10,298 research outputs found
Exact Classification with Two-Layer Neural Nets
AbstractThis paper considers the classification properties of two-layer networks of McCulloch–Pitts units from a theoretical point of view. In particular we consider their ability to realise exactly, as opposed to approximate, bounded decision regions in R2. The main result shows that a two-layer network can realise exactly any finite union of bounded polyhedra in R2whose bounding lines lie in general position, except for some well-characterised exceptions. The exceptions are those unions whose boundaries contain a line which is “inconsistent,” as described in the text. Some of the results are valid for Rn,n⩾2, and the problem of generalising the main result to higher-dimensional situations is discussed
Deep supervised learning using local errors
Error backpropagation is a highly effective mechanism for learning
high-quality hierarchical features in deep networks. Updating the features or
weights in one layer, however, requires waiting for the propagation of error
signals from higher layers. Learning using delayed and non-local errors makes
it hard to reconcile backpropagation with the learning mechanisms observed in
biological neural networks as it requires the neurons to maintain a memory of
the input long enough until the higher-layer errors arrive. In this paper, we
propose an alternative learning mechanism where errors are generated locally in
each layer using fixed, random auxiliary classifiers. Lower layers could thus
be trained independently of higher layers and training could either proceed
layer by layer, or simultaneously in all layers using local error information.
We address biological plausibility concerns such as weight symmetry
requirements and show that the proposed learning mechanism based on fixed,
broad, and random tuning of each neuron to the classification categories
outperforms the biologically-motivated feedback alignment learning technique on
the MNIST, CIFAR10, and SVHN datasets, approaching the performance of standard
backpropagation. Our approach highlights a potential biological mechanism for
the supervised, or task-dependent, learning of feature hierarchies. In
addition, we show that it is well suited for learning deep networks in custom
hardware where it can drastically reduce memory traffic and data communication
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