In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector @math . Then, we use @math to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1 in the worst case.
Previous research has employed neural nets in order to complement local search heuristics @cite_37 @cite_20 . One recent example is that authors in @cite_37 use Kohonen nets and devise a solver. Self organizing nature of Kohononen net iteratively executes and tries to map neurons which are dispersed onto the 2-D euclidean plane to the cities. At each iteration neurons attempt to decrease the distance between the cities in the neighborhood region which is a parametric set that consists of the nearby cities. The learning rate and the neighborhood function are the hyperparameters. Due to the fact that the number of neurons are higher than the cities, the algorithm presents an ordering mechanism for selecting the best fit neurons that represent the cities.
@cite_37 @cite_20
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We investigate the convergence properties of the self-organizing feature map algorithm for a simple, but very instructive case: the formation of a topographic representation of the unit interval [0,1] by a linear chain of neurons. We extend the proofs of convergence of Kohonen and of Cottrell and Fort to hold in any case where the neighborhood function, which is used to scale the change in the weight values at each neuron, is a monotonically decreasing function of distance from the winner neuron. We prove that the learning dynamics cannot be described by a gradient descent on a single energy function, but may be described using a set of potential functions, one for each neuron, which are independently minimized following a stochastic gradient descent. We derive the correct potential functions for the oneand multi-dimensional case, and show that the energy functions given by Tolat (1990) are an approximation which is no longer valid in the case of highly disordered maps or steep neighborhood functions. Information garnered from activity on location-based social networks can be harnessed to characterize urban spaces and organize them into neighborhoods. We represent geographic points in the city using spatio-temporal information about Foursquare user check-ins and semantic information about places, with the goal of developing features to input into a novel neighborhood detection algorithm. The algorithm first employs a similarity metric that assesses the homogeneity of a geographic area, and then with a simple mechanism of geographic navigation, it detects the boundaries of a city's neighborhoods. The models and algorithms devised are subsequently integrated into a publicly available, map-based tool named Hood square that allows users to explore activities and neighborhoods in cities around the world. Finally, we evaluate Hood square in the context of are commendation application where user profiles are matched to urban neighborhoods. By comparing with a number of baselines, we demonstrate how Hood square can be used to accurately predict the home neighborhood of Twitter users. We also show that we are able to suggest neighborhoods geographically constrained in size, a desirable property in mobile recommendation scenarios for which geographical precision is key. Abstract The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e., threshold gates), respectively, sigmoidal gates. In particular it is shown that networks of spiking neurons are, with regard to the number of neurons that are needed, computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. On the other hand, it is known that any function that can be computed by a small sigmoidal neural net can also be computed by a small network of spiking neurons. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neurobiology. We present a method for automatically identifying and validating predictive relationships between the visual appearance of a city and its non-visual attributes (e.g. crime statistics, housing prices, population density etc.). Given a set of street-level images and (location, city-attribute-value) pairs of measurements, we first identify visual elements in the images that are discriminative of the attribute. We then train a predictor by learning a set of weights over these elements using non-linear Support Vector Regression. To perform these operations efficiently, we implement a scalable distributed processing framework that speeds up the main computational bottleneck (extracting visual elements) by an order of magnitude. This speedup allows us to investigate a variety of city attributes across 6 different American cities. We find that indeed there is a predictive relationship between visual elements and a number of city attributes including violent crime rates, theft rates, housing prices, population density, tree presence, graffiti presence, and the perception of danger. We also test human performance for predicting theft based on street-level images and show that our predictor outperforms this baseline with 33 higher accuracy on average. Finally, we present three prototype applications that use our system to (1) define the visual boundary of city neighborhoods, (2) generate walking directions that avoid or seek out exposure to city attributes, and (3) validate user-specified visual elements for prediction.