1. Memory Network Maintenance Using Spike-Timing Dependent Plasticity David Jangraw, ELE ’07 Advisor: John Hopfield, Department of Molecular Biology 12 T 21 T 12 Synaptic Drift Associative MemoryStabilization of Firing Spike-Timing Dependent Plasticity Synchronization Figure (except titles) from J. J. Hopfield (2006). “Searching for memories, Sudoku, implicit check-bits, and the iterative use of not-always-correct rapid neural computation.” arXiv.org, 19 Sep 2006. + δ T  + δ I  – δ t  – δ T  – δ I Associative Memory: Learned connections between ideas one remembers as being associated Associative memory is not fully understood; here we refine a simplified model of it Each property of the person or thing being remembered is represented by the activity of one neuron All neurons active in a memory are connected, so thinking of one thing about a memory (i.e. a name) will recall other things (i.e. height, eye color) We will model the activity of these neurons using MATLAB Synapse: A connection between two neurons Synaptic Strength (matrix T): T 21 is proportional to the size of the electrical response in neuron 2 evoked by an electrical spike in neuron 1 Synaptic Drift ( δ T): Small, random changes in synaptic strength due to “noisy” cellular processes The Problem: Normal memories have equal activity in each participating neuron, but synaptic drift causes unequal activity (a corrupted memory) or even memory loss. …Can the system correct itself? Spike-Timing Dependent Plasticity (STDP): Experimentally observed phenomenon by which relative spike timing changes synaptic strength Each neuron is modeled as a parallel RC circuit with a firing threshold When the membrane voltage exceeds threshold, the cell fires. The firing frequency ‘f’ is our measure of activity. If we feed an AC input of the form: I=Io + A sin(2π wt) into a neuron, a large range of DC offsets (Io) will drive the cell to fire at a frequency w, creating a plateau on the f-I curve (below left). Modeled disconnected neurons given slightly different input currents, causing varying delays in spike timing STDP applied based on average delay after 50 spikes of each neuron STDP successfully used to synchronize firing of many neurons Slope of STDP rule affects speed and stability of synchronization Drift Correction Simplified memory network using continuous-variable neurons with spiking neuron’s f-I curve and spike timing patterns Applied random synaptic drift (≤5%) to each active connection in a memory. Each drifted memory did converge to an ideal memory This indicates that spiking neurons could correct for synaptic drift using STDP Future Directions Load multiple, overlapping memories into network and test performance Create converging memory network of spiking neurons Use more realistic STDP rule I = Io + 0.05 sin(2π wt) Io = I AC t Ideal Memory Drifted Memory Non-Memory - Neuron Activity Eyes: Br Bl Gr … Each black square in this grid represents an active neuron encoding something about a person. For example, if the bottom row of neurons encodes eye color, and the ‘green’ neuron is active, this person has green eyes. Stability Analysis: A small positive change in T (synaptic drift, + δ T) will produce a proportional positive change in the input current (+ δ I) to the receiving neuron This will make the neuron fire more quickly than the neurons connected to it (- δ t) STDP would transform this spike timing delay into negative changes in synaptic strength (- δ T) This would produce a proportional negative change in input current (+ δ I) that could stabilize the memory! Changes in input current (while still on the f-I plateau) lead to changes in spike timing. Changes in spike timing are converted to proportional changes in synaptic strength. Spikes too far separated are ignored. AC input produces a plateau on the neuron’s f-I curve. Two neurons with slightly different input currents are synchronized using STDP rules with different slopes (m). Low m produced slow convergence; high m produced damped oscillation; extremely high m (not shown) produced instability.