Paper:
Deep CNNs have achieved state-of-the-art performance on numerous machine learning and computer vision tasks in recent years, but as they have become increasingly deep, the number of parameters they use has also increased, making them hard to deploy in memory-constrained environments and difficult to interpret. Machine learning theory implies that such networks are highly overparameterised and that it should be possible to reduce their size without sacrificing accuracy, and indeed many recent studies have begun to highlight specific redundancies that can be exploited to achieve this. In this paper, we take a further step in this direction by proposing a filter-sharing approach that reformulates deep, complex CNNs as an iterative application of shallower modules (a single convolutional mapping in the simplest case). We show, via experiments on CIFAR-10, CIFAR-100, Tiny ImageNet and ImageNet that this allows us to reduce the parameter counts of networks based on common designs such as VGGNet and ResNet by a factor proportional to their depth, whilst leaving their accuracy largely unaffected. At a broader level, our approach represents a way of rethinking neural network architectures so as to leverage the scale-space regularities found in visual signals, resulting in models that are both parsimonious and easier to interpret.

Review:
This paper proposes to modify a standard CNN by requiring all of its layers to share the same filter set, essentially allowing it to be expressed as an iterative (or recurrent) network.  This also has the effect of forcing the same number of feature channels to be used throughout the network.  For ResNet-like architectures with bottleneck blocks, sharing occurs at the level of the block (3 conv layers in series that are repeated).  Another variant of the sharing pattern inserts unshared 1x1 convolutional layers after shared layers or blocks; this adds some flexibility while still reducing parameters compared to standard CNNs.
On CIFAR-10, CIFAR-100, and Tiny ImageNet, experiments demonstrate the ability of the sharing scheme to reduce parameters without impacting accuracy (or more drastically reduce parameters at the cost of accuracy) (Tables 1ab, 2a).
However, results are less compelling on ImageNet (Table 2b), where SL-ResNet-50 and SL-ResNet-34 are both less accurate than the baseline standard ResNets as well as ShaResNet [Boulch, 2018].  The accuracy gap between SL-ResNet and ResNet on ImageNet (Table 2b) is significant (approx 5% Top-1 and 2% Top-5 accuracy) and might make it difficult to justify use of the proposed method in this setting.  As ImageNet is the most challenging of the datasets used, this is cause for concern.
There is also a major concern with respect to novelty and related work.  Unfortunately, the paper appears to have completely missed the following highly related publication from ICLR 2019:
Learning Implicitly Recurrent CNNs Through Parameter Sharing
Pedro Savarese, Michael Maire
ICLR 2019
This prior work proposes a network structure in which a set of L layers share a set of k parameter templates.  The templates and sharing coefficients are learned as part of the standard training procedure.  This prior work demonstrates both parameter savings and accuracy improvements when training networks in this manner.  Additionally, this prior work shows that some learned networks can be converted into explicitly recurrent forms as a post-processing step.
The paper under review appears be a special case of this prior work with the number of templates k = 1 (shared between all layers).  It is possible this is an important special case, worthy of significant attention on its own.  Notably, [Savarese and Maire, 2019] considered sharing across at most all layers within the same stage of a residual network, rather than all layers in the network.  However, arguing for the importance of this special case would require focused experimental comparison and analysis, which is not present in the current version of the paper.
Novelty is clearly limited in light of this overlooked prior work.  At minimum, citation, discussion, and experimental comparison to the above ICLR 2019 paper is necessary.