An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebb-like learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has no parameters which change over time and is able to continue learning, adding units and connections, until a performance criterion has been met. Applications of the model include vector quantization, clustering, and interpolation.

Ni1000 was designed to calculate "city block" distances (Le.

The localization and orientation to various novel or interesting events in the environment is a critical sensorimotor ability in all animals, predator or prey. In mammals, the superior colliculus (SC) plays a major role in this behavior, the deeper layers exhibiting topographically mapped responses to visual, auditory, and somatosensory stimuli. Sensory information arriving from different modalities should then be represented in the same coordinate frame. Auditory cues, in particular, are thought to be computed in head-based coordinates which must then be transformed to retinal coordinates. In this paper, an analog VLSI implementation for auditory localization in the azimuthal plane is described which extends the architecture proposed for the barn owl to a primate eye movement system where further transformation is required. This transformation is intended to model the projection in primates from auditory cortical areas to the deeper layers of the primate superior colliculus. This system is interfaced with an analog VLSI-based saccadic eye movement system also being constructed in our laboratory.

AM techniques were first introduced in soft-competitive learning algorithms[l]. This training procedure was later shown to be closely related to Expectation-Maximization algorithms used by the statistical estimation community[2]. Alternating minimizations search for optimal network weights by breaking the search into two distinct minimization problems. A given network performance functional is extremalized first with respect to one set of network weights and then with respect to the remaining weights. These learning procedures have found applications in the training of local expert systems [3], and in Boltzmann machine training [4]. More recently, convergence rates have been derived by viewing the AM 570 Michael Lemmon.

Experiments were performed to reveal some of the computational properties of the human motor memory system. We show that as humans practice reaching movements while interacting with a novel mechanical environment, they learn an internal model of the inverse dynamics of that environment. The representation of the internal model in memory is such that there is interference when there is an attempt to learn a new inverse dynamics map immediately after an anticorrelated mapping was learned. We suggest that this interference is an indication that the same computational elements used to encode the first inverse dynamics map are being used to learn the second mapping. We predict that this leads to a forgetting of the initially learned skill. 1 Introduction In tasks where we use our hands to interact with a tool, our motor system develops a model of the dynamics of that tool and uses this model to control the coupled dynamics of our arm and the tool (Shadmehr and Mussa-Ivaldi 1994). In physical systems theory, the tool is a mechanical analogue of an admittance, mapping a force as input onto a change in state as output (Hogan 1985).

Current understanding of the effects of damage on neural networks is rudimentary, even though such understanding could lead to important insights concerning neurological and psychiatric disorders. Motivated by this consideration, we present a simple analytical framework for estimating the functional damage resulting from focal structural lesions to a neural network.

We study the asymptotic properties of the sequence of iterates of weight-vector estimates obtained by training a multilayer feed forward neural network with a basic gradient-descent method using a fixed learning constant and no batch-processing. In the onedimensional case, an exact analysis establishes the existence of a limiting distribution that is not Gaussian in general. For the general case and small learning constant, a linearization approximation permits the application of results from the theory of random matrices to again establish the existence of a limiting distribution. We study the first few moments of this distribution to compare and contrast the results of our analysis with those of techniques of stochastic approximation. 1 INTRODUCTION The wide applicability of neural networks to problems in pattern classification and signal processing has been due to the development of efficient gradient-descent algorithms for the supervised training of multilayer feedforward neural networks with differentiable node functions. A basic version uses a fixed learning constant and updates all weights after each training input is presented (online mode) rather than after the entire training set has been presented (batch mode). The properties of this algorithm as exhibited by the sequence of iterates are not yet well-understood. There are at present two major approaches.

We first rederive the known results for the'thermodynamic limit' of infinite perceptron size N and show explicitly that 9

Unsupervised learning procedures have been successful at low-level feature extraction and preprocessing of raw sensor data. So far, however, they have had limited success in learning higher-order representations, e.g., of objects in visual images. A promising approach is to maximize some measure of agreement between the outputs of two groups of units which receive inputs physically separated in space, time or modality, as in (Becker and Hinton, 1992; Becker, 1993; de Sa, 1993). Using the same approach, a much simpler learning procedure is proposed here which discovers features in a single-layer network consisting of several populations of units, and can be applied to multi-layer networks trained one layer at a time. When trained with this algorithm on image sequences of moving geometric objects a two-layer network can learn to perform accurate position-invariant object classification. 1 LEARNING COHERENT CLASSIFICATIONS A powerful constraint in sensory data is coherence over time, in space, and across different sensory modalities.

To compress text files, a neural predictor network P is used to approximate the conditional probability distribution of possible "next characters", given n previous characters. P's outputs are fed into standard coding algorithms that generate short codes for characters with high predicted probability and long codes for highly unpredictable characters. Tested on short German newspaper articles, our method outperforms widely used Lempel-Ziv algorithms (used in UNIX functions such as "compress" and "gzip").