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

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(C) 2007 SNU CSE Biointelligence Lab 3 Spikes: What kind of Code?
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1 2 Spike Coding 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]
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Page 1: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

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2 Spike Coding2 Spike Coding

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

[Bayesian Brain]

Page 2: 1 2 Spike Coding Adrienne Fairhall Summary 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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Page 3: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab 3

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

Page 4: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

Spikes: Timing and InformationSpikes: Timing and Information

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Entropy

Mutual Information S: stimulus, R: response

Total Entropy Noise Entropy

Page 5: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 6: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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))

Page 7: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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

Page 8: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 9: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 10: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

Encoding and Decoding: Cascade ModelsEncoding and Decoding: Cascade Models

Modified cascade model

Integrate-and-fire model

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Page 11: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 12: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 13: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 14: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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

Page 15: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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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Page 16: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

Fly large monopolar cells

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

Adaptation (cat’s toepad)

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Page 17: 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]

(C) 2007 SNU CSE Biointelligence Lab

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


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