11,433 research outputs found
Temporal difference learning for the game Tic-Tac-Toe 3D: Applying structure to neural networks
When reinforcement learning is applied to large state spaces, such as those occurring in playing board games, the use of a good function approximator to learn to approximate the value function is very important. In previous research, multi-layer perceptrons have often been quite successfully used as function approximator for learning to play particular games with temporal difference learning. With the recent developments in deep learning, it is important to study if using multiple hidden layers or particular network structures can help to improve learning the value function. In this paper, we compare five different structures of multilayer perceptrons for learning to play the game Tic-Tac-Toe 3D, both when training through self-play and when training against the same fixed opponent they are tested against. We compare three fully connected multilayer perceptrons with a different number of hidden layers and/or hidden units, as well as two structured ones. These structured multilayer perceptrons have a first hidden layer that is only sparsely connected to the input layer, and has units that correspond to the rows in Tic-Tac-Toe 3D. This allows them to more easily learn the contribution of specific patterns on the corresponding rows. One of the two structured multilayer perceptrons has a second hidden layer that is fully connected to the first one, which allows the neural network to learn to non-linearly integrate the information in these detected patterns. The results on Tic-Tac-Toe 3D show that the deep structured neural network with integrated pattern detectors has the strongest performance out of the compared multilayer perceptrons against a fixed opponent, both through self-training and through training against this fixed opponent
Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds
Image denoising can be described as the problem of mapping from a noisy image
to a noise-free image. The best currently available denoising methods
approximate this mapping with cleverly engineered algorithms. In this work we
attempt to learn this mapping directly with plain multi layer perceptrons (MLP)
applied to image patches. We will show that by training on large image
databases we are able to outperform the current state-of-the-art image
denoising methods. In addition, our method achieves results that are superior
to one type of theoretical bound and goes a large way toward closing the gap
with a second type of theoretical bound. Our approach is easily adapted to less
extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG
artifacts, salt-and-pepper noise and noise resembling stripes, for which we
achieve excellent results as well. We will show that combining a block-matching
procedure with MLPs can further improve the results on certain images. In a
second paper, we detail the training trade-offs and the inner mechanisms of our
MLPs
How deep is deep enough? -- Quantifying class separability in the hidden layers of deep neural networks
Deep neural networks typically outperform more traditional machine learning
models in their ability to classify complex data, and yet is not clear how the
individual hidden layers of a deep network contribute to the overall
classification performance. We thus introduce a Generalized Discrimination
Value (GDV) that measures, in a non-invasive manner, how well different data
classes separate in each given network layer. The GDV can be used for the
automatic tuning of hyper-parameters, such as the width profile and the total
depth of a network. Moreover, the layer-dependent GDV(L) provides new insights
into the data transformations that self-organize during training: In the case
of multi-layer perceptrons trained with error backpropagation, we find that
classification of highly complex data sets requires a temporal {\em reduction}
of class separability, marked by a characteristic 'energy barrier' in the
initial part of the GDV(L) curve. Even more surprisingly, for a given data set,
the GDV(L) is running through a fixed 'master curve', independently from the
total number of network layers. Furthermore, applying the GDV to Deep Belief
Networks reveals that also unsupervised training with the Contrastive
Divergence method can systematically increase class separability over tens of
layers, even though the system does not 'know' the desired class labels. These
results indicate that the GDV may become a useful tool to open the black box of
deep learning
Bootstrap for neural model selection
Bootstrap techniques (also called resampling computation techniques) have
introduced new advances in modeling and model evaluation. Using resampling
methods to construct a series of new samples which are based on the original
data set, allows to estimate the stability of the parameters. Properties such
as convergence and asymptotic normality can be checked for any particular
observed data set. In most cases, the statistics computed on the generated data
sets give a good idea of the confidence regions of the estimates. In this
paper, we debate on the contribution of such methods for model selection, in
the case of feedforward neural networks. The method is described and compared
with the leave-one-out resampling method. The effectiveness of the bootstrap
method, versus the leave-one-out methode, is checked through a number of
examples.Comment: A la suite de la conf\'{e}rence ESANN 200
A Software Package for Neural Network Applications Development
Original Backprop (Version 1.2) is an MS-DOS package of four stand-alone C-language programs that enable users to develop neural network solutions to a variety of practical problems. Original Backprop generates three-layer, feed-forward (series-coupled) networks which map fixed-length input vectors into fixed length output vectors through an intermediate (hidden) layer of binary threshold units. Version 1.2 can handle up to 200 input vectors at a time, each having up to 128 real-valued components. The first subprogram, TSET, appends a number (up to 16) of classification bits to each input, thus creating a training set of input output pairs. The second subprogram, BACKPROP, creates a trilayer network to do the prescribed mapping and modifies the weights of its connections incrementally until the training set is leaned. The learning algorithm is the 'back-propagating error correction procedures first described by F. Rosenblatt in 1961. The third subprogram, VIEWNET, lets the trained network be examined, tested, and 'pruned' (by the deletion of unnecessary hidden units). The fourth subprogram, DONET, makes a TSR routine by which the finished product of the neural net design-and-training exercise can be consulted under other MS-DOS applications
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