1. 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

2. (C) 2007 SNU CSE Biointelligence Lab Spike Coding Spikes information  Single  Sequences Spike encoding  Cascade model  Covariance Method Spike decoding Adaptive spike coding 2

3. (C) 2007 SNU CSE Biointelligence Lab 3 Spikes: What kind of Code?

4. (C) 2007 SNU CSE Biointelligence Lab Spikes: Timing and Information 4 Entropy Mutual Information  S: stimulus, R: response  Total Entropy Noise Entropy

5. (C) 2007 SNU CSE Biointelligence Lab Spikes: Information in Single Spikes Spike (r=1) No spike (r=0) Noise Entropy Information Information per spike 5

6. (C) 2007 SNU CSE Biointelligence Lab Spikes: Information in Spike Sequences (1) A spike train and its representation in terms of binary “letters.” N bins : N-letter binary words, w. 6 P(w) P(w|s(t))

7. (C) 2007 SNU CSE Biointelligence Lab Spikes: Information in Spike Sequences (2) Two parameters  dt: bin width  L=N*dtTotal : duration of the word The issue of finite sampling poses something of a problem for information-theoretic approaches 7 Information rate

8. (C) 2007 SNU CSE Biointelligence Lab Encoding and Decoding : Linear Decoding Optimal linear kernel K(t) C rs : spike-triggered average (STA) C ss : autocorrelation Using white noise stimulus 8

9. (C) 2007 SNU CSE Biointelligence Lab Encoding and Decoding: Cascade Models Cascade Models Decision function EX) Two principal weakness  It is limited to only one linear feature  The model as a predictor for neural output is that it generate only a time-varying probability, or rate.  Poisson spike train (Every spike is independent.) 9

10. (C) 2007 SNU CSE Biointelligence Lab Encoding and Decoding: Cascade Models Modified cascade model Integrate-and-fire model 10

11. (C) 2007 SNU CSE Biointelligence Lab Encoding and Decoding: Finding Multiple Features Spike-triggered covariance matrix Eigenvalue decomposition of :  Irrelevant dimensions : eigenvalues close to zero  Relevant dimensions : variance either less than the prior or greater. Principal component analysis (PCA) 11

12. (C) 2007 SNU CSE Biointelligence Lab Examples of the Application of Covariance Methods (1) Neural Model Second filter Two significant modes(negative) STA is linear combination of f and f’. Noise effect Spike interdependence 12

13. (C) 2007 SNU CSE Biointelligence Lab Examples of the Application of Covariance Methods (2) Leaky integrate-and-fire neuron (LIF) C: capacitance, R: resistance, Vc: theshold, V: membrane potential Causal exponential kernel Low limit of integration 13

14. (C) 2007 SNU CSE Biointelligence Lab Examples of the Application of Covariance Methods (3) How change in the neuron’s biophysics  Nucleus magnocellularis(NM)  DTX effect 14 Reverse correlation

15. (C) 2007 SNU CSE Biointelligence Lab Using Information to Assess Decoding Decoding : to what extent has one captured what is relevant about the stimulus? Use Bayse rule N-dimensional model Single-spike information 1D STA-based model recovers ~ 63%, 2D model recovers ~75%. 15

16. (C) 2007 SNU CSE Biointelligence Lab Fly large monopolar cells Adaptive Spike Coding (1) Adaptation (cat’s toepad) 16

17. (C) 2007 SNU CSE Biointelligence Lab Adaptive Spike Coding (2) Although the firing rate is changing, we can use a variant of the information methods. White noise stimulus Standard deviation 17 Input/output relation