Abstract
Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model simplicity and the locality of the synaptic update rules come at the cost of a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error signal, relying only upon locally accessible information. The fully-connected network consists of excitatory binary neurons with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the memory patterns to be memorized are presented online as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs. Synapses corresponding to active inputs are modified as a function of the value of the local fields with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. We simulated and analyzed a network of binary neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction. The storage capacity obtained through numerical simulations is shown to be close to the value predicted by analytical calculations. We also measured the dependence of capacity on the strength of external inputs. Finally, we quantified the statistics of the resulting synaptic connectivity matrix, and found that both the fraction of zero weight synapses and the degree of symmetry of the weight matrix increase with the number of stored patterns.
Highlights
One of the fundamental challenges in neuroscience is to understand how we store and retrieve memories for a long period of time
A Learning Rule for Optimal Storage in Recurrent Neural Networks memories in attractor neural networks is Hebbian learning, which can store up to 0.138N uncorrelated patterns in a recurrent network of N neurons. This is very far from the maximal capacity 2N, which can be achieved by supervised rules, e.g. by the perceptron learning rule
These rules are problematic for neurons in the neocortex or the hippocampus, since they rely on the computation of a supervisory error signal for each neuron of the network
Summary
One of the fundamental challenges in neuroscience is to understand how we store and retrieve memories for a long period of time Such long-term memory is fundamental for a variety of our cognitive functions. Synaptic plasticity rules specify how the efficacy of a synapse is affected by pre- and post-synaptic neural activity. Hebbian synaptic plasticity rules lead to long-term potentiation (LTP) for correlated pre- and post-synaptic activities, and long-term depression (LTD) for anticorrelated activities. These learning rules build excitatory feedback loops in the synaptic connectivity, resulting in the emergence of attractors that are correlated with the patterns of activity that were imposed on the network through external inputs. The attractor neural network scenario was originally explored in networks of binary neurons [1, 2], and extended from the 90s to networks of spiking neurons [4,5,6,7]
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