Hopfield Networks Jessica Yarnall John Hopfield • Son of two physicists • Earned PhD in physics from Cornell University in 1958 • Currently a professor of molecular biology at Princeton University • Developed a model in 1982 to explain how memories are recalled by the brain Now known as the Hopfield model Hebbian Theory and Associative Memory Hebbian Theory was introduced in 1949 to explain associative learning “Neurons that fire together, wire together.” Associative memory is the ability to learn and remember the relationship between two unrelated things Hopfield Network • Network is trained to store a number of patterns or memories • Can recognize partial or corrupted information about a pattern and returns the closest pattern or best guess • Comparable to human brain, it has stability in pattern recognition Hopfield Network • Single-layered, recurrent network Neurons are fully connected • Symmetric weights Given neurons i and j, wij = wji • Neuron is either on (firing) or off (not firing) On corresponds to 1 Off corresponds to -1 Training • Hebbian learning rule: Incremental – does not require information about patterns previously learnt Local - uses information from both nodes whose connectivity weight is updated • Formula: • Where µ εx is the state of node x in pattern µ Updating Hopfield Networks • Generally update nodes asynchronously Node chosen randomly • Update Rule: • Example: • http://faculty.etsu.edu/knisleyj/neural/ Energy Function • The energy function either decreases or stays the same with asynchronous updating • Energy Function: • Converges to a local minima Problems with Hopfield Networks • The more complex the thing being recalled, the more pixels and weights you’ll need • Spurious states References • https://www.fi.edu/laureates/john-j-hopfield • https://humans101.wordpress.com/tag/associative-memory/ • https://www.doc.ic.ac.uk/~ae/papers/Hopfield-networks-15.pdf • https://www.doc.ic.ac.uk/~sd4215/hopfield.html • https://www.youtube.com/watch?v=gfPUWwBkXZY.