Diving into Optimization of Topology in Neural Networks
Seeking effective networks has become one of the most crucial and practical areas in deep learning. The architecture of a neural network can be represented as a directed acyclic graph, whose nodes denote transformation of layers and edges represent information flow. Despite the selection of 	extit{micro} node operations, 	extit{macro} connections among the whole network, noted as 	extit{topology}, largely affects the optimization process. We first rethink the residual connections via a new 	extit{topological view} and observe the benefits provided by dense connections to the optimization. Motivated by which, we propose an innovation method to optimize the topology of a neural network. The optimization space is defined as a complete graph, through assigning learnable weights which reflect the importance of connections, the optimization of topology is transformed into learning a set of continuous variables of edges. To extend the optimization to larger search spaces, a new series of networks, named as TopoNet, are designed. To further focus on critical edges and promote generalization ablity in dense topologies, auxiliary sparsity constraint is adopted to constrain the distribution of edges. Experiments on classical networks prove the effectiveness of the optimization of topology. Experiments with TopoNets further verify both availability and transferability of the proposed method in different tasks e.g. image classification, object detection and face recognition.
*UPDATE* I have read the other reviews, authors* comments and the revised version of the manuscript. I have modified my rating to accept. The updated version, with variance across runs reported, comparison to randomly wired networks, and clearer writing, is substantially better. The core idea is simple to understand in retrospect, and could lead to more follow-up work in the vein of DenseNets and DART (with a more constrained search space). The paper proposes a refinement of the idea behind DenseNets -- rather than summing over all previous layers* outputs, sum a weighted combination instead where the weights are learned. This idea can be extended to search through the space of all possible residual connections, which they call TopoNet. This is practically achieved by enforcing a sparsity constraint on the learned weights. There is an additional nuance when enforcing the sparsity constraint: downstream layers have many more incoming residual connections, and may need an appropriately scaled sparsity penalty. It may help to clarify in the text that weights can be positive or negative (the current motivation from the point of view of residuals at different intervals suggests all the weights should be non-negative). Table 3 is baffling. Were the initial edge values (column 2) chosen so as to make the number of params and FLOPS somewhat comparable across different rows? How were these initial edge values set (seems very specific for N_3 to go from 46 to 103 when residual interval goes from 4 to 2, etc.)? The comment that number of params and FLOPS changes are negligible is puzzling; clearly Random, p=0.01 should use much fewer FLOPS than Random, p=0.99. Without additional information behind the numbers for the baselines in Table 3, it is unclear if TopoNets indeed give an improvement over the baselines (Random and Residual). The text will also benefit from a careful elaboration of the differences in the Random baselines in the paper vs. the Xie et al approach of trying random architectures.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Diving into Optimization of Topology in Neural Networks
Seeking effective networks has become one of the most crucial and practical areas in deep learning. The architecture of a neural network can be represented as a directed acyclic graph, whose nodes denote transformation of layers and edges represent information flow. Despite the selection of 	extit{micro} node operations, 	extit{macro} connections among the whole network, noted as 	extit{topology}, largely affects the optimization process. We first rethink the residual connections via a new 	extit{topological view} and observe the benefits provided by dense connections to the optimization. Motivated by which, we propose an innovation method to optimize the topology of a neural network. The optimization space is defined as a complete graph, through assigning learnable weights which reflect the importance of connections, the optimization of topology is transformed into learning a set of continuous variables of edges. To extend the optimization to larger search spaces, a new series of networks, named as TopoNet, are designed. To further focus on critical edges and promote generalization ablity in dense topologies, auxiliary sparsity constraint is adopted to constrain the distribution of edges. Experiments on classical networks prove the effectiveness of the optimization of topology. Experiments with TopoNets further verify both availability and transferability of the proposed method in different tasks e.g. image classification, object detection and face recognition.
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>



*UPDATE* I have read the other reviews, authors* comments and the revised version of the manuscript. I have modified my rating to accept. The updated version, with variance across runs reported, comparison to randomly wired networks, and clearer writing, is substantially better. The core idea is simple to understand in retrospect, and could lead to more follow-up work in the vein of DenseNets and DART (with a more constrained search space). The paper proposes a refinement of the idea behind DenseNets -- rather than summing over all previous layers* outputs, sum a weighted combination instead where the weights are learned. This idea can be extended to search through the space of all possible residual connections, which they call TopoNet. This is practically achieved by enforcing a sparsity constraint on the learned weights. There is an additional nuance when enforcing the sparsity constraint: downstream layers have many more incoming residual connections, and may need an appropriately scaled sparsity penalty. It may help to clarify in the text that weights can be positive or negative (the current motivation from the point of view of residuals at different intervals suggests all the weights should be non-negative). Table 3 is baffling. Were the initial edge values (column 2) chosen so as to make the number of params and FLOPS somewhat comparable across different rows? How were these initial edge values set (seems very specific for N_3 to go from 46 to 103 when residual interval goes from 4 to 2, etc.)? The comment that number of params and FLOPS changes are negligible is puzzling; clearly Random, p=0.01 should use much fewer FLOPS than Random, p=0.99. Without additional information behind the numbers for the baselines in Table 3, it is unclear if TopoNets indeed give an improvement over the baselines (Random and Residual). The text will also benefit from a careful elaboration of the differences in the Random baselines in the paper vs. the Xie et al approach of trying random architectures.
assistant
*UPDATE* I have read the other reviews, authors* comments and the revised version of the manuscript. I have modified my rating to accept. The updated version, with variance across runs reported, comparison to randomly wired networks, and clearer writing, is substantially better. The core idea is simple to understand in retrospect, and could lead to more follow-up work in the vein of DenseNets and DART (with a more constrained search space). The paper proposes a refinement of the idea behind DenseNets -- rather than summing over all previous layers* outputs, sum a weighted combination instead where the weights are learned. This idea can be extended to search through the space of all possible residual connections, which they call TopoNet. This is practically achieved by enforcing a sparsity constraint on the learned weights. There is an additional nuance when enforcing the sparsity constraint: downstream layers have many more incoming residual connections, and may need an appropriately scaled sparsity penalty. It may help to clarify in the text that weights can be positive or negative (the current motivation from the point of view of residuals at different intervals suggests all the weights should be non-negative). Table 3 is baffling. Were the initial edge values (column 2) chosen so as to make the number of params and FLOPS somewhat comparable across different rows? How were these initial edge values set (seems very specific for N_3 to go from 46 to 103 when residual interval goes from 4 to 2, etc.)? The comment that number of params and FLOPS changes are negligible is puzzling; clearly Random, p=0.01 should use much fewer FLOPS than Random, p=0.99. Without additional information behind the numbers for the baselines in Table 3, it is unclear if TopoNets indeed give an improvement over the baselines (Random and Residual). The text will also benefit from a careful elaboration of the differences in the Random baselines in the paper vs. the Xie et al approach of trying random architectures.