Biologically-Inspired Neural Nets Modeling the Hippocampus

Hippocampus 101 In 1957, Scoville and Milner reported on patient HM Since then, numerous studies have used fMRI and PET scans to demonstrate use of hippocampus during learning and recall Numerous rat studies that monitor individual neurons demonstrate the existence of place cells Generally, hippocampus is associated with intermediate term memory (ITM).

Hippocampus 101 In 1994, Wilson and McNaughton demonstrated that sharp wave bursts (SPW) during sleep are time-compressed sequences learned earlier Levy hypothesizes that the hippocampus teaches learned sequences to the neocortex as part of a biased random processes Levy also hypothesizes that erasure/bias demotion happens when the neocortex signals to the hippocampus that the sequence was acquired, probably during slow-wave sleep (SWS).

Cornus Ammon The most significant feature in the hippocampus is the Cornus Ammon (CA) Most work in the Levy Lab focuses specifically on the CA3 region, although recently we’ve started re-examining the CA1 region as well

Minimal Model CA3 recurrent activity

Typical Equations Definitions y j net excitation of j x j external input to j z j output state of j θthreshold to fire K I feedforward inhibition K R feedback inhibition K 0 resting conductance c ij connectivity from i to j w ij weight between i and j εrate constant of synaptic modification αspike decay rate ttime

Fundamental Properties Neurons are McCulloch-Pitts-type threshold elements Synapses modify associatively on a local Hebbian-type rule Most connections are excitatory Recurrent excitation is sparse, asymmetric, and randomly connected Inhibitory neurons approximately control net activity In CA3, recurrent excitation contributes more to activity than external excitation Activity is low, but not too low

Model Variables Functional 1.Average activity 2.Activity fluctuations 3.Sequence length memory capacity 4.Average lifetime of local context neurons 5.Speed of learning 6.Ratio of external to recurrent excitations Actual 1.Number of neurons 2.Percent connectivity 3.Time span of synaptic associations 4.Threshold to fire 5.Feedback inhibition weight constant 6.Feedforward inhibition weight constant 7.Resting conductance 8.Rate constant of synaptic modification 9.Input code

Eleven Problems 1.Simple sequence completion 2.Spontaneous rebroadcast 3.One-trial learning 4.Jump-ahead recall 5.Sequence disambiguation (context past) 6.Finding a shortcut 7.Goal finding (context future) 8.Combining appropriate subsequences 9.Transverse patterning 10.Transitive inference 11.Trace conditioning

Sequence Completion Train on sequence ABCDEFG Provide input A Network recalls BCDEFG

Rebroadcast Train network on one or more sequences Provide random input patterns All or part of one of the trained sequences is recalled

One-trial learning Requires high synaptic modification Does not use same parameters as other problems Models short-term memory (STM) instead of intermediate-term memory (ITM- hippocampus)

Jump-ahead recall With adjusted inhibition, sequence completion can be short-circuited Train network on ABCDEFG Provide A Network recalls G or possibly BDG, etc. Inhibition in hippocampus does vary

Disambiguation Train network on patterns ABC456GHI and abc456ghi Present pattern A to the network Network recalls BC456GHI Requires patterns 4, 5, and 6 to be coded differently depending on past context

Shortcuts Train network on pattern ABC456GHIJKL456PQR Present pattern A to the network Network recalls BC456PQR Uses common neurons of patterns 4, 5, and 6 to generate a shortcut

Goal Finding Train network on pattern ABC456GHIJKL456PQR Present pattern A and part of pattern K to the network Network recalls BC456GHIJK… Requires use of context future

Combinations Train network on patterns ABC456GHI and abc456ghi Present pattern A and part of pattern i to the network Network recalls BC456ghi Also requires use of context future

Transverse Patterning Similar to rock, paper, scissors Train network on sequences [AB]a+, [AB]b-, [BC]b+, [BC]c-, [AC]c+, [AC]a- Present [AB] and part of + to network and network will generate a Present [BC] and part of + to network and network will generate b Present [AC] and part of + to network and network will generate c

Transitive Inference Transitivity: if A>B and B>C, then A>C Train network on [AB]a+, [AB]b-, [BC]b+, [BC]c-, [CD]c+, [CD]d-, [DE]d+, [DE]e- Present [BD] and part of + to network, and it will generate b

Trace Conditioning Train network on sequence A……B Vary the amount of time between presentation of pattern A and pattern B Computational results match experimental results on trace conditioning in rabbits

Important Recent Discoveries Addition of random “starting pattern” improves performance of network Synaptic failures improve performance (and reduce energy requirements) Addition of CA1 decoder improves performance