Rate- and phase-coded autoassociative memories: Bayesian inference

Substantial evidence suggests that hippocampal area CA3 is involved in autoassociative memory. The most popular computational models of this make two key approximations: all-or-nothing activities for each unit in each memory, and attractor dynamics. Neither of these characteristics well describes CA3, which shows graded activity and prominent theta frequency oscillations. Other memory structures behave in a similar manner. Even theoretical approaches to autoassociative memories with graded activities are computationally brittle. We study graded and oscillatory autoassociative memories. First, we interpret recall as Bayesian inference based on information given by the noisy input, the synaptic weight matrix, and prior knowledge about the distribution of possible activity patterns coding for memories. We show that biologically plausible neuronal update dynamics, in which each neuron thresholds the weighted sum of its inputs, can effectively approximate optimal Bayesian inference. Optimal values for parameters of the update dynamics, such as level of inhibition or membrane time constant, are inherently provided by our formalism. This graded memory exhibits robust recall in the face of noise. We then extend the model to a phase-coded setting with spiking neurons, in which all neurons are subject to a coherent local field potential oscillation. Memories are coded by the the phase of the oscillation at which each neuron fires, as well as whether or not the neuron spikes in a given cycle. They are stored by a hippocampal form of spike timing-dependent plasticity. We again find a biophysically plausible neuronal update rule to be optimal: presynaptic firing accelerates the postsynaptic cell and the amount of acceleration is proportional to the synaptic weight. This model offers a more complete dynamical understanding of how hippocampal dynamics may support autoassociation under biological constraints