Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to experimental data. 1 Introduction One of the most popular approaches to binary pattern classification, underlying many statistical techniques, is based on perceptrons or linear discriminants; see for instance the classical reference (Duda and Hart, 1973).

We derive a smoothing regularizer for recurrent network models by requiring robustness in prediction performance to perturbations of the training data. The regularizer can be viewed as a generalization of the first order Tikhonov stabilizer to dynamic models. The closed-form expression of the regularizer covers both time-lagged and simultaneous recurrent nets, with feedforward nets and onelayer linear nets as special cases. We have successfully tested this regularizer in a number of case studies and found that it performs better than standard quadratic weight decay. 1 Introd uction One technique for preventing a neural network from overfitting noisy data is to add a regularizer to the error function being minimized. Regularizers typically smooth the fit to noisy data. Well-established techniques include ridge regression, see (Hoerl & Kennard 1970), and more generally spline smoothing functions or Tikhonov stabilizers that penalize the mth-order squared derivatives of the function being fit, as in (Tikhonov & Arsenin 1977), (Eubank 1988), (Hastie & Tibshirani 1990) and (Wahba 1990). Thes(-ilethods have recently been extended to networks of radial basis functions (Girosi, Jones & Poggio 1995), and several heuristic approaches have been developed for sigmoidal neural networks, for example, quadratic weight decay (Plaut, Nowlan & Hinton 1986), weight elimination (Scalettar & Zee 1988),(Chauvin 1990),(Weigend, Rumelhart & Huberman 1990) and soft weight sharing (Nowlan & Hinton 1992).

We consider the problem of online gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process. Two-layer networks with an arbitrary number of hidden units have been shown to be universal approximators [1] for such N-to-one dimensional maps. We investigate the emergence of generalization ability in an online learning scenario [2], in which the couplings are modified after the presentation of each example so as to minimize the corresponding error. The resulting changes in {J} are described as a dynamical evolution; the number of examples plays the role of time.

This paper describes a neural network based controller for allocating capacity in a telecommunications network. This system was proposed in order to overcome a "real time" response constraint. Two basic architectures are evaluated: 1) a feedforward network-heuristic and; 2) a feedforward network-recurrent network. These architectures are compared against a linear programming (LP) optimiser as a benchmark. This LP optimiser was also used as a teacher to label the data samples for the feedforward neural network training algorithm. It is found that the systems are able to provide a traffic throughput of 99% and 95%, respectively, of the throughput obtained by the linear programming solution. Once trained, the neural network based solutions are found in a fraction of the time required by the LP optimiser.

Recent experiments show that the neural codes at work in a wide range of creatures share some common features. At first sight, these observations seem unrelated. However, we show that these features arise naturally in a linear filtered threshold crossing (LFTC) model when we set the threshold to maximize the transmitted information. This maximization process requires neural adaptation to not only the DC signal level, as in conventional light and dark adaptation, but also to the statistical structure of the signal and noise distributions. We also present a new approach for calculating the mutual information between a neuron's output spike train and any aspect of its input signal which does not require reconstruction of the input signal. This formulation is valid provided the correlations in the spike train are small, and we provide a procedure for checking this assumption. This paper is based on joint work (DeWeese [1], 1995). Preliminary results from the LFTC model appeared in a previous proceedings (DeWeese [2], 1995), and the conclusions we reached at that time have been reaffirmed by further analysis of the model.

However, ANNs are usually costly to train, preventing one from trying many different representations. In this paper, we address this problem by introducing and evaluating three new measures for quickly estimating ANN input representation quality. Two of these, called [DBleaves and Min (leaves), consistently outperform Rendell and Ragavan's (1993) blurring measure in accurately ranking different input representations for ANN learning on three difficult, real-world datasets.

Elucidation of the relationship between TD learning and dynamic programming (DP) has provided good theoretical insights (Barto et al., 1995). However, conventional TD algorithms were based on discrete-time, discrete-state formulations. In applying these algorithms to control problems, time, space and action had to be appropriately discretized using a priori knowledge or by trial and error. Furthermore, when a TD algorithm is used for neurobiological modeling, discrete-time operation is often very unnatural. There have been several attempts to extend TD-like algorithms to continuous cases. Bradtke et al. (1994) showed convergence results for DPbased algorithms for a discrete-time, continuous-state linear system with a quadratic cost. Bradtke and Duff (1995) derived TD-like algorithms for continuous-time, discrete-state systems (semi-Markov decision problems). Baird (1993) proposed the "advantage updating" algorithm by modifying Q-Iearning so that it works with arbitrary small time steps.

We propose a new learning method, "Generalized Learning Vector Quantization (GLVQ)," in which reference vectors are updated based on the steepest descent method in order to minimize the cost function. The cost function is determined so that the obtained learning rule satisfies the convergence condition. We prove that Kohonen's rule as used in LVQ does not satisfy the convergence condition and thus degrades recognition ability. Experimental results for printed Chinese character recognition reveal that GLVQ is superior to LVQ in recognition ability.

Harmony networks have been proposed as a means by which connectionist models can perform symbolic computation. Indeed, proponents claim that a harmony network can be built that constructs parse trees for strings in a context free language. This paper shows that harmony networks do not work in the following sense: they construct many outputs that are not valid parse trees. In order to show that the notion of systematicity is compatible with connectionism, Paul Smolensky, Geraldine Legendre and Yoshiro Miyata (Smolensky, Legendre, and Miyata 1992; Smolen sky 1993; Smolen sky, Legendre, and Miyata 1994) proposed a mechanism, "Harmony Theory," by which connectionist models purportedly perform structure sensitive operations without implementing classical algorithms. Harmony theory describes a "harmony network" which, in the course of reaching a stable equilibrium, apparently computes parse trees that are valid according to the rules of a particular context-free grammar.

We have recently developed a theory of spatial representations in which the position of an object is not encoded in a particular frame of reference but, instead, involves neurons computing basis functions of their sensory inputs. This type of representation is able to perform nonlinear sensorimotor transformations and is consistent with the response properties of parietal neurons. We now ask whether the same theory could account for the behavior of human patients with parietal lesions. These lesions induce a deficit known as hemineglect that is characterized by a lack of reaction to stimuli located in the hemispace contralateral to the lesion. A simulated lesion in a basis function representation was found to replicate three of the most important aspects of hemineglect: i) The models failed to cross the leftmost lines in line cancellation experiments, ii) the deficit affected multiple frames of reference and, iii) it could be object centered. These results strongly support the basis function hypothesis for spatial representations and provide a computational theory of hemineglect at the single cell level. 1 Introduction According to current theories of spatial representations, the positions of objects are represented in multiple modules throughout the brain, each module being specialized for a particular sensorimotor transformation and using its own frame of reference. For instance, the lateral intraparietal area (LIP) appears to encode the location of objects in oculocentric coordinates, presumably for the control of saccadic eye movements.