**Tensor Network (TN)**

The harnessing of modern computational abilities for many-body wave-function representations is naturally placed as a prominent avenue in contemporary condensed matter physics. Specifically, highly expressive computational schemes that are able to efficiently represent the entanglement properties of many-particle systems are of interest. In the seemingly unrelated field of machine learning, deep network architectures have exhibited an unprecedented ability to tractably encompass the dependencies characterizing hard learning tasks such as image classification. However, key questions regarding deep learning architecture design still have no adequate theoretical answers. In this paper, we establish a Tensor Network (TN) based common language between the two disciplines, which allows us to offer bidirectional contributions. By showing that many-body wave-functions are structurally equivalent to mappings of ConvACs and RACs, we construct their TN equivalents, and suggest quantum entanglement measures as natural quantifiers of dependencies in such networks. Accordingly, we propose a novel entanglement based deep learning design scheme. In the other direction, we identify that an inherent re-use of information in state-of-the-art deep learning architectures is a key trait that distinguishes them from TNs. We suggest a new TN manifestation of information re-use, which enables TN constructs of powerful architectures such as deep recurrent networks and overlapping convolutional networks. This allows us to theoretically demonstrate that the entanglement scaling supported by these architectures can surpass that of commonly used TNs in 1D, and can support volume law entanglement in 2D polynomially more efficiently than RBMs. We thus provide theoretical motivation to shift trending neural-network based wave-function representations closer to state-of-the-art deep learning architectures. … **Quegel**

Pioneered by Google’s Pregel, many distributed systems have been developed for large-scale graph analytics. These systems expose the user-friendly ‘think like a vertex’ programming interface to users, and exhibit good horizontal scalability. However, these systems are designed for tasks where the majority of graph vertices participate in computation, but are not suitable for processing light-workload graph queries where only a small fraction of vertices need to be accessed. The programming paradigm adopted by these systems can seriously under-utilize the resources in a cluster for graph query processing. In this work, we develop a new open-source system, called Quegel, for querying big graphs, which treats queries as first-class citizens in the design of its computing model. Users only need to specify the Pregel-like algorithm for a generic query, and Quegel processes light-workload graph queries on demand using a novel superstep-sharing execution model to effectively utilize the cluster resources. Quegel further provides a convenient interface for constructing graph indexes, which significantly improve query performance but are not supported by existing graph-parallel systems. Our experiments verified that Quegel is highly efficient in answering various types of graph queries and is up to orders of magnitude faster than existing systems. … **T-Net**

Recent advances in meta-learning demonstrate that deep representations combined with the gradient descent method have sufficient capacity to approximate any learning algorithm. A promising approach is the model-agnostic meta-learning (MAML) which embeds gradient descent into the meta-learner. It optimizes for the initial parameters of the learner to warm-start the gradient descent updates, such that new tasks can be solved using a small number of examples. In this paper we elaborate the gradient-based meta-learning, developing two new schemes. First, we present a feedforward neural network, referred to as T-net, where the linear transformation between two adjacent layers is decomposed as T W such that W is learned by task-specific learners and the transformation T, which is shared across tasks, is meta-learned to speed up the convergence of gradient updates for task-specific learners. Second, we present MT-net where gradient updates in the T-net are guided by a binary mask M that is meta-learned, restricting the updates to be performed in a subspace. Empirical results demonstrate that our method is less sensitive to the choice of initial learning rates than existing meta-learning methods, and achieves the state-of-the-art or comparable performance on few-shot classification and regression tasks. …

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**11**
*Thursday*
Oct 2018

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