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2 Spike Coding

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

  2. Spike Coding • Spikes information • Single • Sequences • Spike encoding • Cascade model • Covariance Method • Spike decoding • Adaptive spike coding

  3. Spikes: What kind of Code?

  4. Spikes: Timing and Information • Entropy • Mutual Information • S: stimulus, R: response • Total Entropy Noise Entropy

  5. Spikes: Information in Single Spikes • Spike (r=1) • No spike (r=0) • Noise Entropy • Information • Information per spike

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

  7. 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 Information rate

  8. Encoding and Decoding : Linear Decoding • Optimal linear kernel K(t) • Crs : spike-triggered average (STA) • Css : autocorrelation • Using white noise stimulus

  9. 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.)

  10. Encoding and Decoding: Cascade Models • Modified cascade model • Integrate-and-fire model

  11. 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)

  12. 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

  13. 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

  14. Examples of the Application of Covariance Methods (3) Reverse correlation • How change in the neuron’s biophysics • Nucleus magnocellularis(NM) • DTX effect

  15. 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%.

  16. Adaptive Spike Coding (1) • Adaptation (cat’s toepad) • Fly large monopolar cells

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

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