In this talk, I will present three different pieces of work, unified by a common theme, that of memory.
The first involves the modelling of eyetracking data – specifically, we have analysed the visual movements of sample populations subjected to simultaneous visual and aural inputs. We looked for correlations between these two forms of sensory stimuli via the analysis of the probability distributions of saccades and fixations. As our sample populations involved literate as well as illiterate people, we were able to investigate the effect of literacy on cognitive processing. This was particularly manifest in the case of fixations, where it appears that literacy leads to the presence of a characteristic (attentional) time scale in the appropriate probability distribution. On the other hand, scale-invariance is observed in the saccadic distributions, independent of the literacy level of the subjects. We suggest that these are characterised by Levy-like dynamics.
Another piece of work involves the role of synaptic metaplasticity to model the separate storage of long- and short-term memories in the human brain. We have presented and analysed two models of metaplastic synapses, whose main difference lies in the effect of a contrarian event on long-term memories. In one model, the effect is to build up an opposite memory of similar depth, while in the other, the effect is more short-term. Although the transient properties of the models reflect this difference, their asymptotic behaviour is robustly the same – power-law forgetting with the same universal exponent, is manifested.
A third research area involves that of game-theoretic formulations of synaptic plasticity. The main motivation for this work is that competitive dynamics are thought to occur in many processes of learning involving synapses. We have shown that the competition between synapses in their weak and strong states gives rise to a natural framework of learning, with the prediction of memory inherent in a timescale for forgetting a learned signal. Among our main results is the prediction that memory is optimized if the weak synapses are really weak, and the strong synapses are really strong. We have also studied the dynamic responses of the effective system to various signal types, particularly with reference to an existing empirical motor adaptation model. The dependence of the system-level behaviour on the synaptic parameters and the signal strength has been analysed with a view to optimal performance, and illustrates the functional role of multiple timescales.