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2 Spike Coding2 Spike Coding

Adrienne FairhallSummary by Kim, Hoon Hee (SNU-BI LAB)

[Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

Spike CodingSpike Coding

Spikes information Single Sequences

Spike encoding Cascade model Covariance Method

Spike decoding

Adaptive spike coding

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Spikes: What kind of Code?Spikes: What kind of Code?

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Spikes: Timing and InformationSpikes: Timing and Information

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Entropy

Mutual Information S: stimulus, R: response

Total Entropy Noise Entropy

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Spikes: Information in Single Spikes Spikes: Information in Single Spikes

Spike (r=1) No spike (r=0)

Noise Entropy

Information

Information per spike

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Spikes: Information in Spike Sequences (1)Spikes: Information in Spike Sequences (1)

A spike train and its representation in terms of binary “letters.” N bins : N-letter binary words, w.

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P(w)

P(w|s(t))

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Spikes: Information in Spike Sequences (2)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

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Information rate

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Encoding and Decoding : Linear DecodingEncoding and Decoding : Linear Decoding

Optimal linear kernel K(t) Crs : spike-triggered average (STA) Css : autocorrelation

Using white noise stimulus

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Encoding and Decoding: Cascade ModelsEncoding 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.)

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Encoding and Decoding: Cascade ModelsEncoding and Decoding: Cascade Models

Modified cascade model

Integrate-and-fire model

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Encoding and Decoding: Finding Multiple FeaturesEncoding 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)

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Examples of the Application of Covariance Methods (1)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

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Examples of the Application of Covariance Methods (2)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

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Examples of the Application of Covariance Methods (3)Examples of the Application of Covariance Methods (3)

How change in the neuron’s biophysics Nucleus magnocellularis(NM) DTX effect

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Reverse correlation

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Using Information to Assess DecodingUsing 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%.

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Fly large monopolar cells

Adaptive Spike Coding (1)Adaptive Spike Coding (1)

Adaptation (cat’s toepad)

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Adaptive Spike Coding (2)Adaptive Spike Coding (2)

Although the firing rate is changing, we can use a variant of the information methods.

White noise stimulus Standard deviation

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Input/output relation