Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage

Mitigation of Catastrophic Interference in Neural Networks and Ensembles using a Fixed Expansion Layer

Catastrophic forgetting (also known in the literature as catastrophic interference) is the phenomenon by which learning systems exhibit a severe exponential loss of learned information when exposed to relatively small amounts of new training data. This loss of information is not caused by constraints due to the lack of resources available to the learning system, but rather is caused by representational overlap within the learning system and by side-effects of the training methods used. Catastrophic forgetting in auto-associative pattern recognition is a well-studied attribute of most parameterized supervised learning systems. A variation of this phenomenon, in the context of feedforward neural networks, arises when non-stationary inputs lead to loss of previously learned mappings. The majority of the schemes proposed in the literature for mitigating catastrophic forgetting are not data-driven, but rather rely on storage of prior representations of the learning system. We introduce the Fixed Expansion Layer (FEL) feedforward neural network that embeds an expansion layer which sparsely encodes the information contained within the hidden layer, in order to help mitigate forgetting of prior learned representations. The fixed expansion layer approach is generally applicable to feedforward neural networks, as demonstrated by the application of the FEL technique to a recurrent neural network algorithm built on top of a standard feedforward neural network. Additionally, we investigate a novel framework for training ensembles of FEL networks, based on exploiting an information-theoretic measure of diversity between FEL learners, to further control undesired plasticity. The proposed methodology is demonstrated on a several tasks, clearly emphasizing its advantages over existing techniques. The architecture proposed can be applied to address a range of computational intelligence tasks, including classification problems, regression problems and system control

Art Neural Networks for Remote Sensing: Vegetation Classification from Landsat TM and Terrain Data

A new methodology for automatic mapping from Landsat Thematic Mapper (TM) and terrain data, based on the fuzzy ARTMAP neural network, is developed. System capabilities are tested on a challenging remote sensing classification problem, using spectral and terrain features for vegetation classification in the Cleveland National Forest. After training at the pixel level, system performance is tested at the stand level, using sites not seen during training. Results are compared to those of maximum likelihood classifiers, as well as back propagation neural networks and K Nearest Neighbor algorithms. ARTMAP dynamics are fast, stable, and scalable, overcoming common limitations of back propagation, which did not give satisfactory performance. Best results are obtained using a hybrid system based on a convex combination of fuzzy ARTMAP and maximum likelihood predictions. A prototype remote sensing example introduces each aspect of data processing and fuzzy ARTMAP classification. The example shows how the network automatically constructs a minimal number of recognition categories to meet accuracy criteria. A voting strategy improves prediction and assigns confidence estimates by training the system several times on different orderings of an input set.National Science Foundation (IRI 94-01659, SBR 93-00633); Office of Naval Research (N00014-95-l-0409, N00014-95-0657