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

01

11

1111

0

11

11

1

0

tztz

tztz

twtztztwtw

otherwise

txtytx

txKKtzKtzcw

tzcwty

jj

jj

ijijijij

jjj

i iiIiR

iiijij

iiijij

j

Definitions

yj net excitation of j

xj external input to j

zj output state of j

θ threshold to fire

KI feedforward inhibition

KR feedback inhibition

K0 resting conductance

cij connectivity from i to j

wij weight between i and j

ε rate constant of synaptic modification

α spike decay rate

t time

FundamentalProperties

• 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

Functional1. Average activity2. Activity fluctuations3. Sequence length memory

capacity4. Average lifetime of local

context neurons5. Speed of learning6. 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 completion2. Spontaneous rebroadcast3. One-trial learning4. Jump-ahead recall5. Sequence disambiguation (context past)6. Finding a shortcut7. Goal finding (context future)8. Combining appropriate subsequences9. Transverse patterning10. Transitive inference11. 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

TransversePatterning

• 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

TransitiveInference

• 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

ImportantRecent Discoveries

• Addition of random “starting pattern” improves performance of network

• Synaptic failures improve performance (and reduce energy requirements)

• Addition of CA1 decoder improves performance