Training Compressed Fully-Connected Networks with a Density-Diversity Penalty
Deep models have achieved great success on a variety of challenging tasks. How- ever, the models that achieve great performance often have an enormous number of parameters, leading to correspondingly great demands on both computational and memory resources, especially for fully-connected layers. In this work, we propose a new “density-diversity penalty” regularizer that can be applied to fully-connected layers of neural networks during training. We show that using this regularizer results in significantly fewer parameters (i.e., high sparsity), and also significantly fewer distinct values (i.e., low diversity), so that the trained weight matrices can be highly compressed without any appreciable loss in performance. The resulting trained models can hence reside on computational platforms (e.g., portables, Internet-of-Things devices) where it otherwise would be prohibitive.
The method proposes to compress the weight matrices of deep networks using a new density-diversity penalty together with a computing trick (sorting weights) to make computation affordable and a strategy of tying weights. This density-diversity penalty consists of an added cost corresponding to the l2-norm of the weights (density) and the l1-norm of all the pairwise differences in a layer. Regularly, the most frequent value in the weight matrix is set to zero to encourage sparsity. As weights collapse to the same values with the diversity penalty, they are tied together and then updated using the averaged gradient. The training process then alternates between training with 1. the density-diversity penalty and untied weights, and 2. training without this penalty but with tied weights. The experiments on two datasets (MNIST for vision and TIMIT for speech) shows that the method achieves very good compression rates without loss of performance. The paper is presented very clearly, presents very interesting ideas and seems to be state of the art for compression. The approach opens many new avenues of research and the strategy of weight-tying may be of great interest outside of the compression domain to learn regularities in data. The result tables are a bit confusing unfortunately. minor issues: p1 english mistake: “while networks *that* consist of convolutional layers”. p6-p7 Table 1,2,3 are confusing. Compared to the baseline (DC), your method (DP) seems to perform worse: In Table 1 overall, Table 2 overall FC, Table 3 overall, DP is less sparse and more diverse than the DC baseline. This would suggest a worse compression rate for DP and is inconsistent with the text which says they should be similar or better. I assume the sparsity value is inverted and that you in fact report the number of non-modal values as a fraction of the total.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Training Compressed Fully-Connected Networks with a Density-Diversity Penalty
Deep models have achieved great success on a variety of challenging tasks. How- ever, the models that achieve great performance often have an enormous number of parameters, leading to correspondingly great demands on both computational and memory resources, especially for fully-connected layers. In this work, we propose a new “density-diversity penalty” regularizer that can be applied to fully-connected layers of neural networks during training. We show that using this regularizer results in significantly fewer parameters (i.e., high sparsity), and also significantly fewer distinct values (i.e., low diversity), so that the trained weight matrices can be highly compressed without any appreciable loss in performance. The resulting trained models can hence reside on computational platforms (e.g., portables, Internet-of-Things devices) where it otherwise would be prohibitive.
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 method proposes to compress the weight matrices of deep networks using a new density-diversity penalty together with a computing trick (sorting weights) to make computation affordable and a strategy of tying weights. This density-diversity penalty consists of an added cost corresponding to the l2-norm of the weights (density) and the l1-norm of all the pairwise differences in a layer. Regularly, the most frequent value in the weight matrix is set to zero to encourage sparsity. As weights collapse to the same values with the diversity penalty, they are tied together and then updated using the averaged gradient. The training process then alternates between training with 1. the density-diversity penalty and untied weights, and 2. training without this penalty but with tied weights. The experiments on two datasets (MNIST for vision and TIMIT for speech) shows that the method achieves very good compression rates without loss of performance. The paper is presented very clearly, presents very interesting ideas and seems to be state of the art for compression. The approach opens many new avenues of research and the strategy of weight-tying may be of great interest outside of the compression domain to learn regularities in data. The result tables are a bit confusing unfortunately. minor issues: p1 english mistake: “while networks *that* consist of convolutional layers”. p6-p7 Table 1,2,3 are confusing. Compared to the baseline (DC), your method (DP) seems to perform worse: In Table 1 overall, Table 2 overall FC, Table 3 overall, DP is less sparse and more diverse than the DC baseline. This would suggest a worse compression rate for DP and is inconsistent with the text which says they should be similar or better. I assume the sparsity value is inverted and that you in fact report the number of non-modal values as a fraction of the total.
assistant
The method proposes to compress the weight matrices of deep networks using a new density-diversity penalty together with a computing trick (sorting weights) to make computation affordable and a strategy of tying weights. This density-diversity penalty consists of an added cost corresponding to the l2-norm of the weights (density) and the l1-norm of all the pairwise differences in a layer. Regularly, the most frequent value in the weight matrix is set to zero to encourage sparsity. As weights collapse to the same values with the diversity penalty, they are tied together and then updated using the averaged gradient. The training process then alternates between training with 1. the density-diversity penalty and untied weights, and 2. training without this penalty but with tied weights. The experiments on two datasets (MNIST for vision and TIMIT for speech) shows that the method achieves very good compression rates without loss of performance. The paper is presented very clearly, presents very interesting ideas and seems to be state of the art for compression. The approach opens many new avenues of research and the strategy of weight-tying may be of great interest outside of the compression domain to learn regularities in data. The result tables are a bit confusing unfortunately. minor issues: p1 english mistake: “while networks *that* consist of convolutional layers”. p6-p7 Table 1,2,3 are confusing. Compared to the baseline (DC), your method (DP) seems to perform worse: In Table 1 overall, Table 2 overall FC, Table 3 overall, DP is less sparse and more diverse than the DC baseline. This would suggest a worse compression rate for DP and is inconsistent with the text which says they should be similar or better. I assume the sparsity value is inverted and that you in fact report the number of non-modal values as a fraction of the total.