this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the ill-defined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.

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Compositional Q-Learning (CQ-L) (Singh 1992) is a modular approach to learning to perform composite tasks made up of several elemental tasks by reinforcement learning. Skills acquired while performing elemental tasks are also applied to solve composite tasks. Individual skills compete for the right to act and only winning skills are included in the decomposition of the composite task. We extend the original CQ-L concept in two ways: (1) a more general reward function, and (2) the agent can have more than one actuator. We use the CQ-L architecture to acquire skills for performing composite tasks with a simulated twolinked manipulator having large state and action spaces. The manipulator is a non-linear dynamical system and we require its end-effector to be at specific positions in the workspace. Fast function approximation in each of the Q-modules is achieved through the use of an array of Cerebellar Model Articulation Controller (CMAC) (Albus 1975) structures. 1 INTRODUCTION Reinforce...

We propose a new learning algorithm for regression modeling. The method is especially suitable for optimizing neural network structures that are amenable to a statistical description as mixture models. These include mixture of experts, hierarchical mixture of experts (HME), and normalized radial basis functions (NRBF). Unlike recent maximum likelihood (ML) approaches, we directly minimize the (squared) regression error. We use the probabilistic framework as means to define an optimization method that avoids many shallow local minima on the complex cost surface. Our method is based on deterministic annealing (DA), where the entropy of the system is gradually reduced, with the expected regression cost (energy) minimized at each entropy level. The corresponding Lagrangian is the system's "free-energy," and this annealing process is controlled by variation of the Lagrange multiplier, which acts as a "temperature" parameter. The new method consistently and substantially outperformed the com...

To embed modularity (i.e. to perform a local and encapsulated computation) into neural networks (NN) leads to many advantages. Hence, the development of a general model of modular neural networks (MNN) will enable a broader use of Neural Networks (NN). However, some important issues remain to be solved to enable a systematic use of MNN. In a practical point of view, the most important matter concerns the decomposition of the task into subtasks. We have introduced here the concept of vertical and horizontal decomposition in order to classify the existing modular models capable of performing a selfdecomposition. The modular models available for a horizontal self-decomposition (i.e. a clustering of the input space) are mainly the Local Model Network (LMN) and the algorithm of Jacobs and Jordan. Those two algorithms appear complementary. The convergence of the latter one is not ensured but the criterion it uses for decomposing the input space is far more ambitious and efficient than the s...

The use of "global neural networks" (as the back propagation neural network) and "clustering neural networks" (as the radial basis function neural network) leads each other to different advantages and inconvenients. The combination of the desirable features ot those two neural ways of computation is achieved by the use of Modular Neural Networks (MNN). In addition, a considerable advantage can emerge from the use of such a MNN: an interpreatable and relevant neural representation about the plant's behaviour. This very desirable feature for function approximation and especially for control problems, is what lake other neural models. This feature is so important that we introduce it as a way to differenciate MNN between other local computation models. However, to enable a systematic use of MNN three steps have to be achieved. First of all, the task has to be decomposed into subtasks, then the neural modules have to be properly organised considering the subtasks and finally a way of commu...

Complex multidimensional data may naturally require the decomposition of a regression/classification problem over local regions. Moreover, both global and local anisotropy can be present. We propose to address both problems with a flexible neural network structure embedding data quantization and coordinate transformations. The solution is applied in this paper to speaker normalization. The spectral mapping is realized as a weighted superposition of local neural mappings, estimated between subregions of a new speaker acoustic space and that of a reference speaker, combined with global and local space transformations. The local mappings are realized using the Generalized Resource Allocating Network (GRAN) model, a general RBF scheme that allows recursive allocation of kernels. The space transformations are based upon projections over the principal components, separately estimated for the global space and for the local subregions of the input and output acoustic spaces. 1 INTRODUCTION Th...

Local Model Networks are learning systems which are able to model and control unknown northnear dynamic processes from their observed input-output behaviour. Simple, locally accurate models are used to represent a globally complex process. The framework supports the modelhug process in real apphcations better than most artificial neural network architectures. This paper shows how their structure also allows them to more easily integrate knowledge, methods and a priori models from other paradigms such as fuzzy logic, system identification and statistics. Algorithms for automatic parameter estimation and model structure identification are given.

Biological sensorimotor systems are not static maps that transform input (sensory information) into output (motor behavior). Evidence from many lines of research suggests that their representations are plastic, experience-dependent entities. While this plasticity is essential for flexible behavior, it presents the nervous system with difficult organizational challenges. If the sensorimotor system adapts itself to perform well under one set of circumstances, will it then perform poorly when placed in an environment with different demands (negative transfer)? Will a later experience-dependent change undo the benefits of previous learning (catastrophic interference) ? We explore the first question in a separate paper in this volume (Shadmehr et al. 1995). Here we present psychophysical and computational results that explore the question of catastrophic interference in the context of a dynamic motor learning task. Under some conditions, subjects show evidence of catastrophic ...

This paper presents a modular network architecture that learns to cluster multiple views of multiple three-dimensional (3D) objects. The proposed network model is based on a mixture of non-linear autoencoders, which compete to encode multiple views of each 3D object. The main advantage of using a mixture of autoencoders is that it can capture multiple non-linear sub-spaces, rather than multiple centers for describing complex shapes of the view distributions. The unsupervised training algorithm is formulated within a maximum-likelihood estimation framework. The performance of the modular network model is evaluated through experiments using synthetic 3D wire-frame objects and gray-level images of real 3D objects. It is shown that the performance of the modular network model is superior to the performance of the conventional clustering algorithms, such as the K-means algorithm and the Gaussian mixture model.