Biologically-Inspired Neural Nets

1. Biologically-Inspired Neural Nets Modeling the Hippocampus

2. 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).

3. 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).

4. 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

5. Minimal Model CA3 recurrent activity

6. Typical Equations 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

7. 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

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

9. Eleven Problems • Simple sequence completion • Spontaneous rebroadcast • One-trial learning • Jump-ahead recall • Sequence disambiguation (context past) • Finding a shortcut • Goal finding (context future) • Combining appropriate subsequences • Transverse patterning • Transitive inference • Trace conditioning

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

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

12. 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)

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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