23,871 research outputs found
Stochastic Weight Matrix-based Regularization Methods for Deep Neural Networks
The aim of this paper is to introduce two widely applicable regularization methods based on the direct modification of weight matrices. The first method, Weight Reinitialization, utilizes a simplified Bayesian assumption with partially resetting a sparse subset of the parameters.
The second one, Weight Shuffling, introduces an entropy- and weight distribution-invariant non-white noise to the parameters. The latter can also be interpreted as an ensemble approach. The proposed methods are evaluated on benchmark datasets, such as MNIST, CIFAR-10 or the JSB Chorales database, and also on time series modeling masks. We report gains both regarding performance and entropy of the analyzed networks. We also made our code available as a GitHub repository
Blockout: Dynamic Model Selection for Hierarchical Deep Networks
Most deep architectures for image classification--even those that are trained
to classify a large number of diverse categories--learn shared image
representations with a single model. Intuitively, however, categories that are
more similar should share more information than those that are very different.
While hierarchical deep networks address this problem by learning separate
features for subsets of related categories, current implementations require
simplified models using fixed architectures specified via heuristic clustering
methods. Instead, we propose Blockout, a method for regularization and model
selection that simultaneously learns both the model architecture and
parameters. A generalization of Dropout, our approach gives a novel
parametrization of hierarchical architectures that allows for structure
learning via back-propagation. To demonstrate its utility, we evaluate Blockout
on the CIFAR and ImageNet datasets, demonstrating improved classification
accuracy, better regularization performance, faster training, and the clear
emergence of hierarchical network structures
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
Stochastic Training of Neural Networks via Successive Convex Approximations
This paper proposes a new family of algorithms for training neural networks
(NNs). These are based on recent developments in the field of non-convex
optimization, going under the general name of successive convex approximation
(SCA) techniques. The basic idea is to iteratively replace the original
(non-convex, highly dimensional) learning problem with a sequence of (strongly
convex) approximations, which are both accurate and simple to optimize.
Differently from similar ideas (e.g., quasi-Newton algorithms), the
approximations can be constructed using only first-order information of the
neural network function, in a stochastic fashion, while exploiting the overall
structure of the learning problem for a faster convergence. We discuss several
use cases, based on different choices for the loss function (e.g., squared loss
and cross-entropy loss), and for the regularization of the NN's weights. We
experiment on several medium-sized benchmark problems, and on a large-scale
dataset involving simulated physical data. The results show how the algorithm
outperforms state-of-the-art techniques, providing faster convergence to a
better minimum. Additionally, we show how the algorithm can be easily
parallelized over multiple computational units without hindering its
performance. In particular, each computational unit can optimize a tailored
surrogate function defined on a randomly assigned subset of the input
variables, whose dimension can be selected depending entirely on the available
computational power.Comment: Preprint submitted to IEEE Transactions on Neural Networks and
Learning System
Variational Dropout and the Local Reparameterization Trick
We investigate a local reparameterizaton technique for greatly reducing the
variance of stochastic gradients for variational Bayesian inference (SGVB) of a
posterior over model parameters, while retaining parallelizability. This local
reparameterization translates uncertainty about global parameters into local
noise that is independent across datapoints in the minibatch. Such
parameterizations can be trivially parallelized and have variance that is
inversely proportional to the minibatch size, generally leading to much faster
convergence. Additionally, we explore a connection with dropout: Gaussian
dropout objectives correspond to SGVB with local reparameterization, a
scale-invariant prior and proportionally fixed posterior variance. Our method
allows inference of more flexibly parameterized posteriors; specifically, we
propose variational dropout, a generalization of Gaussian dropout where the
dropout rates are learned, often leading to better models. The method is
demonstrated through several experiments
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