Online Memorization of Random Firing Sequences by a Recurrent Neural Network
It addresses the problem of understanding short-term and long-term memory mechanisms in neuroscience, but the approach is incremental as it builds on classical models like Hopfield networks.
This paper investigates a recurrent neural network's ability to memorize random firing sequences using a local learning rule, showing that single-pass memorization scales similarly to the Hopfield model, while multiple passes achieve higher capacity with nonvanishing bits per synapse.
This paper studies the capability of a recurrent neural network model to memorize random dynamical firing patterns by a simple local learning rule. Two modes of learning/memorization are considered: The first mode is strictly online, with a single pass through the data, while the second mode uses multiple passes through the data. In both modes, the learning is strictly local (quasi-Hebbian): At any given time step, only the weights between the neurons firing (or supposed to be firing) at the previous time step and those firing (or supposed to be firing) at the present time step are modified. The main result of the paper is an upper bound on the probability that the single-pass memorization is not perfect. It follows that the memorization capacity in this mode asymptotically scales like that of the classical Hopfield model (which, in contrast, memorizes static patterns). However, multiple-rounds memorization is shown to achieve a higher capacity (with a nonvanishing number of bits per connection/synapse). These mathematical findings may be helpful for understanding the functions of short-term memory and long-term memory in neuroscience.