24,446 research outputs found
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Training a Feed-forward Neural Network with Artificial Bee Colony Based Backpropagation Method
Back-propagation algorithm is one of the most widely used and popular
techniques to optimize the feed forward neural network training. Nature
inspired meta-heuristic algorithms also provide derivative-free solution to
optimize complex problem. Artificial bee colony algorithm is a nature inspired
meta-heuristic algorithm, mimicking the foraging or food source searching
behaviour of bees in a bee colony and this algorithm is implemented in several
applications for an improved optimized outcome. The proposed method in this
paper includes an improved artificial bee colony algorithm based
back-propagation neural network training method for fast and improved
convergence rate of the hybrid neural network learning method. The result is
analysed with the genetic algorithm based back-propagation method, and it is
another hybridized procedure of its kind. Analysis is performed over standard
data sets, reflecting the light of efficiency of proposed method in terms of
convergence speed and rate.Comment: 14 Pages, 11 figure
Generalization Error in Deep Learning
Deep learning models have lately shown great performance in various fields
such as computer vision, speech recognition, speech translation, and natural
language processing. However, alongside their state-of-the-art performance, it
is still generally unclear what is the source of their generalization ability.
Thus, an important question is what makes deep neural networks able to
generalize well from the training set to new data. In this article, we provide
an overview of the existing theory and bounds for the characterization of the
generalization error of deep neural networks, combining both classical and more
recent theoretical and empirical results
Neural Networks for Cross-Sectional Employment Forecasts: A Comparison of Model Specifications for Germany
In this paper, we present a review of various computational experiments – and consequent results – concerning Neural Network (NN) models developed for regional employment forecasting. NNs are widely used in several fields because of their flexible specification structure. Their utilization in studying/predicting economic variables, such as employment or migration, is justified by the ability of NNs of learning from data, in other words, of finding functional relationships – by means of data – among the economic variables under analysis. A series of NN experiments is presented in the paper. Using two data sets on German NUTS 3 districts (326 and 113 labour market districts in the former West and East Germany, respectively), the results emerging from the implementation of various NN models – in order to forecast variations in full-time employment – are provided and discussed In our approach, single forecasts are computed by the models for each district. Different specifications of the NN models are first tested in terms of: (a) explanatory variables; and (b) NN structures. The average statistical results of simulated out-of-sample forecasts on different periods are summarized and commented on. In addition to variable and structure specification, the choice of NN learning parameters and internal functions is also critical to the success of NNs. Comprehensive testing of these parameters is, however, limited in the literature. A sensitivity analysis is therefore carried out and discussed, in order to evaluate different combinations of NN parameters. The paper concludes with methodological and empirical remarks, as well as with suggestions for future research.neural networks, sensitivity analysis, employment forecasts, Germany
Competitive Gradient Descent
We introduce a new algorithm for the numerical computation of Nash equilibria
of competitive two-player games. Our method is a natural generalization of
gradient descent to the two-player setting where the update is given by the
Nash equilibrium of a regularized bilinear local approximation of the
underlying game. It avoids oscillatory and divergent behaviors seen in
alternating gradient descent. Using numerical experiments and rigorous
analysis, we provide a detailed comparison to methods based on \emph{optimism}
and \emph{consensus} and show that our method avoids making any unnecessary
changes to the gradient dynamics while achieving exponential (local)
convergence for (locally) convex-concave zero sum games. Convergence and
stability properties of our method are robust to strong interactions between
the players, without adapting the stepsize, which is not the case with previous
methods. In our numerical experiments on non-convex-concave problems, existing
methods are prone to divergence and instability due to their sensitivity to
interactions among the players, whereas we never observe divergence of our
algorithm. The ability to choose larger stepsizes furthermore allows our
algorithm to achieve faster convergence, as measured by the number of model
evaluations.Comment: Appeared in NeurIPS 2019. This version corrects an error in theorem
2.2. Source code used for the numerical experiments can be found under
http://github.com/f-t-s/CGD. A high-level overview of this work can be found
under http://f-t-s.github.io/projects/cgd
Neural Lyapunov Control
We propose new methods for learning control policies and neural network
Lyapunov functions for nonlinear control problems, with provable guarantee of
stability. The framework consists of a learner that attempts to find the
control and Lyapunov functions, and a falsifier that finds counterexamples to
quickly guide the learner towards solutions. The procedure terminates when no
counterexample is found by the falsifier, in which case the controlled
nonlinear system is provably stable. The approach significantly simplifies the
process of Lyapunov control design, provides end-to-end correctness guarantee,
and can obtain much larger regions of attraction than existing methods such as
LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality
solutions for challenging control problems.Comment: NeurIPS 201
- …