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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Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. 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. Currently, the field of sensory-motor neuroscience lacks a computational model that can replicate real-time control of biological brain. Due to incomplete neural and anatomical data, traditional neural network training methods fail to model the sensory-motor systems. Here we introduce a novel modeling method based on stochastic optimal control framework which is well suited for this purpose. Our controller is implemented with a recurrent neural network (RNN) whose goal is approximating the optimal global control law for the given plant and cost function. We employ a risk-sensitive objective function proposed by Jacobson (1973) for robustness of controller. For maximum optimization efficiency, we introduce a step response sampling method, which minimizes complexity of the optimization problem. We use conjugate gradient descent method for optimization, and gradient is calculated via Pontryagins maximum principle. In the end, we obtain highly stable and robust RNN controllers that can generate infinite varieties of attractor dynamics of the plant, which are proposed as building blocks of movement generation. We show two such examples, a point attractor based and a limit-cycle based dynamics. Abstract Many neural net learning algorithms aim at finding “simple” nets to explain training data. The expectation is that the “simpler” the networks, the better the generalization on test data (→ Occam's razor). Previous implementations, however, use measures for “simplicity” that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the “Bayesian” kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learing, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding “algorithmically simple” problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded generalization of Kolmogorov complexity) and inspired by Levin's optimal universal search algorithm. For a given problem, solution candidates are computed by efficient “self-sizing” programs that influence their own runtime and storage size. The probabilistic search algorithm finds the “good” programs (the ones quickly computing algorithmically probable solutions fitting the training data). Simulations focus on the task of discovering “algorithmically simple” neural networks with low Kolmogorov complexity and high generalization capability. It is demonstrated that the method, at least with certain toy problems where it is computationally feasible, can lead to generalization results unmatchable by previous neural network algorithms. Much remains to be done, however, to make large scale applications and “incremental learning” feasible. © 1997 Elsevier Science Ltd.