It is well known that a given cortical neuron can respond with a different firing pattern for the same synaptic input, depending on its firing history and on the effects of modulator transmitters (see [Connors and Gutnick, 1990] for a review). The time span of different channel conductances is very broad, and the influence of some ionic currents varies with the history of the membrane potential [Lytton, 1991]. Motivated by the history-dependent nature of neuronal firing, we continue.our

Abstract: There exist a number of negative results ([J), [BR), [KV]) about learning on neural nets in Valiant's model [V) for probably approximately correct learning ("PAClearning"). These negative results are based on an asymptotic analysis where one lets the number of nodes in the neural net go to infinit.y. Hence this analysis is less adequate for the investigation of learning on a small fixed neural net.

A gradient descent algorithm for parameter estimation which is similar to those used for continuous-time recurrent neural networks was derived for Hodgkin-Huxley type neuron models. Using membrane potential trajectories as targets, the parameters (maximal conductances, thresholds and slopes of activation curves, time constants) were successfully estimated. The algorithm was applied to modeling slow non-spike oscillation of an identified neuron in the lobster stomatogastric ganglion. A model with three ionic currents was trained with experimental data. It revealed a novel role of A-current for slow oscillation below -50 mY. 1 INTRODUCTION Conductance-based neuron models, first formulated by Hodgkin and Huxley [10], are commonly used for describing biophysical mechanisms underlying neuronal behavior.

Bumptrees are geometric data structures introduced by Omohundro (1991) to provide efficient access to a collection of functions on a Euclidean space of interest. We describe a modified bumptree structure that has been employed as a neural network classifier, and compare its performance on several classification tasks against that of radial basis function networks and the standard mutIi-Iayer perceptron. 1 INTRODUCTION A number of neural network studies have demonstrated the utility of the multi-layer perceptron (MLP) and shown it to be a highly effective paradigm. Studies have also shown, however, that the MLP is not without its problems, in particular it requires an extensive training time, is susceptible to local minima problems and its perfonnance is dependent upon its internal network architecture. In an attempt to improve upon the generalisation performance and computational efficiency a number of studies have been undertaken principally concerned with investigating the parametrisation of the MLP. It is well known, for example, that the generalisation performance of the MLP is affected by the number of hidden units in the network, which have to be determined empirically since theory provides no guidance.

The recurrent network, containing six continuous-time analog neurons and 42 free parameters (connection strengths and thresholds), is trained to generate time-varying outputs approximating given periodic signals presented to the network. The chip implements a stochastic perturbative algorithm, which observes the error gradient along random directions in the parameter space for error-descent learning. In addition to the integrated learning functions and the generation of pseudo-random perturbations, the chip provides for teacher forcing and long-term storage of the volatile parameters. The network learns a 1 kHz circular trajectory in 100 sec. The chip occupies 2mm x 2mm in a 2JLm CMOS process, and dissipates 1.2 m W. 1 Introduction Exact gradient-descent algorithms for supervised learning in dynamic recurrent networks [1-3] are fairly complex and do not provide for a scalable implementation in a standard 2-D VLSI process. We have implemented a fairly simple and scalable ·Present address: Johns Hopkins University, ECE Dept., Baltimore MD 21218-2686.

There is an increasing interest in the area of Learning in Computer Vision and Image Understanding, both from researchers in the learning community and from researchers involved with the computer vision world. The field is characterized by a shift away from the classical, purely model-based, computer vision techniques, towards data-driven learning paradigms for solving real-world vision problems. Using learning in segmentation or recognition tasks has several advantages over classical model-based techniques. These include adaptivity to noise and changing environments, as well as in many cases, a simplified system generation procedure. Yet, learning from examples introduces a new challenge - getting a representative data set of examples from which to learn.

An autoencoder network uses a set of recognition weights to convert an input vector into a code vector. It then uses a set of generative weights to convert the code vector into an approximate reconstruction of the input vector. We derive an objective function for training autoencoders based on the Minimum Description Length (MDL) principle. The aim is to minimize the information required to describe both the code vector and the reconstruction error. We show that this information is minimized by choosing code vectors stochastically according to a Boltzmann distribution, where the generative weights define the energy of each possible code vector given the input vector. Unfortunately, if the code vectors use distributed representations, it is exponentially expensive to compute this Boltzmann distribution because it involves all possible code vectors. We show that the recognition weights of an autoencoder can be used to compute an approximation to the Boltzmann distribution and that this approximation gives an upper bound on the description length. Even when this bound is poor, it can be used as a Lyapunov function for learning both the generative and the recognition weights. We demonstrate that this approach can be used to learn factorial codes.

The problem of learning from examples in multilayer networks is studied within the framework of statistical mechanics. Using the replica formalism we calculate the average generalization error of a fully connected committee machine in the limit of a large number of hidden units. If the number of training examples is proportional to the number of inputs in the network, the generalization error as a function of the training set size approaches a finite value. If the number of training examples is proportional to the number of weights in the network we find first-order phase transitions with a discontinuous drop in the generalization error for both binary and continuous weights. 1 INTRODUCTION Feedforward neural networks are widely used as nonlinear, parametric models for the solution of classification tasks and function approximation. Trained from examples of a given task, they are able to generalize, i.e. to compute the correct output for new, unknown inputs.

To control such complex systems it is computationally more efficient to decompose the problem into smaller subtasks, with different control strategies for different operating points. When detailed information about the plant is available, gain scheduling has proven a successful method for designing a global control (Shamma and Athans, 1992). The system is partitioned by choosing several operating points and a linear model for each operating point. A controller is designed for each linear model and a method for interpolating or'scheduling' the gains of the controllers is chosen. The control problem becomes even more challenging when the system to be controlled is non-stationary, and the mode of the system is not explicitly observable.

We built a high-speed, digital mean-field Boltzmann chip and SBus board for general problems in constraint satjsfaction and learning. Each chip has 32 neural processors and 4 weight update processors, supporting an arbitrary topology of up to 160 functional neurons. On-chip learning is at a theoretical maximum rate of 3.5 x 10