality of the learnt structure is evaluated in the context of image classification, analyzing the impact of the number of parameters and layers on the performance. The presentation of the paper could be improved. Moreover, the paper largely exceeds the recommended page limit (11 pages without references). My main comments are related to the experimental section: - Section 5 highlights that experiments were repeated 5 times; however, the standard deviation of the results is only reported for some cases. It would be beneficial to include the standard deviations of all experiments in the tables summarizing the obtained results. - Are the differences among results presented in table 1 (MNIST) and table 2 (CIFAR10) statistically significant? - It is not clear how the numbers of table 4 were computed (size replaced, size total, t-size, replaced-size). Would it be possible to provide the number of parameters of the vanilla model, the pre-trained feature extractor and the learned structure separately? - In section 5.2., there is only one sentence mentioning comparisons to alternative approaches. It might be worth expanding this and including numerical comparisons. - It seems that the main focus of the experiments is to highlight the parameter reduction achieved by the proposed algorithm. There is a vast literature on model compression, which might be worth reviewing, especially given that all the experiments are performed on standard image classification tasks.
assistant
 This paper tackles the important problem of structure learning by introducing an unsupervised algorithm, which encodes a hierarchy of independencies in the input distribution and allows introducing skip connections among neurons in different layers. The quality of the learnt structure is evaluated in the context of image classification, analyzing the impact of the number of parameters and layers on the performance. The presentation of the paper could be improved. Moreover, the paper largely exceeds the recommended page limit (11 pages without references). My main comments are related to the experimental section: - Section 5 highlights that experiments were repeated 5 times; however, the standard deviation of the results is only reported for some cases. It would be beneficial to include the standard deviations of all experiments in the tables summarizing the obtained results. - Are the differences among results presented in table 1 (MNIST) and table 2 (CIFAR10) statistically significant? - It is not clear how the numbers of table 4 were computed (size replaced, size total, t-size, replaced-size). Would it be possible to provide the number of parameters of the vanilla model, the pre-trained feature extractor and the learned structure separately? - In section 5.2., there is only one sentence mentioning comparisons to alternative approaches. It might be worth expanding this and including numerical comparisons. - It seems that the main focus of the experiments is to highlight the parameter reduction achieved by the proposed algorithm. There is a vast literature on model compression, which might be worth reviewing, especially given that all the experiments are performed on standard image classification tasks.