**Cosmos DB**

Azure Cosmos DB is Microsoft’s proprietary globally-distributed, multi-model database service ‘for managing data at planet-scale’ launched in May 2017. It is schema-agnostic, horizontally scalable and generally classified as a NoSQL database. Internally, Cosmos DB stores ‘items’ in ‘containers’, with these 2 concepts being surfaced differently depending on the API used (these would be ‘documents’ in ‘collections’ when using the MongoDB-compatible API, for example). Containers are grouped in ‘databases’, which are analogous to namespaces above containers. Containers are schema-agnostic, which means that no schema is enforced when adding items. … **Complex Systems**

Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex. The physical manifestations of such systems are difficult to define, so a common choice is to identify ‘the system’ with the mathematical information model rather than referring to the undefined physical subject the model represents. Such systems are used to model processes in computer science, biology, economics, physics, chemistry, and many other fields. It is also called complex systems theory, complexity science, study of complex systems, sciences of complexity, non-equilibrium physics, and historical physics. A variety of abstract theoretical complex systems is studied as a field of mathematics. The key problems of complex systems are difficulties with their formal modelling and simulation. From such a perspective, in different research contexts complex systems are defined on the basis of their different attributes. Since all complex systems have many interconnected components, the science of networks and network theory are important aspects of the study of complex systems. A consensus regarding a single universal definition of complex system does not yet exist. For systems that are less usefully represented with equations various other kinds of narratives and methods for identifying, exploring, designing and interacting with complex systems are used. … **Diagonalwise Refactorization**

Depthwise convolutions provide significant performance benefits owing to the reduction in both parameters and mult-adds. However, training depthwise convolution layers with GPUs is slow in current deep learning frameworks because their implementations cannot fully utilize the GPU capacity. To address this problem, in this paper we present an efficient method (called diagonalwise refactorization) for accelerating the training of depthwise convolution layers. Our key idea is to rearrange the weight vectors of a depthwise convolution into a large diagonal weight matrix so as to convert the depthwise convolution into one single standard convolution, which is well supported by the cuDNN library that is highly-optimized for GPU computations. We have implemented our training method in five popular deep learning frameworks. Evaluation results show that our proposed method gains $15.4\times$ training speedup on Darknet, $8.4\times$ on Caffe, $5.4\times$ on PyTorch, $3.5\times$ on MXNet, and $1.4\times$ on TensorFlow, compared to their original implementations of depthwise convolutions. … **Neural Nearest Neighbors Block (N3 Block)**

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces. …

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