Solution (source code)

= Solution

To an experimental neuroscientist, a <Hopfield network> offers a concrete hypothesis about associative memory: information is distributed over a population, a partial cue can complete a learned pattern through recurrent interactions, and synaptic changes can alter which persistent activity patterns are accessible. It predicts attraction basins, interference between similar memories and resilience to some corrupted inputs. These are useful qualitative questions for experiments, and the connection between <Hebbian learning>, collective dynamics and stored patterns is mathematically testable.

Its limitations are equally concrete. Binary units suppress spike timing, <neural adaptation>, heterogeneous conductances and dendritic computation. Exact symmetric effective interactions, unrestricted signs and the absence of delays are idealizations; individual biological neurons generally do not implement arbitrary positive and negative outgoing synapses in the way the unrestricted weight matrix permits. The simple learning rule supplies neither realistic forgetting nor a complete account of biological long-term <synaptic plasticity>. Memory capacity and retrieval reliability depend on load and pattern correlations, and spurious attractors occur. Moreover, a stable activity pattern is not by itself an account of consolidation, behavioral readout or the anatomical location of a memory. \b[It is an explanatory model of associative retrieval, not a literal complete circuit diagram of the brain.]