Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that

We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological implications of having large spectral gaps. We also introduce related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we discuss two different dynamical feautures of networks: synchronizability and flow of random walkers and so that they are optimized if the corresponding Laplacian matrix have a large spectral gap. From this, we show, by developing a numerical optimization algorithm that maximum synchronizability and fast random walk spreading are obtained for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, that we call entangled networks. These turn out to be related to Ramanujan and Cage graphs. We argue also that these graphs are very good finite-size approximations to Bethe lattices, and provide almost or almost optimal solutions to many other problems as, for instance, searchability in the presence of congestion or performance of neural networks. Finally, we study how these results are modified when studying dynamical processes controlled by a normalized (weighted and directed) dynamics; much more heterogeneous graphs are optimal in this case. Finally, a critical discussion of the limitations and possible extensions of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted for pub. in JSTA

A survey of machine learning techniques applied to self organizing cellular networks

In this paper, a survey of the literature of the past fifteen years involving Machine Learning (ML) algorithms applied to self organizing cellular networks is performed. In order for future networks to overcome the current limitations and address the issues of current cellular systems, it is clear that more intelligence needs to be deployed, so that a fully autonomous and flexible network can be enabled. This paper focuses on the learning perspective of Self Organizing Networks (SON) solutions and provides, not only an overview of the most common ML techniques encountered in cellular networks, but also manages to classify each paper in terms of its learning solution, while also giving some examples. The authors also classify each paper in terms of its self-organizing use-case and discuss how each proposed solution performed. In addition, a comparison between the most commonly found ML algorithms in terms of certain SON metrics is performed and general guidelines on when to choose each ML algorithm for each SON function are proposed. Lastly, this work also provides future research directions and new paradigms that the use of more robust and intelligent algorithms, together with data gathered by operators, can bring to the cellular networks domain and fully enable the concept of SON in the near future

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications

Improving Connectionist Energy Minimization

Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an improvement to the standard local activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm, called activate, is uniform and does not assume that the network is tree-like. It can identify tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid local minima along these trees. For acyclic networks, the algorithm is guaranteed to converge to a global minimum from any initial state of the system (self-stabilization) and remains correct under various types of schedulers. On the negative side, we show that in the presence of cycles, no uniform algorithm exists that guarantees optimality even under a sequential asynchronous scheduler. An asynchronous scheduler can activate only one unit at a time while a synchronous scheduler can activate any number of units in a single time step. In addition, no uniform algorithm exists to optimize even acyclic networks when the scheduler is synchronous. Finally, we show how the algorithm can be improved using the cycle-cutset scheme. The general algorithm, called activate-with-cutset, improves over activate and has some performance guarantees that are related to the size of the network's cycle-cutset.Comment: See http://www.jair.org/ for any accompanying file

swTVM: Exploring the Automated Compilation for Deep Learning on Sunway Architecture

The flourish of deep learning frameworks and hardware platforms has been demanding an efficient compiler that can shield the diversity in both software and hardware in order to provide application portability. Among the exiting deep learning compilers, TVM is well known for its efficiency in code generation and optimization across diverse hardware devices. In the meanwhile, the Sunway many-core processor renders itself as a competitive candidate for its attractive computational power in both scientific and deep learning applications. This paper combines the trends in these two directions. Specifically, we propose swTVM that extends the original TVM to support ahead-of-time compilation for architecture requiring cross-compilation such as Sunway. In addition, we leverage the architecture features during the compilation such as core group for massive parallelism, DMA for high bandwidth memory transfer and local device memory for data locality, in order to generate efficient code for deep learning application on Sunway. The experimental results show the ability of swTVM to automatically generate code for various deep neural network models on Sunway. The performance of automatically generated code for AlexNet and VGG-19 by swTVM achieves 6.71x and 2.45x speedup on average than hand-optimized OpenACC implementations on convolution and fully connected layers respectively. This work is the first attempt from the compiler perspective to bridge the gap of deep learning and high performance architecture particularly with productivity and efficiency in mind. We would like to open source the implementation so that more people can embrace the power of deep learning compiler and Sunway many-core processor