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William Whyte

wwhyte@gmail.com

Journal articles

2008
1996
W Whyte, D Sherrington (1996)  Replica-symmetry breaking in perceptrons   Journal of Physics A : Mathematical and General 29: 12. 3063-3073  
Abstract: In the problem of optimization of pattern stabilization in perceptrons the replica-symmetric ansatz is known to be mathematically unstable for storage capacities greater than some . In this paper we demonstrate that for greater than the one-step replica-symmetry broken (RSB) solution is also unstable. We further show that in this region, full RSB is necessary for an exact solution. Direct evaluation of the two-step RSB solution yields a minimum storage error which is only slightly greater than the one-step RSB, which itself is greater than that given by the (unstable) replica-symmetric ansatz by a much larger amount.
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1995
W Whyte, D Sherrington, A C C Coolen (1995)  Competition between pattern recall and sequence processing in a neural network storing correlated patterns   Journal of Physics A : Mathematical and General 28: 12. 3421-3437  
Abstract: We investigate the effects on a network that stores a sequence of patterns without time delays of introducing patterns that are correlated in a way that depends only on their separation from each other in the sequence. We demonstrate that with a carefully chosen form for the synaptic matrix, the introduction of these correlations can, under certain circumstances, aid the recall of the individual patterns while still preserving the limit-cycle behaviour of the net.
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W Whyte, D Sherrington, K Y M Wong (1995)  Replica-symmetry breaking in noise-optimal neural networks   Journal of Physics A : Mathematical and General 28: 24. 7105-7111  
Abstract: Recent studies of optimization in neural networks trained with noisy data have shown that replica-symmetric solutions are unstable in the low-noise region of parameter space. We calculate the 1-step replica-symmetry broken solution in this region, which joins the replica-symmetric solution continuously at the de Almeida-Thouless line. These solutions yield satisfactory agreement with simulations for the aligning field distribution, better than those given by the replica-symmetric ansatz.
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Conference papers

2007
2005
2003

Other

2006
2005
2003
2002
1999
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