Visualizing Episodic Memory with Hopfield Network

In 2018, I wrote anarticledescribing the neural model and its relation to artificial neural networks. One chapter of the book that I refer to explains that certain properties could emerge when a set of neurons work together and form a network. A lot of theories are there in the book, but what attracts me more is a network that can simulate how human memory works called Hopfield Network [Hopfield, J.J. 1982].

Hopfield Network is the predecessor of Restricted Boltzmann Machine (RBM) and Multilayer Perceptron (MLP). It is an energy-based auto-associative memory, recurrent, and biologically inspired network .

• It is an energy-based network since it uses energy function and minimize the energy to train the weight. Imagine a neuron is triggered caused by an external impulse energy and the energy is propagated throughout the network excites all other connected neurons.
• It is an auto-associative memory network means the trained network can recover full memorized information given only partial information as input. For example, let’s say we have a network consists of 10 neurons connected to each other. When we trigger 8 neurons with so-called input A state , the network will react and calculate back and forth until all the neurons and neuron synapses (the connection between neuron) are stable. Let’s say this stable state called S but now actually the network is implicitly memorized input A state . After that, when we trigger some neurons (same neurons that previously being triggered but not all of them, less than 8), the network will react again until all neurons are stable. And the stable condition is where the previous 8 neurons are in input A state .
• It is a recurrent network means the network output goes back to the network input the network forms a directed graph. In this case, a directed cyclic graph.
• It is a biologically-inspired network since the structure of CA3 region of hippocampus form the similar structure and behavior with Hopfield Network.

It has been shown behaviorally that the CA3 supports spatial rapid one-trial learning, learning of arbitrary associations where space is a component, pattern completion, spatial short-term memory, and sequence learning by associations formed between successive items. [ Cutsuridis, V. & Wennekers, T . 2006]

Different with other neural networks that use backpropagation to learn the weight, Hopfield Network uses Hebb’s learning or Hebbian Learning [ Hebb, D.O. 1949 ] which is also a biologically-inspired learning. The idea behind Hebbian Learning is the connection between two neurons (synapse) will be stronger if the neurons at both ends are actively correlated. In Hopfield Network, neurons only have two states, activated and non-activated. Sometimes people quantified the activated state with 1 and non-activated state with 0. Sometimes they also quantified the activated state with 1 and non-activated state with -1.