doi:10.1016/j.neucom.2006.10.148
Copyright © 2007 Elsevier B.V. All rights reserved.
Nonlinear transient computation
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Nigel Crook
, a, 
aDepartment of Computing, Oxford Brookes University, Wheatley Campus, Oxford OX33 1HX, UK
Available online 19 December 2006.
Abstract
A novel transient computation device is presented which performs computations on time-varying input signals. The inputs perturb the device causing transients in its internal dynamics. These transients are characteristic of the inputs and are reflected in the device's output. Previous approaches to transient computation have used large reservoirs of neurons. The proposed device consists of only two neurons with nonlinear internal dynamics. Experimental evidence is given to demonstrate that this device possesses two properties required for performing computations on time-dependent signals: a separation and an approximation property. It is also shown that this device can perform noise resistant pattern recognition.
Keywords: Transient computation; Chaos; Liquid state machine; Spiking neural network
Fig. 1. A diagram of the NTCM.
Fig. 2. The phase space of xP(t) vs uP(t) in a chaotic state (a) and a stabilized orbit (c). Part of the corresponding time series of uP(t) and γP(t) in the chaotic state (b) and stable orbit (d).
Fig. 3. Each graph plots the average of the results from 50 pairs of single spike experiments with pattern A being a spike at time 1 (a), 50 (b) or 90 (c) and the spike in pattern B is varied from 1 to 100.
Fig. 4. The property of separation for multiple-spike input patterns. Graphs (a), (c), and (e) show distances between random inputs and the prototype vs the distances in the corresponding outputs of NT. Graphs (b), (d) and (f) show the average of these distances for the 1000 randomized versions of the prototype.
Fig. 5. Increasing sensitivity to small differences in inputs for a given pattern and a slightly jittered version of it (a). The convolution of Gaussians for γT(t) with t=[1…100] (b) and t=[101…200] (c). Increasing sensitivity averaged over 50 random patterns (d).
Fig. 6. Input distances vs output distances for four prototype patterns ((a) pattern 1, (b) pattern 2, (c) pattern 3, (d) pattern 4). Each graph plots the distance from the given prototype pattern to the 100 noisy versions of all the prototype patterns vs the distance between the corresponding outputs of NT.
Fig. 7. The time series of the activation values of the three SRM readout neurons (rows) in response to the prototype input (first column), the prototype with a noise level of 0.75 (second column) and the prototype with a noise level of 2.0 (third column).
Fig. 8. The percentage of firing events by readout neurons SRM1, SRM2 and SRM3 for increasing levels of noise.
Table 1.
The percentage of spikes jittered by from -9 to +9 time steps for two different levels of noise
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