Richard S. Zemel and Geoffrey E. Hinton Department of Computer Science University of Toronto Toronto, ONT M5S lA4 Abstract Using an unsupervised learning procedure, a network is trained on an ensemble of images of the same two-dimensional object at different positions, orientations and sizes. Each half of the network "sees" one fragment of the object, and tries to produce as output a set of 4 parameters that have high mutual information with the 4 parameters output by the other half of the network. Given the ensemble of training patterns, the 4 parameters on which the two halves of the network can agree are the position, orientation, and size of the whole object, or some recoding of them. After training, the network can reject instances of other shapes by using the fact that the predictions made by its two halves disagree. If two competing networks are trained on an unlabelled mixture of images of two objects, they cluster the training cases on the basis of the objects' shapes, independently of the position, orientation, and size. 1 INTRODUCTION A difficult problem for neural networks is to recognize objects independently of their position, orientation, or size.

Although color TV is an established technology, there are a number of longstanding problems for which neural networks may be suited. Impulse noise is such a problem, and a modular neural network approach is presented in this paper. The training and analysis was done on conventional computers, while real-time simulations were performed on a massively parallel computer called the Princeton Engine. The network approach was compared to a conventional alternative, a median filter. Real-time simulations and quantitative analysis demonstrated the technical superiority of the neural system. Ongoing work is investigating the complexity and cost of implementing this system in hardware.

The three problems that concern us are identifying a natural domain of pattern classification applications of feed forward neural networks, selecting an appropriate feedforward network architecture, and assessing the tradeoff between network complexity, training set size, and statistical reliability as measured by the probability of incorrect classification. We close with some suggestions, for improving the bounds that come from Vapnik Chervonenkis theory, that can narrow, but not close, the chasm between theory and practice. Neural networks are appropriate as pattern classifiers when the pattern sources are ones of which we have little understanding, beyond perhaps a nonparametric statistical model, but we have been provided with classified samples of features drawn from each of the pattern categories. Neural networks should be able to provide rapid and reliable computation of complex decision functions. The issue in doubt is their statistical response to new inputs.

We describe a recurrent connectionist network, called CONCERT, that uses a set of melodies written in a given style to compose new melodies in that style. CONCERT is an extension of a traditional algorithmic composition technique in which transition tables specify the probability of the next note as a function of previous context. A central ingredient of CONCERT is the use of a psychologically-grounded representation of pitch.

Combining neuropharmacological experiments with computational modeling, we have shown that cholinergic modulation may enhance associative memory function in piriform (olfactory) cortex. We have shown that the acetylcholine analogue carbachol selectively suppresses synaptic transmission between cells within piriform cortex, while leaving input connections unaffected. When tested in a computational model of piriform cortex, this selective suppression, applied during learning, enhances associative memory performance.

We compare the performance of the modular architecture, composed of competing expert networks, suggested by Jacobs, Jordan, Nowlan and Hinton (1991) to the performance of a single back-propagation network on a complex, but low-dimensional, vowel recognition task. Simulations reveal that this system is capable of uncovering interesting decompositions in a complex task. The type of decomposition is strongly influenced by the nature of the input to the gating network that decides which expert to use for each case. The modular architecture also exhibits consistently better generalization on many variations of the task.

Harmonic grammar (Legendre, et al., 1990) is a connectionist theory of linguistic well-formed ness based on the assumption that the well-formedness of a sentence can be measured by the harmony (negative energy) of the corresponding connectionist state. Assuming a lower-level connectionist network that obeys a few general connectionist principles but is otherwise unspecified, we construct a higher-level network with an equivalent harmony function that captures the most linguistically relevant global aspects of the lower level network. In this paper, we extend the tensor product representation (Smolensky 1990) to fully recursive representations of recursively structured objects like sentences in the lower-level network. We show theoretically and with an example the power of the new technique for parallel distributed structure processing.

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

We consider different types of single-hidden-Iayer feedforward nets: with or without direct input to output connections, and using either threshold or sigmoidal activation functions. The main results show that direct connections in threshold nets double the recognition but not the interpolation power, while using sigmoids rather than thresholds allows (at least) doubling both. Various results are also given on VC dimension and other measures of recognition capabilities.

Competitive learning is an unsupervised algorithm that classifies input patterns into mutually exclusive clusters. In a neural net framework, each cluster is represented by a processing unit that competes with others in a winnertake-all pool for an input pattern. I present a simple extension to the algorithm that allows it to construct discrete, distributed representations. Discrete representations are useful because they are relatively easy to analyze and their information content can readily be measured. Distributed representations are useful because they explicitly encode similarity. The basic idea is to apply competitive learning iteratively to an input pattern, and after each stage to subtract from the input pattern the component that was captured in the representation at that stage. This component is simply the weight vector of the winning unit of the competitive pool. The subtraction procedure forces competitive pools at different stages to encode different aspects of the input. The algorithm is essentially the same as a traditional data compression technique known as multistep vector quantization, although the neural net perspective suggests potentially powerful extensions to that approach.