Traditionally, deep learning algorithms update the network weights whereas the network architecture is chosen manually, using a process of trial and error. In this work, we propose two novel approaches that automatically update the network structure while also learning its weights. The novelty of our approach lies in our parameterization where the depth, or additional complexity, is encapsulated continuously in the parameter space through control parameters that add additional complexity. We propose two methods: In tunnel networks, this selection is done at the level of a hidden unit, and in budding perceptrons, this is done at the level of a network layer; updating this control parameter introduces either another hidden unit or another hidden layer. We show the effectiveness of our methods on the synthetic two-spirals data and on two real data sets of MNIST and MIRFLICKR, where we see that our proposed methods, with the same set of hyperparameters, can correctly adjust the network complexity to the task complexity.
Early work on searching for the optimal network focused on incremental methods. Most such methods fix the depth to one and so the problem reduces to a search over the number of hidden units @cite_9 @cite_6 @cite_8 @cite_32 . Among these, there are those that add hidden units one by one; such as dynamic node creation @cite_9 , upstart algorithm @cite_10 , and feedforward neural network construction using cross-validation @cite_7 . A related method is cascade-correlation, where a new hidden unit that has the rest of the network as input, is trained while the rest of the network weights are fixed @cite_34 @cite_16 @cite_35 @cite_26 . This process technically increases the depth of the network for each addition of a unit. A recent related work applies a similar methodology to convolutional networks where a pre-trained network is widened or deepened on a new task to achieve better knowledge transfer @cite_11 .
@cite_35 @cite_26 @cite_7 @cite_8 @cite_9 @cite_32 @cite_6 @cite_16 @cite_34 @cite_10 @cite_11
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This article presents an algorithm that constructs feedforward neural networks with a single hidden layer for pattern classification. The algorithm starts with a small number of hidden units in the network and adds more hidden units as needed to improve the network's predictive accuracy. To determine when to stop adding new hidden units, the algorithm makes use of a subset of the available training samples for cross validation. New hidden units are added to the network only if they improve the classification accuracy of the network on the training samples and on the cross-validation samples. Extensive experimental results show that the algorithm is effective in obtaining networks with predictive accuracy rates that are better than those obtained by state-of-the-art decision tree methods. Abstract This paper introduces a new method called Dynamic Node Creation (DNC) which automatically grows BP networks until the target problem is solved. DNC sequentially adds nodes one at a time to the hidden layer(s) of the network until the desired approximation accuracy is achieved. Simulation results for parity, symmetry, binary addition, and the encoder problem are presented. The procedure was capable of finding known minimal topologies in many cases, and was always within three nodes of the minimum. Computational expense for finding the solutions was comparable to training normal BP networks with the same final topologies. Starting out with fewer nodes than needed to solve the problem actually seems to help find a solution. The method yielded a solution for every problem tried. Cascade-Correlation is a new architecture and supervised learning algorithm for artificial neural networks. Instead of just adjusting the weights in a network of fixed topology. Cascade-Correlation begins with a minimal network, then automatically trains and adds new hidden units one by one, creating a multi-layer structure. Once a new hidden unit has been added to the network, its input-side weights are frozen. This unit then becomes a permanent feature-detector in the network, available for producing outputs or for creating other, more complex feature detectors. The Cascade-Correlation architecture has several advantages over existing algorithms: it learns very quickly, the network determines its own size and topology, it retains the structures it has built even if the training set changes, and it requires no back-propagation of error signals through the connections of the network. A general method for building and training multilayer perceptrons composed of linear threshold units is proposed. A simple recursive rule is used to build the structure of the network by adding units as they are needed, while a modified perceptron algorithm is used to learn the connection strengths. Convergence to zero errors is guaranteed for any boolean classification on patterns of binary variables. Simulations suggest that this method is efficient in terms of the numbers of units constructed, and the networks it builds can generalize over patterns not in the training set. CNNs have made an undeniable impact on computer vision through the ability to learn high-capacity models with large annotated training sets. One of their remarkable properties is the ability to transfer knowledge from a large source dataset to a (typically smaller) target dataset. This is usually accomplished through fine-tuning a fixed-size network on new target data. Indeed, virtually every contemporary visual recognition system makes use of fine-tuning to transfer knowledge from ImageNet. In this work, we analyze what components and parameters change during fine-tuning, and discover that increasing model capacity allows for more natural model adaptation through fine-tuning. By making an analogy to developmental learning, we demonstrate that growing a CNN with additional units, either by widening existing layers or deepening the overall network, significantly outperforms classic fine-tuning approaches. But in order to properly grow a network, we show that newly-added units must be appropriately normalized to allow for a pace of learning that is consistent with existing units. We empirically validate our approach on several benchmark datasets, producing state-of-the-art results.