A method of training a neural network having at least an input layer, an output layer and a hidden layer, and a weight matrix encoding connection weights between two of the layers, the method comprising the steps of (a) providing an input to the input layer, the input having an associated expected output, (b) receiving a generated output at the output layer, (c) generating an error vector from the difference between the generated output and expected output, (d) generating a change matrix, the change matrix being the product of a random weight matrix and the error vector, and (e) modifying the weight matrix in accordance with the change matrix.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of training a neural network having at least an input layer, a hidden layer and an output layer, and a plurality of forward weight matrices encoding connection weights between successive pairs of layers, the method comprising the steps of: (a) providing an input to the input layer, the input having an associated expected output, (b) receiving a generated output at the output layer, (c) generating an error vector from the difference between the generated output and expected output, (d) for at least one pair of the layers, generating a change matrix, the change matrix being the product of a fixed random feedback weight matrix and the error vector, and (e) modifying the forward weight matrix for the at least one pair of the layers in accordance with the change matrix. 2. A method according to claim 1 wherein the change matrix is the cross product of the fixed random feedback weight matrix and the error vector. 3. A method according to claim 1 comprising an initial step of initialising the neural network with random connection weight values. 4. A method according to claim 1 comprising an initial step of generating the fixed random feedback weight matrix. 5. A method according to claim 4 wherein the fixed random feedback weight matrix elements comprise random values from a uniform distribution over [−α, α] where α is a scalar. 6. A method according to claim 1 comprising iteratively performing steps (a) to (e) for a plurality of input values. 7. A method according to claim 1 wherein step (e) comprises modifying the forward weight matrix encoding connection weights between the pair of layers comprising the input layer and the hidden layer. 8. A method according to claim 1 wherein step (e) comprises modifying the forward weight matrix encoding connection weights between the pair of layers comprising the hidden layer and the output layer 9. A method according to claim 1 wherein the neural network comprises a plurality of hidden layers, each hidden layer having an associated forward weight matrix and an associated fixed random backward weight matrix, the method comprising the steps of; generating a change matrix for each hidden layer using the associated fixed random weight matrix and; modifying each forward weight matrix in accordance with the respective change matrix. 10. A method according to claim 9 wherein the hidden layers comprise a first hidden layer and a second hidden layer, the second hidden layer being deeper than the first hidden layer, wherein the step of generating a change matrix for the second hidden layer comprises calculating a product of the associated random weight matrix and the error vector. 11. A method according to claim 9 wherein the hidden layers comprise a first hidden layer and a second hidden layer, the second hidden layer being deeper than the first hidden layer, wherein the step of generating a change matrix for the second hidden layer comprises calculating a product of the fixed random weight matrix associated with the first hidden layer, the random weight matrix associated with the second hidden layer, and the error vector. 12. A method according to claim 9 wherein the elements of the fixed random weight matrices comprise random values from a uniform distribution over [−α, α] where α is a scalar and where α is different for each fixed random weight matrix. 13. A system comprising a neural network where the neural network is trained by a method according to any one of the preceding claims.