R S Neville | PubMed Health

PubMed2002

Transformations of sigma-pi nets: obtaining reflected functions by reflecting weight matrices.

This paper presents a methodology that reflected functions by reflecting the weight matrices of an artificial neural network. One of the major problems with the connectionist approach is that trained neural networks can only associate fixed sets of input-output mappings. We provide a methodology which allows the post-trained net to associate different input-output mappings. The different mappings are reflected in a horizontal axis, reflected in a vertical axis and scaling of the initial mapping. The methodology does not train the net on the different mappings but it transforms the weight matrix of the neural network. This paper describes a novel way of utilising sigma-pi neural networks. Our new methodology manipulates sigma-pi unit's weight matrices which transform the unit's output. The weights are cast in a matrix formulation, and then transformations can be performed on the weight matrix of the sigma-pi net. To test the new methodology, the following three steps were carried out on a neural network: (1) the network was trained to perform a mapping function, f; (2) the weights of the network were transformed; and (3) the network was tested to evaluate whether it performs the reflection in the vertical axis,f(ref-vert)(x) = a - f(x). This reflects the function in one dimension. A reflection transformation was used to manipulate the network's weight matrices to obtain a reflection in the vertical axis. Note that the network was not trained to perform the reflection in the vertical axis. The transformation of the weight matrix transformed the function the output performs. This article explains the theory which enables us to perform transformations of sigma-pi networks and obtain reflections of the output by reflecting the weight matrices. These transforms empower the network to perform related mapping tasks once one mapping task has been learnt. This article explains how each transformation is performed and it considers whether a set of 'standard' transformations can indeed be derived.

Neural Networks, Computer↗

PubMed2000

Partially pre-calculated weights for the backpropagation learning regime and high accuracy function mapping using continuous input RAM-based sigma-pi nets.

In this article we present a methodology that partially pre-calculates the weight updates of the backpropagation learning regime and obtains high accuracy function mapping. The paper shows how to implement neural units in a digital formulation which enables the weights to be quantised to 8-bits and the activations to 9-bits. A novel methodology is introduced to enable the accuracy of sigma-pi units to be increased by expanding their internal state space. We, also, introduce a novel means of implementing bit-streams in ring memories instead of utilising shift registers. The investigation utilises digital "Higher Order" sigma-pi nodes and studies continuous input RAM-based sigma-pi units. The units are trained with the backpropagation learning regime to learn functions to a high accuracy. The neural model is the sigma-pi units which can be implemented in digital microelectronic technology. The ability to perform tasks that require the input of real-valued information, is one of the central requirements of any cognitive system that utilises artificial neural network methodologies. In this article we present recent research which investigates a technique that can be used for mapping accurate real-valued functions to RAM-nets. One of our goals was to achieve accuracies of better than 1% for target output functions in the range Y epsilon [0,1], this is equivalent to an average Mean Square Error (MSE) over all training vectors of 0.0001 or an error modulus of 0.01. We present a development of the sigma-pi node which enables the provision of high accuracy outputs. The sigma-pi neural model was initially developed by Gurney (Learning in nets of structured hypercubes. PhD Thesis, Department of Electrical Engineering, Brunel University, Middlessex, UK, 1989; available as Technical Memo CN/R/144). Gurney's neuron models, the Time Integration Node (TIN), utilises an activation that was derived from a bit-stream. In this article we present a new methodology for storing sigma-pi node's activations as single values which are averages. In the course of the article we state what we define as a real number; how we represent real numbers and input of continuous values in our neural system. We show how to utilise the bounded quantised site-values (weights) of sigma-pi nodes to make training of these neurocomputing systems simple, using pre-calculated look-up tables to train the nets. In order to meet our accuracy goal, we introduce a means of increasing the bandwidth capability of sigma-pi units by expanding their internal state-space. In our implementation we utilise bit-streams when we calculate the real-valued outputs of the net. To simplify the hardware implementation of bit-streams we present a method of mapping them to RAM-based hardware using 'ring memories'. Finally, we study the sigma-pi units' ability to generalise once they are trained to map real-valued, high accuracy, continuous functions. We use sigma-pi units as they have been shown to have shorter training times than their analogue counterparts and can also overcome some of the drawbacks of semi-linear units (Gurney, 1992. Neural Networks, 5, 289-303).

Artificial Intelligence↗