Capsule Networks (CapsNet) use the Softmax function to convert the logits of the routing coefficients into a set of normalized values that signify the assignment probabilities between capsules in adjacent layers. We show that the use of Softmax prevents capsule layers from forming optimal couplings between lower and higherlevel capsules. Softmax constrains the dynamic range of the routing coefficients and leads to probabilities that remain mostly uniform after several routing iterations. Instead, we propose the use of Max-Min normalization. Max-Min performs a scale-invariant normalization of the logits that allows each lower-level capsule to take on an independent value, constrained only by the bounds of normalization. Max-Min provides consistent improvement in test accuracy across five datasets and allows more routing iterations without a decrease in network performance. A single CapsNet trained using Max-Min achieves an improved test error of 0.20% on the MNIST dataset. With a simple 3-model majority vote, we achieve a test error of 0.17% on MNIST.

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Abstract-Analytical workloads abound in application domains ranging from computational finance and risk analytics to engineering and manufacturing settings. In this paper we describe a Platform for Parallel R-based Analytics on the Cloud (P2RAC). The goal of this platform is to allow an Analyst to take a simulation or optimization job (both the code and associated data) that runs on their personal workstations and with minimum effort have them run on large-scale parallel cloud infrastructure. If this can be facilitated gracefully, an Analyst with strong quantitative but perhaps more limited development skills can harness the computational power of the cloud to solve larger analytically problems in less time. P2RAC is currently designed for executing parallel R scripts on the Amazon Elastic Computing Cloud infrastructure. Preliminary results obtained from an experiment confirm the feasibility of the platform.

This paper addresses how the benefits of cloud-based infrastructure can be harnessed for analytical workloads. Often, the software handling analytical workloads is not developed by a professional programmer but on an ad hoc basis by analysts in high-level programming environments such as R or MATLAB. The goal of this research is to allow Analysts to take an analytical job that executes on their personal workstations and with minimum effort execute it on cloud infrastructure and manage both the resources and the data required by the job. If this can be facilitated gracefully, then the Analyst benefits from on-demand resources, low maintenance cost and scalability of computing resources, all of which are offered by the cloud. In this paper, a Platform for Parallel R-based Analytics on the Cloud (P2RAC) that is placed between an Analyst and a cloud infrastructure is proposed and implemented. P2RAC offers a set of command-line tools for managing the resources, such as instances and clusters, the data and the execution of the software on the Amazon Elastic Computing Cloud infrastructure. Experimental studies are pursued using two parallel problems and the results obtained confirm the feasibility of employing P2RAC for solving large-scale analytical problems on the cloud. Analytical workloads abound in application domains ranging from computational finance and risk analytics to engineering and manufacturing settings. In our experience, these workloads that often involve simulation [8] and optimisation [9] tasks share common features as follows:(1) The associated codes are developed by Analysts, not professional developers, in high-level programming environments such as R or Matlab.(2) These codes and the related input data are generally created by Analysts for either one time use or are heavily modified each time they are used to adapt them to the analytical question at hand. (3) The codes are often computationally intensive or require a large number of independent runs with varying input parameters making some form of parallelism attractive.Cloud computing is a potential solution that can be beneficial not only to meet the computational requirements of analytical workloads [10] but also to achieve speed-up [11]. A wide range of analytical workloads are already harnessing the benefits of cloud computing. For example, analytical workloads related to data processing [12], online games [13], climate [14], medical records [15], risk [16], social networks [17] and neuroscience [18].Our goal has been to develop a platform that allows Analysts to take an analytical job (both the code and associated data) that runs on their personal workstations and with minimum effort and minimum change to the code have them run on large-scale parallel cloud infrastructure. If this can be facilitated gracefully, the Analyst can solve larger problems or perform more experiments in less time. Our approach is somewhat different from other 'cluster on cloud' projects such as [19][20][21][22] in that our focus is to simplify an Analyst's use of cl...

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